Back| T- |
| T11 T11 if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( T11 ) n-p p if p >= n, t = ( T11 ) n , or if p < n, t = ( t11 t12 ) p n if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( T11 ) n-p p if p >= n, t = ( T11 ) n , or if p < n, t = ( t11 t12 ) p n if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( T11 ) n-p p if p >= n, t = ( T11 ) n , or if p < n, t = ( t11 t12 ) p n if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( T11 ) n-p p if p >= n, t = ( T11 ) n , or if p < n, t = ( t11 t12 ) p n |
| T12 T12 if n <= p, t = ( 0 T12 ) n, or if n > p, t = ( t11 ) n-p p if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 T12 ) p n if n <= p, t = ( 0 T12 ) n, or if n > p, t = ( t11 ) n-p p if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 T12 ) p n if n <= p, t = ( 0 T12 ) n, or if n > p, t = ( t11 ) n-p p if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 T12 ) p n if n <= p, t = ( 0 T12 ) n, or if n > p, t = ( t11 ) n-p p if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 T12 ) p n |
| T21 T21 if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, p-n n ( T21 ) if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, p-n n ( T21 ) if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, p-n n ( T21 ) if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, p-n n ( T21 ) |
| tail tail copy from a and af into block bidiagonal matrix (tail of af dbptr = pointer to diagonal blocks in a copy from a and af into block bidiagonal matrix (tail of af dbptr = pointer to diagonal blocks in a copy from a and af into block bidiagonal matrix (tail of af dbptr = pointer to diagonal blocks in a copy from a and af into block bidiagonal matrix (tail of af dbptr = pointer to diagonal blocks in a |
| tailored tailored pchentrd is a prototype version of pchetrd which uses tailored when the workspace provided by the user is adequate. pdsyntrd is a prototype version of pdsytrd which uses tailored when the workspace provided by the user is adequate. pjlaenv is called from the scalapack symmetric and hermitian tailored eigen-routines to choos for a description of the parameters. pssyntrd is a prototype version of pssytrd which uses tailored when the workspace provided by the user is adequate. pzhentrd is a prototype version of pzhetrd which uses tailored when the workspace provided by the user is adequate. |
| tain tain = 'f': on entry, af(iaf:iaf+n-1,jaf:jaf+n-1) and ipiv con- tain the factored form of a(ia:ia+n-1,ja:ja+n-1) a(ia:ia+n-1,ja:ja+n-1) has been equilibrated with = 'f': on entry, af(iaf:iaf+n-1,jaf:jaf+n-1) and ipiv con- tain the factored form of a(ia:ia+n-1,ja:ja+n-1) a(ia:ia+n-1,ja:ja+n-1) has been equilibrated with = 'f': on entry, af(iaf:iaf+n-1,jaf:jaf+n-1) and ipiv con- tain the factored form of a(ia:ia+n-1,ja:ja+n-1) a(ia:ia+n-1,ja:ja+n-1) has been equilibrated with = 'f': on entry, af(iaf:iaf+n-1,jaf:jaf+n-1) and ipiv con- tain the factored form of a(ia:ia+n-1,ja:ja+n-1) a(ia:ia+n-1,ja:ja+n-1) has been equilibrated with |
| tains tains to an array of dimension ( lld_a, locc(ja+n-1) ). this array contains the local pieces of the triangular distribute n-by-n upper triangular part of this distributed matrix con- to an array of dimension ( lld_a, locc(ja+n-1) ). this array contains the local pieces of the triangular distribute n-by-n upper triangular part of this distributed matrix con- to an array of dimension ( lld_a, locc(ja+n-1) ). this array contains the local pieces of the triangular distribute n-by-n upper triangular part of this distributed matrix con- to an array of dimension ( lld_a, locc(ja+n-1) ). this array contains the local pieces of the triangular distribute n-by-n upper triangular part of this distributed matrix con- |
| taken taken this is the lookahead loop, going until we have convergence or too many steps have been taken if the elements of sub( x ) are all zero and x(iax,jax) is real, then tau = 0 and h is taken to be the unit matrix otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1. magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y| further details if the elements of sub( x ) are all zero, then tau = 0 and h is taken to be the unit matrix otherwise 1 <= tau <= 2. if the elements of sub( x ) are all zero, then tau = 0 and h is taken to be the unit matrix otherwise 1 <= tau <= 2. if the elements of sub( x ) are all zero and x(iax,jax) is real, then tau = 0 and h is taken to be the unit matrix otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1. magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y| further details this is the lookahead loop, going until we have convergence or too many steps have been taken |
| takes takes parts: 1.) the minimum amount of work it takes to determin the critical path.) (loops 50-120) pdlabad takes as input the values computed by pdlamch for underflo the log of large is sufficiently large. this subroutine is intended parts: 1.) the minimum amount of work it takes to determin the critical path.) (loops 130-180) ictxt (global input) integer the blacs context handle in which the computation takes pslabad takes as input the values computed by pslamch for underflo the log of large is sufficiently large. this subroutine is intended parts: 1.) the minimum amount of work it takes to determin the critical path.) (loops 130-180) ictxt (global input) integer the blacs context handle in which the computation takes parts: 1.) the minimum amount of work it takes to determin the critical path.) (loops 50-120) |
| tall tall work ( invt ), or v^t, is stored as a tall skinn triangular portion of a is updated, av is computed as: work ( invt ), or v^t, is stored as a tall skinn triangular portion of a is updated, av is computed as: work ( invt ), or v^t, is stored as a tall skinn triangular portion of a is updated, av is computed as: work ( invt ), or v^t, is stored as a tall skinn triangular portion of a is updated, av is computed as: |
| tary tary where q is a complex unitary distributed matrix defined as th where q is a complex unitary distributed matrix defined as th where q is a complex unitary distributed matrix defined as th where q is a complex unitary distributed matrix defined as th where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(k) . . . h(2) h(1) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(1) h(2) . . . h(k) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(k) . . . h(2) h(1) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(1) h(2) . . . h(k) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(k) . . . h(2) h(1) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(1) h(2) . . . h(k) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(k) . . . h(2) h(1) where q is a real orthogonal distributed matrix defined as the product of k elementary reflector q = h(1) h(2) . . . h(k) where q is a complex unitary distributed matrix defined as th where q is a complex unitary distributed matrix defined as th where q is a complex unitary distributed matrix defined as th where q is a complex unitary distributed matrix defined as th |
| task task the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. set all values for bulges. all bulges are stored in intermediate steps as loops over ki. their current "task however, because there are many bulges, k1(ki) & k2(ki) might the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. set all values for bulges. all bulges are stored in intermediate steps as loops over ki. their current "task however, because there are many bulges, k1(ki) & k2(ki) might the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. set all values for bulges. all bulges are stored in intermediate steps as loops over ki. their current "task however, because there are many bulges, k1(ki) & k2(ki) might the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. set all values for bulges. all bulges are stored in intermediate steps as loops over ki. their current "task however, because there are many bulges, k1(ki) & k2(ki) might the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. the mapping for matrices must be blocked, reflecting the nature of the divide and conquer algorithm as a task-parallel algorithm chunk of the matrix. |
| tation tation used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). |
| TAU TAU overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). trapezoidal matrix l; the remaining elements, with the array TAU, represent the unitary matrix q as a product o trapezoidal matrix l; the remaining elements, with the array TAU, represent the unitary matrix q as a product o upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU, repre reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAU, represent the unitary matrix q as a product o trapezoidal matrix r; the remaining elements, with the array TAU, represent the unitary matrix q as a product o matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix q as a product of elementar unchanged. see further details. this is an auxiliary routine called by pchetrd to redistribute d, e and TAU notes send v and TAU to the process column icco send v and TAU to the process column icco h = i - TAU * ( 1 ) * ( 1 v' ) TAU (local input) complex, array, dimension locr(iv+k-1 contains the householder scalars related to the householder send v and TAU to the process column iccol send v and TAU to the process column iccol TAU (local input) complex, array, dimension locr(iv+k-1 contains the householder scalars related to the householder the diagonal elements of sub( a ); the elements above the diagonal with the array TAU, represent the unitary matrix first nb columns have been reduced to tridiagonal form, with gular matrix r, and elements n-l+1 to n of the first m rows of sub( a ), with the array TAU, represent the unitary matri gular matrix r, and elements m+1 to n of the first m rows of sub( a ), with the array TAU, represent the unitary matrix TAU (local input) complex, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pcgeqlf. TAU (local input) complex, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pcgeqrf. TAU (local input) complex, array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by pcgelqf. TAU (local input) complex, array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by pcgelqf. TAU (local input) complex, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pcgeqlf. TAU (local input) complex, array, dimension locc(ja+k-1 elementary reflectors h(j) as returned by pcgeqrf. TAU (local input) complex, array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by pcgerqf. TAU (local input) complex, array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by pcgerqf. TAU (local input) complex, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pcgeqlf. TAU (local input) complex, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pcgeqrf. TAU (local input) complex array, dimensio vect = 'p', tau(i) must contain the scalar factor of the TAU (local input) complex, array, dimension locc(ja+m-2 contains the scalar factors tau(j) of the elementary TAU (local input) complex, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pcgelqf. TAU (local input) complex, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pcgelqf. TAU (local input) complex, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pcgeqlf. TAU (local input) complex, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pcgeqrf. TAU (local input) complex, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pcgerqf. TAU (local input) complex, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pctzrzf. TAU (local input) complex, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pcgerqf. TAU (local input) complex, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pctzrzf. TAU (local input) complex array, dimension ltau, wher if side = 'l' and uplo = 'l', ltau = locc(ja+m-2), overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). trapezoidal matrix l; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o trapezoidal matrix l; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU, repre reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o trapezoidal matrix r; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix q as a product of elementar unchanged. see further details. this is an auxiliary routine called by pdsytrd to redistribute d, e and TAU notes send v and TAU to the process column icco h = i - TAU * ( 1 ) * ( 1 v' ) TAU (local input) double precision array, dimension locr(iv+k-1 contains the householder scalars related to the householder send v and TAU to the process column iccol TAU (local input) double precision array, dimension locr(iv+k-1 contains the householder scalars related to the householder the diagonal elements of sub( a ); the elements above the diagonal with the array TAU, represent the orthogonal matri first nb columns have been reduced to tridiagonal form, with gular matrix r, and elements n-l+1 to n of the first m rows of sub( a ), with the array TAU, represent the orthogona TAU (local input) double precision array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pdgeqlf. TAU (local input) double precision array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pdgeqrf. TAU (local input) double precision array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by pdgelqf. TAU (local input) double precision array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by pdgelqf. TAU (local input) double precision array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pdgeqlf. TAU (local input) double precision array, dimension locc(ja+k-1 elementary reflectors h(j) as returned by pdgeqrf. TAU (local input) double precision array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by pdgerqf. TAU (local input) double precision array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by pdgerqf. TAU (local input) double precision array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pdgeqlf. TAU (local input) double precision array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pdgeqrf. TAU (local input) double precision array, dimensio vect = 'p', tau(i) must contain the scalar factor of the TAU (local input) double precision array, dimension locc(ja+m-2 contains the scalar factors tau(j) of the elementary TAU (local input) double precision array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pdgelqf. TAU (local input) double precision array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pdgelqf. TAU (local input) double precision array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pdgeqlf. TAU (local input) double precision array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pdgeqrf. TAU (local input) double precision array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pdgerqf. TAU (local input) double precision array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pdtzrzf. TAU (local input) double precision array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pdgerqf. TAU (local input) double precision array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pdtzrzf. TAU (local input) double precision array, dimension ltau, wher if side = 'l' and uplo = 'l', ltau = locc(ja+m-2), matrix t, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the gular matrix r, and elements m+1 to n of the first m rows of sub( a ), with the array TAU, represent the orthogonal matri overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). trapezoidal matrix l; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o trapezoidal matrix l; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU, repre reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o trapezoidal matrix r; the remaining elements, with the array TAU, represent the orthogonal matrix q as a product o matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix q as a product of elementar unchanged. see further details. this is an auxiliary routine called by pssytrd to redistribute d, e and TAU notes send v and TAU to the process column icco h = i - TAU * ( 1 ) * ( 1 v' ) TAU (local input) real, array, dimension locr(iv+k-1 contains the householder scalars related to the householder send v and TAU to the process column iccol TAU (local input) real, array, dimension locr(iv+k-1 contains the householder scalars related to the householder the diagonal elements of sub( a ); the elements above the diagonal with the array TAU, represent the orthogonal matri first nb columns have been reduced to tridiagonal form, with gular matrix r, and elements n-l+1 to n of the first m rows of sub( a ), with the array TAU, represent the orthogona TAU (local input) real, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by psgeqlf. TAU (local input) real, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by psgeqrf. TAU (local input) real, array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by psgelqf. TAU (local input) real, array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by psgelqf. TAU (local input) real, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by psgeqlf. TAU (local input) real, array, dimension locc(ja+k-1 elementary reflectors h(j) as returned by psgeqrf. TAU (local input) real, array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by psgerqf. TAU (local input) real, array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by psgerqf. TAU (local input) real, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by psgeqlf. TAU (local input) real, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by psgeqrf. TAU (local input) real array, dimensio vect = 'p', tau(i) must contain the scalar factor of the TAU (local input) real, array, dimension locc(ja+m-2 contains the scalar factors tau(j) of the elementary TAU (local input) real, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by psgelqf. TAU (local input) real, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by psgelqf. TAU (local input) real, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by psgeqlf. TAU (local input) real, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by psgeqrf. TAU (local input) real, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by psgerqf. TAU (local input) real, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pstzrzf. TAU (local input) real, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by psgerqf. TAU (local input) real, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pstzrzf. TAU (local input) real array, dimension ltau, wher if side = 'l' and uplo = 'l', ltau = locc(ja+m-2), matrix t, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the orthogonal matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the gular matrix r, and elements m+1 to n of the first m rows of sub( a ), with the array TAU, represent the orthogonal matri overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. overwritten with the upper hessenberg matrix h, and the ele- ments below the first subdiagonal, with the array TAU, repre reflectors. see further details. lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). lower trapezoidal matrix l (l is lower triangular if m <= n); the elements above the diagonal, with the array TAU, repre reflectors (see further details). trapezoidal matrix l; the remaining elements, with the array TAU, represent the unitary matrix q as a product o trapezoidal matrix l; the remaining elements, with the array TAU, represent the unitary matrix q as a product o upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU, repre reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). upper trapezoidal matrix r (r is upper triangular if m >= n); the elements below the diagonal, with the array TAU reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAU, represent the unitary matrix q as a product o trapezoidal matrix r; the remaining elements, with the array TAU, represent the unitary matrix q as a product o matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix t, and the elements above the first superdiagonal, with the array TAU, represent the unitary matrix q as and first subdiagonal of sub( a ) are overwritten by the matrix; the elements below the k-th subdiagonal, with the array TAU, represent the matrix q as a product of elementar unchanged. see further details. this is an auxiliary routine called by pzhetrd to redistribute d, e and TAU notes send v and TAU to the process column icco send v and TAU to the process column icco h = i - TAU * ( 1 ) * ( 1 v' ) TAU (local input) complex*16, array, dimension locr(iv+k-1 contains the householder scalars related to the householder send v and TAU to the process column iccol send v and TAU to the process column iccol TAU (local input) complex*16, array, dimension locr(iv+k-1 contains the householder scalars related to the householder the diagonal elements of sub( a ); the elements above the diagonal with the array TAU, represent the unitary matrix first nb columns have been reduced to tridiagonal form, with gular matrix r, and elements n-l+1 to n of the first m rows of sub( a ), with the array TAU, represent the unitary matri gular matrix r, and elements m+1 to n of the first m rows of sub( a ), with the array TAU, represent the unitary matrix TAU (local input) complex*16, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pzgeqlf. TAU (local input) complex*16, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pzgeqrf. TAU (local input) complex*16, array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by pzgelqf. TAU (local input) complex*16, array, dimension locr(ia+k-1) elementary reflectors h(i) as returned by pzgelqf. TAU (local input) complex*16, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pzgeqlf. TAU (local input) complex*16, array, dimension locc(ja+k-1 elementary reflectors h(j) as returned by pzgeqrf. TAU (local input) complex*16, array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by pzgerqf. TAU (local input) complex*16, array, dimension locr(ia+m-1 elementary reflectors h(i) as returned by pzgerqf. TAU (local input) complex*16, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pzgeqlf. TAU (local input) complex*16, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pzgeqrf. TAU (local input) complex*16 array, dimensio vect = 'p', tau(i) must contain the scalar factor of the TAU (local input) complex*16, array, dimension locc(ja+m-2 contains the scalar factors tau(j) of the elementary TAU (local input) complex*16, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pzgelqf. TAU (local input) complex*16, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pzgelqf. TAU (local input) complex*16, array, dimension locc(ja+n-1 elementary reflectors h(j) as returned by pzgeqlf. TAU (local input) complex*16, array, dimension locc(ja+k-1) elementary reflectors h(j) as returned by pzgeqrf. TAU (local input) complex*16, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pzgerqf. TAU (local input) complex*16, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pztzrzf. TAU (local input) complex*16, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pzgerqf. TAU (local input) complex*16, array, dimension locc(ia+k-1) elementary reflectors h(i) as returned by pztzrzf. TAU (local input) complex*16 array, dimension ltau, wher if side = 'l' and uplo = 'l', ltau = locc(ja+m-2), |
| TAUA TAUA upper trapezoidal matrix r (r is upper triangular if n >= m); the elements below the diagonal, with the array TAUA elementary reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAUA, represent the unitary matrix q as a product o upper trapezoidal matrix r (r is upper triangular if n >= m); the elements below the diagonal, with the array TAUA elementary reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAUA, represent the orthogonal matrix q as a product o upper trapezoidal matrix r (r is upper triangular if n >= m); the elements below the diagonal, with the array TAUA elementary reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAUA, represent the orthogonal matrix q as a product o upper trapezoidal matrix r (r is upper triangular if n >= m); the elements below the diagonal, with the array TAUA elementary reflectors (see further details). trapezoidal matrix r; the remaining elements, with the array TAUA, represent the unitary matrix q as a product o |
| TAUB TAUB trapezoidal matrix t; the remaining elements, with the array TAUB, represent the unitary matrix z as a product o upper trapezoidal matrix t (t is upper triangular if p >= n); the elements below the diagonal, with the array TAUB reflectors (see further details). trapezoidal matrix t; the remaining elements, with the array TAUB, represent the orthogonal matrix z as a product o upper trapezoidal matrix t (t is upper triangular if p >= n); the elements below the diagonal, with the array TAUB reflectors (see further details). trapezoidal matrix t; the remaining elements, with the array TAUB, represent the orthogonal matrix z as a product o upper trapezoidal matrix t (t is upper triangular if p >= n); the elements below the diagonal, with the array TAUB reflectors (see further details). trapezoidal matrix t; the remaining elements, with the array TAUB, represent the unitary matrix z as a product o upper trapezoidal matrix t (t is upper triangular if p >= n); the elements below the diagonal, with the array TAUB reflectors (see further details). |
| TAUP TAUP the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a product o subdiagonal are overwritten with the lower bidiagonal the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a product o subdiagonal are overwritten with the lower bidiagonal elements above the diagonal in the first nb rows, with the array TAUP, represent the unitary matrix p as a produc if m < n, elements below the diagonal in the first nb elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument tauq or TAUP and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a produc first subdiagonal are overwritten with the lower bidiagonal and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a produc first subdiagonal are overwritten with the lower bidiagonal elements above the diagonal in the first nb rows, with the array TAUP, represent the orthogonal matrix p as a produc if m < n, elements below the diagonal in the first nb elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument tauq or TAUP and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a produc first subdiagonal are overwritten with the lower bidiagonal and the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a produc first subdiagonal are overwritten with the lower bidiagonal elements above the diagonal in the first nb rows, with the array TAUP, represent the orthogonal matrix p as a produc if m < n, elements below the diagonal in the first nb elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument tauq or TAUP the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a product o subdiagonal are overwritten with the lower bidiagonal the elements above the first superdiagonal, with the array TAUP, represent the orthogonal matrix p as a product o subdiagonal are overwritten with the lower bidiagonal elements above the diagonal in the first nb rows, with the array TAUP, represent the unitary matrix p as a produc if m < n, elements below the diagonal in the first nb elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument tauq or TAUP |
| TAUQ TAUQ overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th the elements above the first superdiagonal, with the array overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th the elements above the first superdiagonal, with the array if m >= n, elements on and below the diagonal in the first nb columns, with the array TAUQ, represent the unitar elements above the diagonal in the first nb rows, with the elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument TAUQ or taup overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th and the elements above the first superdiagonal, with the overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th and the elements above the first superdiagonal, with the if m >= n, elements on and below the diagonal in the first nb columns, with the array TAUQ, represent the orthogona elements above the diagonal in the first nb rows, with the elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument TAUQ or taup overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th and the elements above the first superdiagonal, with the overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th and the elements above the first superdiagonal, with the if m >= n, elements on and below the diagonal in the first nb columns, with the array TAUQ, represent the orthogona elements above the diagonal in the first nb rows, with the elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument TAUQ or taup overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th the elements above the first superdiagonal, with the array overwritten with the upper bidiagonal matrix b; the elements below the diagonal, with the array TAUQ, represent th the elements above the first superdiagonal, with the array if m >= n, elements on and below the diagonal in the first nb columns, with the array TAUQ, represent the unitar elements above the diagonal in the first nb rows, with the elementary reflector h(i) or g(i), which determines q or p, as returned by pdgebrd in its array argument TAUQ or taup |
| technical technical are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! are temporary and will be removed in future releases, while others may reflect fundamental technical limitations non-cyclic restriction: very important! |
| ted ted where a(1:n, ja:ja+n-1) is an n-by-n complex banded diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n complex banded diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n complex banded distributed a(1:n, ja:ja+n-1) is an n-by-n complex banded distributed pcgebd2 reduces a complex general m-by-n distributed matri form b by an unitary transformation: q' * sub( a ) * p = b. pcgebrd reduces a complex general m-by-n distributed matri form b by an unitary transformation: q' * sub( a ) * p = b. pcgecon estimates the reciprocal of the condition number of a general distributed complex matrix a(ia:ia+n-1,ja:ja+n-1), in either th pcgetrf. pcgeequ computes row and column scalings intended to equilibrate an m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) an the column scale factors, chosen to try to make the largest entry in pcgehd2 reduces a complex general distributed matrix sub( a q' * sub( a ) * q = h, where pcgehrd reduces a complex general distributed matrix sub( a q' * sub( a ) * q = h, where pcgelq2 computes a lq factorization of a complex distributed m-by- pcgelqf computes a lq factorization of a complex distributed m-by- each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pcgeql2 computes a ql factorization of a complex distributed m-by- pcgeqlf computes a ql factorization of a complex distributed m-by- pcgeqpf computes a qr factorization with column pivoting of a m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) sub( a ) * p = q * r. pcgeqr2 computes a qr factorization of a complex distributed m-by- pcgeqrf computes a qr factorization of a complex distributed m-by- pcgerfs improves the computed solution to a system of linea the solutions. pcgerq2 computes a rq factorization of a complex distributed m-by- pcgerqf computes a rq factorization of a complex distributed m-by- where sub( a ) = a(ia:ia+n-1,ja:ja+n-1) is an n-by-n distributed distributed matrices. only the first min(m,n) columns of u and rows of vt = v**t are computed notes each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pcgetf2 computes an lu factorization of a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) usin pcgetrf computes an lu factorization of a general m-by-n distributed row interchanges. pcgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted pcgetrs solves a system of distributed linear equation op( sub( a ) ) * x = sub( b ) each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pcheev computes selected eigenvalues and, optionally, eigenvector of scalapack routines. pcheevx computes selected eigenvalues and, optionally, eigenvector of scalapack routines. eigenvalues/vectors can be selected by each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process support for uplo='u' is limited to calling the old, slow, pchetr each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding pclabrd reduces the first nb rows and columns of a complex general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to uppe returns the matrices x and y which are needed to apply the transfor- each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pclacon estimates the 1-norm of a square, complex distributed matri products. x and v are aligned with the distributed matrix a, this each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pclacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pclacp3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. notice tha more. the receiving node can be specified precisely, or all nodes pclacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pclaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. or the infinity norm, or the element of largest absolute value of a distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1) pclange returns the value pclapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pclapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pclaqge equilibrates a general m-by-n distributed matri factors in the vectors r and c. pclaqsy equilibrates a symmetric distributed matri vectors sr and sc. pclarfb applies a complex block reflector q or its conjugate transpose q**h to a complex m-by-n distributed matrix sub( c where alpha is a real scalar, and sub( x ) is an (n-1)-element complex distributed vector x(ix:ix+n-2,jx) if incx = 1 an if storev = 'c', the vector which defines the elementary reflector h(i) is stored in the i-th column of the distributed matrix v, an h = i - v * t * v' pclarzb applies a complex block reflector q or its conjugate transpose q**h to a complex m-by-n distributed matrix sub( c currently, only storev = 'r' and direct = 'b' are supported notes pclascl multiplies the m-by-n complex distributed matrix sub( a is done without over/underflow as long as the final result pclase2 initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. pclase2 requires that only dimension of the matrix pclaset initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pclaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pclatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pclatrd reduces nb rows and columns of a complex hermitian distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to comple q' * sub( a ) * q, and returns the matrices v and w which are each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process factor u or l is stored in the upper or lower triangular part of the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) if uplo = 'u' or 'u' then the upper triangle of the result is stored, each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pcmax1 computes the global index of the maximum element in absolute value of a distributed vector sub( x ). the global index is returne where a(1:n, ja:ja+n-1) is an n-by-n complex banded symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n complex banded symmetric positive definite distributed depending on the value of uplo, a stores either u or l in the equn pcpocon estimates the reciprocal of the condition number (in the 1-norm) of a complex hermitian positive definite distributed matri pcpotrf. pcpoequ computes row and column scalings intended to equilibrate a distributed hermitian positive definite matri (with respect to the two-norm). sr and sc contain the scale pcporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is an n-by-n hermitian distributed positive definite matrix and x and sub( b matrices. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pcpotf2 computes the cholesky factorization of a complex hermitian positive definite distributed matrix sub( a )=a(ia:ia+n-1,ja:ja+n-1) the factorization has the form pcpotrf computes the cholesky factorization of an n-by-n complex hermitian positive definite distributed matrix sub( a ) denotin pcpotri computes the inverse of a complex hermitian positive definite distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using th pcpotrf. where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n hermitian positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distributed depending on the value of uplo, a stores either u or l in the equn pcsrscl multiplies an n-element complex distributed vecto underflow as long as the final sub( x )/a does not overflow or of orthogonalization is controlled by the input parameter lwork. eigenvectors that are to be orthogonalized are computed by the sam processes and then calls sstein2 (modified lapack routine) on each pctrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th if all eigenvectors are requested, the routine may either return th products q*x and/or q*y, where q is an input unitary the solution matrix x must be computed by pctrtrs or some othe refinement because doing so cannot improve the backward error. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pctrtri computes the inverse of a upper or lower triangular distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) notes where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a triangular distributed matrix of order n, and b(ib:ib+n-1,jb:jb+nrhs-1) is a to verify that sub( a ) is nonsingular. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pcung2l generates an m-by-n complex distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m pcung2r generates an m-by-n complex distributed matrix q denotin the first n columns of a product of k elementary reflectors of order pcungl2 generates an m-by-n complex distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n pcunglq generates an m-by-n complex distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n pcungql generates an m-by-n complex distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m pcungqr generates an m-by-n complex distributed matrix q denotin the first n columns of a product of k elementary reflectors of order pcungr2 generates an m-by-n complex distributed matrix q denotin last m rows of a product of k elementary reflectors of order n pcungrq generates an m-by-n complex distributed matrix q denotin last m rows of a product of k elementary reflectors of order n pcunm2l overwrites the general complex m-by-n distributed matri pcunm2r overwrites the general complex m-by-n distributed matri if vect = 'q', pcunmbr overwrites the general complex distributed pcunmhr overwrites the general complex m-by-n distributed matri pcunml2 overwrites the general complex m-by-n distributed matri pcunmlq overwrites the general complex m-by-n distributed matri pcunmql overwrites the general complex m-by-n distributed matri pcunmqr overwrites the general complex m-by-n distributed matri pcunmr2 overwrites the general complex m-by-n distributed matri pcunmr3 overwrites the general complex m-by-n distributed matri pcunmrq overwrites the general complex m-by-n distributed matri pcunmrz overwrites the general complex m-by-n distributed matri pcunmtr overwrites the general complex m-by-n distributed matri where a(1:n, ja:ja+n-1) is an n-by-n real banded diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n real banded diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n real banded distributed a(1:n, ja:ja+n-1) is an n-by-n real banded distributed pdgebd2 reduces a real general m-by-n distributed matri form b by an orthogonal transformation: q' * sub( a ) * p = b. pdgebrd reduces a real general m-by-n distributed matri form b by an orthogonal transformation: q' * sub( a ) * p = b. pdgecon estimates the reciprocal of the condition number of a general distributed real matrix a(ia:ia+n-1,ja:ja+n-1), in either the 1-nor pdgeequ computes row and column scalings intended to equilibrate an m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) an the column scale factors, chosen to try to make the largest entry in pdgehd2 reduces a real general distributed matrix sub( a tion: q' * sub( a ) * q = h, where pdgehrd reduces a real general distributed matrix sub( a tion: q' * sub( a ) * q = h, where pdgelq2 computes a lq factorization of a real distributed m-by- pdgelqf computes a lq factorization of a real distributed m-by- each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdgeql2 computes a ql factorization of a real distributed m-by- pdgeqlf computes a ql factorization of a real distributed m-by- pdgeqpf computes a qr factorization with column pivoting of a m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) sub( a ) * p = q * r. pdgeqr2 computes a qr factorization of a real distributed m-by- pdgeqrf computes a qr factorization of a real distributed m-by- pdgerfs improves the computed solution to a system of linea the solutions. pdgerq2 computes a rq factorization of a real distributed m-by- pdgerqf computes a rq factorization of a real distributed m-by- where sub( a ) = a(ia:ia+n-1,ja:ja+n-1) is an n-by-n distributed distributed matrices. only the first min(m,n) columns of u and rows of vt = v**t are computed notes each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdgetf2 computes an lu factorization of a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) usin pdgetrf computes an lu factorization of a general m-by-n distributed row interchanges. pdgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted pdgetrs solves a system of distributed linear equation op( sub( a ) ) * x = sub( b ) each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdlabrd reduces the first nb rows and columns of a real general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to uppe and returns the matrices x and y which are needed to apply the pdlacon estimates the 1-norm of a square, real distributed matrix a x and v are aligned with the distributed matrix a, this information each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdlacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pdlacp3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. notice tha more. the receiving node can be specified precisely, or all nodes pdlacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pdlaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. or the infinity norm, or the element of largest absolute value of a distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1) pdlange returns the value pdlapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pdlapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pdlaqge equilibrates a general m-by-n distributed matri factors in the vectors r and c. pdlaqsy equilibrates a symmetric distributed matri vectors sr and sc. it assumes that the input array, bycol, is distributed acros bycol. the output array, byall, will be identical on all processes it assumes that the input array, byrow, is distributed acros byrow. the output array, byall, will be identical on all processes pdlarfb applies a real block reflector q or its transpose q**t to a real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1 where alpha is a scalar, and sub( x ) is an (n-1)-element real distributed vector x(ix:ix+n-2,jx) if incx = 1 and x(ix,jx:jx+n-2) i if storev = 'c', the vector which defines the elementary reflector h(i) is stored in the i-th column of the distributed matrix v, an h = i - v * t * v' pdlarzb applies a real block reflector q or its transpose q**t to a real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1 currently, only storev = 'r' and direct = 'b' are supported notes pdlascl multiplies the m-by-n real distributed matrix sub( a is done without over/underflow as long as the final result pdlase2 initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. pdlase2 requires that only dimension of the matrix pdlaset initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdlaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pdlatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pdlatrd reduces nb rows and columns of a real symmetric distributed form by an orthogonal similarity transformation q' * sub( a ) * q, each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process factor u or l is stored in the upper or lower triangular part of the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) if uplo = 'u' or 'u' then the upper triangle of the result is stored, each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdorg2l generates an m-by-n real distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m pdorg2r generates an m-by-n real distributed matrix q denotin the first n columns of a product of k elementary reflectors of order pdorgl2 generates an m-by-n real distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n pdorglq generates an m-by-n real distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n pdorgql generates an m-by-n real distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m pdorgqr generates an m-by-n real distributed matrix q denotin the first n columns of a product of k elementary reflectors of order pdorgr2 generates an m-by-n real distributed matrix q denotin last m rows of a product of k elementary reflectors of order n pdorgrq generates an m-by-n real distributed matrix q denotin last m rows of a product of k elementary reflectors of order n pdorm2l overwrites the general real m-by-n distributed matri pdorm2r overwrites the general real m-by-n distributed matri if vect = 'q', pdormbr overwrites the general real distributed m-by- pdormhr overwrites the general real m-by-n distributed matri pdorml2 overwrites the general real m-by-n distributed matri pdormlq overwrites the general real m-by-n distributed matri pdormql overwrites the general real m-by-n distributed matri pdormqr overwrites the general real m-by-n distributed matri pdormr2 overwrites the general real m-by-n distributed matri pdormr3 overwrites the general real m-by-n distributed matri pdormrq overwrites the general real m-by-n distributed matri pdormrz overwrites the general real m-by-n distributed matri pdormtr overwrites the general real m-by-n distributed matri where a(1:n, ja:ja+n-1) is an n-by-n real banded symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n real banded symmetric positive definite distributed depending on the value of uplo, a stores either u or l in the equn pdpocon estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matri pdpotrf. pdpoequ computes row and column scalings intended to equilibrate a distributed symmetric positive definite matri (with respect to the two-norm). sr and sc contain the scale pdporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is an n-by-n symmetric distributed positive definite matrix and x and sub( b matrices. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdpotf2 computes the cholesky factorization of a real symmetric positive definite distributed matrix sub( a )=a(ia:ia+n-1,ja:ja+n-1) the factorization has the form pdpotrf computes the cholesky factorization of an n-by-n real symmetric positive definite distributed matrix sub( a ) denotin pdpotri computes the inverse of a real symmetric positive definite distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using th pdpotrf. where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n symmetric positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distributed pdrscl multiplies an n-element real distributed vector sub( x ) b long as the final result sub( x )/a does not overflow or underflow. of orthogonalization is controlled by the input parameter lwork. eigenvectors that are to be orthogonalized are computed by the sam processes and then calls dstein2 (modified lapack routine) on each ===== a description vector is associated with each 2d block-cyclicly dis establish the mapping between a matrix entry and its corresponding pdsyevx computes selected eigenvalues and, optionally, eigenvector of scalapack routines. eigenvalues/vectors can be selected by each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process support for uplo='u' is limited to calling the old, slow, pdsytr each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding pdtrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th the solution matrix x must be computed by pdtrtrs or some othe refinement because doing so cannot improve the backward error. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdtrtri computes the inverse of a upper or lower triangular distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) notes where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a triangular distributed matrix of order n, and b(ib:ib+n-1,jb:jb+nrhs-1) is a to verify that sub( a ) is nonsingular. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pdzsum1 returns the sum of absolute values of a complex distributed vector sub( x ) in asum where sub( x ) denotes x(ix:ix+n-1,jx:jx), if incx = 1, pscsum1 returns the sum of absolute values of a complex distributed vector sub( x ) in asum where sub( x ) denotes x(ix:ix+n-1,jx:jx), if incx = 1, where a(1:n, ja:ja+n-1) is an n-by-n real banded diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n real banded diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n real banded distributed a(1:n, ja:ja+n-1) is an n-by-n real banded distributed psgebd2 reduces a real general m-by-n distributed matri form b by an orthogonal transformation: q' * sub( a ) * p = b. psgebrd reduces a real general m-by-n distributed matri form b by an orthogonal transformation: q' * sub( a ) * p = b. psgecon estimates the reciprocal of the condition number of a general distributed real matrix a(ia:ia+n-1,ja:ja+n-1), in either the 1-nor psgeequ computes row and column scalings intended to equilibrate an m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) an the column scale factors, chosen to try to make the largest entry in psgehd2 reduces a real general distributed matrix sub( a tion: q' * sub( a ) * q = h, where psgehrd reduces a real general distributed matrix sub( a tion: q' * sub( a ) * q = h, where psgelq2 computes a lq factorization of a real distributed m-by- psgelqf computes a lq factorization of a real distributed m-by- each global data object is described by an associated descriptio the mapping between an object element and its corresponding process psgeql2 computes a ql factorization of a real distributed m-by- psgeqlf computes a ql factorization of a real distributed m-by- psgeqpf computes a qr factorization with column pivoting of a m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) sub( a ) * p = q * r. psgeqr2 computes a qr factorization of a real distributed m-by- psgeqrf computes a qr factorization of a real distributed m-by- psgerfs improves the computed solution to a system of linea the solutions. psgerq2 computes a rq factorization of a real distributed m-by- psgerqf computes a rq factorization of a real distributed m-by- where sub( a ) = a(ia:ia+n-1,ja:ja+n-1) is an n-by-n distributed distributed matrices. only the first min(m,n) columns of u and rows of vt = v**t are computed notes each global data object is described by an associated descriptio the mapping between an object element and its corresponding process psgetf2 computes an lu factorization of a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) usin psgetrf computes an lu factorization of a general m-by-n distributed row interchanges. psgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted psgetrs solves a system of distributed linear equation op( sub( a ) ) * x = sub( b ) each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pslabrd reduces the first nb rows and columns of a real general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to uppe and returns the matrices x and y which are needed to apply the pslacon estimates the 1-norm of a square, real distributed matrix a x and v are aligned with the distributed matrix a, this information each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pslacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pslacp3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. notice tha more. the receiving node can be specified precisely, or all nodes pslacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pslaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. or the infinity norm, or the element of largest absolute value of a distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1) pslange returns the value pslapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pslapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pslaqge equilibrates a general m-by-n distributed matri factors in the vectors r and c. pslaqsy equilibrates a symmetric distributed matri vectors sr and sc. it assumes that the input array, bycol, is distributed acros bycol. the output array, byall, will be identical on all processes it assumes that the input array, byrow, is distributed acros byrow. the output array, byall, will be identical on all processes pslarfb applies a real block reflector q or its transpose q**t to a real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1 where alpha is a scalar, and sub( x ) is an (n-1)-element real distributed vector x(ix:ix+n-2,jx) if incx = 1 and x(ix,jx:jx+n-2) i if storev = 'c', the vector which defines the elementary reflector h(i) is stored in the i-th column of the distributed matrix v, an h = i - v * t * v' pslarzb applies a real block reflector q or its transpose q**t to a real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1 currently, only storev = 'r' and direct = 'b' are supported notes pslascl multiplies the m-by-n real distributed matrix sub( a is done without over/underflow as long as the final result pslase2 initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. pslase2 requires that only dimension of the matrix pslaset initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pslaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pslatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pslatrd reduces nb rows and columns of a real symmetric distributed form by an orthogonal similarity transformation q' * sub( a ) * q, each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process factor u or l is stored in the upper or lower triangular part of the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) if uplo = 'u' or 'u' then the upper triangle of the result is stored, each global data object is described by an associated descriptio the mapping between an object element and its corresponding process psorg2l generates an m-by-n real distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m psorg2r generates an m-by-n real distributed matrix q denotin the first n columns of a product of k elementary reflectors of order psorgl2 generates an m-by-n real distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n psorglq generates an m-by-n real distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n psorgql generates an m-by-n real distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m psorgqr generates an m-by-n real distributed matrix q denotin the first n columns of a product of k elementary reflectors of order psorgr2 generates an m-by-n real distributed matrix q denotin last m rows of a product of k elementary reflectors of order n psorgrq generates an m-by-n real distributed matrix q denotin last m rows of a product of k elementary reflectors of order n psorm2l overwrites the general real m-by-n distributed matri psorm2r overwrites the general real m-by-n distributed matri if vect = 'q', psormbr overwrites the general real distributed m-by- psormhr overwrites the general real m-by-n distributed matri psorml2 overwrites the general real m-by-n distributed matri psormlq overwrites the general real m-by-n distributed matri psormql overwrites the general real m-by-n distributed matri psormqr overwrites the general real m-by-n distributed matri psormr2 overwrites the general real m-by-n distributed matri psormr3 overwrites the general real m-by-n distributed matri psormrq overwrites the general real m-by-n distributed matri psormrz overwrites the general real m-by-n distributed matri psormtr overwrites the general real m-by-n distributed matri where a(1:n, ja:ja+n-1) is an n-by-n real banded symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n real banded symmetric positive definite distributed depending on the value of uplo, a stores either u or l in the equn pspocon estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matri pspotrf. pspoequ computes row and column scalings intended to equilibrate a distributed symmetric positive definite matri (with respect to the two-norm). sr and sc contain the scale psporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is an n-by-n symmetric distributed positive definite matrix and x and sub( b matrices. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pspotf2 computes the cholesky factorization of a real symmetric positive definite distributed matrix sub( a )=a(ia:ia+n-1,ja:ja+n-1) the factorization has the form pspotrf computes the cholesky factorization of an n-by-n real symmetric positive definite distributed matrix sub( a ) denotin pspotri computes the inverse of a real symmetric positive definite distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using th pspotrf. where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n symmetric positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distributed psrscl multiplies an n-element real distributed vector sub( x ) b long as the final result sub( x )/a does not overflow or underflow. of orthogonalization is controlled by the input parameter lwork. eigenvectors that are to be orthogonalized are computed by the sam processes and then calls sstein2 (modified lapack routine) on each ===== a description vector is associated with each 2d block-cyclicly dis establish the mapping between a matrix entry and its corresponding pssyevx computes selected eigenvalues and, optionally, eigenvector of scalapack routines. eigenvalues/vectors can be selected by each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process support for uplo='u' is limited to calling the old, slow, pssytr each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding pstrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th the solution matrix x must be computed by pstrtrs or some othe refinement because doing so cannot improve the backward error. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pstrtri computes the inverse of a upper or lower triangular distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) notes where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a triangular distributed matrix of order n, and b(ib:ib+n-1,jb:jb+nrhs-1) is a to verify that sub( a ) is nonsingular. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process where a(1:n, ja:ja+n-1) is an n-by-n complex banded diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n complex banded diagonally dominant-like distributed pzdrscl multiplies an n-element complex distributed vecto underflow as long as the final sub( x )/a does not overflow or where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distributed a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distributed where a(1:n, ja:ja+n-1) is an n-by-n complex banded distributed a(1:n, ja:ja+n-1) is an n-by-n complex banded distributed pzgebd2 reduces a complex general m-by-n distributed matri form b by an unitary transformation: q' * sub( a ) * p = b. pzgebrd reduces a complex general m-by-n distributed matri form b by an unitary transformation: q' * sub( a ) * p = b. pzgecon estimates the reciprocal of the condition number of a general distributed complex matrix a(ia:ia+n-1,ja:ja+n-1), in either th pzgetrf. pzgeequ computes row and column scalings intended to equilibrate an m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) an the column scale factors, chosen to try to make the largest entry in pzgehd2 reduces a complex general distributed matrix sub( a q' * sub( a ) * q = h, where pzgehrd reduces a complex general distributed matrix sub( a q' * sub( a ) * q = h, where pzgelq2 computes a lq factorization of a complex distributed m-by- pzgelqf computes a lq factorization of a complex distributed m-by- each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzgeql2 computes a ql factorization of a complex distributed m-by- pzgeqlf computes a ql factorization of a complex distributed m-by- pzgeqpf computes a qr factorization with column pivoting of a m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) sub( a ) * p = q * r. pzgeqr2 computes a qr factorization of a complex distributed m-by- pzgeqrf computes a qr factorization of a complex distributed m-by- pzgerfs improves the computed solution to a system of linea the solutions. pzgerq2 computes a rq factorization of a complex distributed m-by- pzgerqf computes a rq factorization of a complex distributed m-by- where sub( a ) = a(ia:ia+n-1,ja:ja+n-1) is an n-by-n distributed distributed matrices. only the first min(m,n) columns of u and rows of vt = v**t are computed notes each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzgetf2 computes an lu factorization of a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) usin pzgetrf computes an lu factorization of a general m-by-n distributed row interchanges. pzgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted pzgetrs solves a system of distributed linear equation op( sub( a ) ) * x = sub( b ) each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzheev computes selected eigenvalues and, optionally, eigenvector of scalapack routines. pzheevx computes selected eigenvalues and, optionally, eigenvector of scalapack routines. eigenvalues/vectors can be selected by each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process support for uplo='u' is limited to calling the old, slow, pzhetr each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding pzlabrd reduces the first nb rows and columns of a complex general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to uppe returns the matrices x and y which are needed to apply the transfor- each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzlacon estimates the 1-norm of a square, complex distributed matri products. x and v are aligned with the distributed matrix a, this each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzlacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pzlacp3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. notice tha more. the receiving node can be specified precisely, or all nodes pzlacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pzlaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. or the infinity norm, or the element of largest absolute value of a distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1) pzlange returns the value pzlapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pzlapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pzlaqge equilibrates a general m-by-n distributed matri factors in the vectors r and c. pzlaqsy equilibrates a symmetric distributed matri vectors sr and sc. pzlarfb applies a complex block reflector q or its conjugate transpose q**h to a complex m-by-n distributed matrix sub( c where alpha is a real scalar, and sub( x ) is an (n-1)-element complex distributed vector x(ix:ix+n-2,jx) if incx = 1 an if storev = 'c', the vector which defines the elementary reflector h(i) is stored in the i-th column of the distributed matrix v, an h = i - v * t * v' pzlarzb applies a complex block reflector q or its conjugate transpose q**h to a complex m-by-n distributed matrix sub( c currently, only storev = 'r' and direct = 'b' are supported notes pzlascl multiplies the m-by-n complex distributed matrix sub( a is done without over/underflow as long as the final result pzlase2 initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. pzlase2 requires that only dimension of the matrix pzlaset initializes an m-by-n distributed matrix sub( a ) denotin offdiagonals. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzlaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pzlatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pzlatrd reduces nb rows and columns of a complex hermitian distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to comple q' * sub( a ) * q, and returns the matrices v and w which are each global data object is described by an associated descriptio the mapping between an object element and its corresponding process each global data object is described by an associated descriptio the mapping between an object element and its corresponding process factor u or l is stored in the upper or lower triangular part of the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) if uplo = 'u' or 'u' then the upper triangle of the result is stored, each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzmax1 computes the global index of the maximum element in absolute value of a distributed vector sub( x ). the global index is returne where a(1:n, ja:ja+n-1) is an n-by-n complex banded symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n complex banded symmetric positive definite distributed depending on the value of uplo, a stores either u or l in the equn pzpocon estimates the reciprocal of the condition number (in the 1-norm) of a complex hermitian positive definite distributed matri pzpotrf. pzpoequ computes row and column scalings intended to equilibrate a distributed hermitian positive definite matri (with respect to the two-norm). sr and sc contain the scale pzporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is an n-by-n hermitian distributed positive definite matrix and x and sub( b matrices. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzpotf2 computes the cholesky factorization of a complex hermitian positive definite distributed matrix sub( a )=a(ia:ia+n-1,ja:ja+n-1) the factorization has the form pzpotrf computes the cholesky factorization of an n-by-n complex hermitian positive definite distributed matrix sub( a ) denotin pzpotri computes the inverse of a complex hermitian positive definite distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using th pzpotrf. where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n hermitian positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distributed a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distributed depending on the value of uplo, a stores either u or l in the equn of orthogonalization is controlled by the input parameter lwork. eigenvectors that are to be orthogonalized are computed by the sam processes and then calls dstein2 (modified lapack routine) on each pztrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th if all eigenvectors are requested, the routine may either return th products q*x and/or q*y, where q is an input unitary the solution matrix x must be computed by pztrtrs or some othe refinement because doing so cannot improve the backward error. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pztrtri computes the inverse of a upper or lower triangular distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) notes where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a triangular distributed matrix of order n, and b(ib:ib+n-1,jb:jb+nrhs-1) is a to verify that sub( a ) is nonsingular. each global data object is described by an associated descriptio the mapping between an object element and its corresponding process pzung2l generates an m-by-n complex distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m pzung2r generates an m-by-n complex distributed matrix q denotin the first n columns of a product of k elementary reflectors of order pzungl2 generates an m-by-n complex distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n pzunglq generates an m-by-n complex distributed matrix q denotin the first m rows of a product of k elementary reflectors of order n pzungql generates an m-by-n complex distributed matrix q denotin the last n columns of a product of k elementary reflectors of order m pzungqr generates an m-by-n complex distributed matrix q denotin the first n columns of a product of k elementary reflectors of order pzungr2 generates an m-by-n complex distributed matrix q denotin last m rows of a product of k elementary reflectors of order n pzungrq generates an m-by-n complex distributed matrix q denotin last m rows of a product of k elementary reflectors of order n pzunm2l overwrites the general complex m-by-n distributed matri pzunm2r overwrites the general complex m-by-n distributed matri if vect = 'q', pzunmbr overwrites the general complex distributed pzunmhr overwrites the general complex m-by-n distributed matri pzunml2 overwrites the general complex m-by-n distributed matri pzunmlq overwrites the general complex m-by-n distributed matri pzunmql overwrites the general complex m-by-n distributed matri pzunmqr overwrites the general complex m-by-n distributed matri pzunmr2 overwrites the general complex m-by-n distributed matri pzunmr3 overwrites the general complex m-by-n distributed matri pzunmrq overwrites the general complex m-by-n distributed matri pzunmrz overwrites the general complex m-by-n distributed matri pzunmtr overwrites the general complex m-by-n distributed matri |
| Temporarily Temporarily Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices sub( x ) and sub( b ) should be Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices sub( x ) and sub( b ) should be Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices sub( x ) and sub( b ) should be Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively this routine Temporarily returns when n <= 1 the distributed submatrices op( a ) and op( af ) (respectively Temporarily set the descriptor type to 1xp typ Temporarily set the descriptor type to 1xp typ this routine Temporarily returns when n <= 1 the distributed submatrices sub( x ) and sub( b ) should be |
| temporary temporary work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. temporary variables. the following variables are used withi iteration to the next: work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex temporary workspace. this space ma the size given in lwork. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. work (local workspace/local output) double precision temporary workspace. this space ma the size given in lwork. temporary variables. the following variables are used withi iteration to the next: work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. work (local workspace/local output) real temporary workspace. this space ma the size given in lwork. temporary variables. the following variables are used withi iteration to the next: work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. temporary variables. the following variables are used withi iteration to the next: work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. discard temporary matrix stored beginning i off_diagonal block of reduced system. work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. first copy and multiply it into temporary storage work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. work (local workspace/local output) complex*16 temporary workspace. this space ma the size given in lwork. |
| Tenn Tenn implemented for scalapack by: andrew j. cleary, livermore national lab and university of Tenn. based on code written by : peter arbenz, eth zurich, 1996. implemented for scalapack by: andrew j. cleary, livermore national lab and university of Tenn. based on code written by : peter arbenz, eth zurich, 1996. implemented for scalapack by: andrew j. cleary, livermore national lab and university of Tenn. based on code written by : peter arbenz, eth zurich, 1996. implemented for scalapack by: andrew j. cleary, livermore national lab and university of Tenn. based on code written by : peter arbenz, eth zurich, 1996. |
| Tennessee Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. code developer: andrew j. cleary, university of Tennessee this version released: august, 2001. |
| term term let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as pcgels solves overdetermined or underdetermined complex linea or its conjugate-transpose, using a qr or lq factorization of let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as in the following comments, the character _ should be read as "of the distributed matrix". let a be a generic term for any 2 let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distribute such a global array has an associated description vector desca. let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as here q and p**h are the unitary distributed matrices determined b bidiagonal form: a(ia:*,ja:*) = q * b * p**h. q and p**h are defined let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as pdgels solves overdetermined or underdetermined real linea or its transpose, using a qr or lq factorization of sub( a ). it is let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as here q and p**t are the orthogonal distributed matrices determined b bidiagonal form: a(ia:*,ja:*) = q * b * p**t. q and p**t are defined let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as in the following comments, the character _ should be read as "of the distributed matrix". let a be a generic term for any 2 let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distribute such a global array has an associated description vector desca. let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as psgels solves overdetermined or underdetermined real linea or its transpose, using a qr or lq factorization of sub( a ). it is let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as here q and p**t are the orthogonal distributed matrices determined b bidiagonal form: a(ia:*,ja:*) = q * b * p**t. q and p**t are defined let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as in the following comments, the character _ should be read as "of the distributed matrix". let a be a generic term for any 2 let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distribute such a global array has an associated description vector desca. let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as pzgels solves overdetermined or underdetermined complex linea or its conjugate-transpose, using a qr or lq factorization of let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as in the following comments, the character _ should be read as "of the distributed matrix". let a be a generic term for any 2 let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distribute such a global array has an associated description vector desca. let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as here q and p**h are the unitary distributed matrices determined b bidiagonal form: a(ia:*,ja:*) = q * b * p**h. q and p**h are defined let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as let a be a generic term for any 2d block cyclicly distributed array in the following comments, the character _ should be read as |
| terminated terminated eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters workspace. hence the eigenvectors corresponding to these clusters may not be orthogonal. iclustr is a zero terminated if and only if k is the number of clusters. workspace. hence the eigenvectors corresponding to these clusters may not be orthogonal. iclustr is a zero terminated if and only if k is the number of clusters. eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters workspace. hence the eigenvectors corresponding to these clusters may not be orthogonal. iclustr is a zero terminated if and only if k is the number of clusters. eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters eigenvectors corresponding to these clusters may not be orthogonal. iclustr() is a zero terminated array k is the number of clusters workspace. hence the eigenvectors corresponding to these clusters may not be orthogonal. iclustr is a zero terminated if and only if k is the number of clusters. |
| Test Test Test the input parameters Test the input parameters Test the input paramters Test the input paramters Test the input parameters Test the input parameters Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameters Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameters Test the input parameter Test the input parameter Test the input parameter Test the input parameter Test the input parameters Test the input paramters Test the input paramters Test the input parameters Test the input parameters Test the input parameters |
| tested tested pclamr1d has not been tested except withint the contect o pdlamr1d has not been tested except withint the contect o pslamr1d has not been tested except withint the contect o pzlamr1d has not been tested except withint the contect o |
| than than on entry, the number of bulges to send through h ( >1 ). nbulge should be less than the maximum determined (jblk) on exit, the maximum number of bulges that can be sent on entry, the number of bulges to send through h ( >1 ). nbulge should be less than the maximum determined (jblk) on exit, the maximum number of bulges that can be sent of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on finally aptr is the pointer to the first element of a. as lapack has a slightly different matrix format than scalapack the pointe of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , pchengst performs the same function as pchegst, but is based on rank 2k updates, which are faster and more scalable than pchentrd is faster than pchetrd on almost all matrices enough workspace is available to use the tailored codes. the node owning h(m,m) does not. this will occur on a border and can happen in no more than 3 locations per block assumin values: a buffer to send diagonally down and right, a buffer scale the column norms by tscal if the maximum element in cnorm is greater than bignum/2 then, the processes which receive the answer will be (note that if an operation involves more than one vector, the processes which re each vector): of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on orthogonality is similar to that obtained from cstein2). note : lwork must be no smaller than and should have the same input value on all processes. of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on finally aptr is the pointer to the first element of a. as lapack has a slightly different matrix format than scalapack the pointe of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form the node owning h(m,m) does not. this will occur on a border and can happen in no more than 3 locations per block assumin values: a buffer to send diagonally down and right, a buffer j = 1,...,minp. it uses and computes the function n(w), which is the count of eigenvalues of a symmetric tridiagonal matrix less than specifies the criterion for "convergence" of an interval. = 0 : when an interval is narrower than abstol, or tha it is considered to have "converged". the shift. pdlapdct finds the number of eigenvalues of t less than or equal to sigma n (input) integer it contains the same values as bycol, but it is replicated across all processes rather than being distribute byall(i) = bycol( numroc(i,desc( nb_ ),myrow,0,nprow ) on the procs it contains the same values as byrow, but it is replicated across all processes rather than being distribute byall(i) = byrow( numroc(i,desc( mb_ ),mycol,0,npcol ) on the procs of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if range='v', the lower bound of the interval to be searched for eigenvalues. eigenvalues less than vl will not b orthogonality is similar to that obtained from dstein2). note : lwork must be no smaller than and should have the same input value on all processes. when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , pdsyngst performs the same function as pdhegst, but is based on rank 2k updates, which are faster and more scalable than pdsyntrd is faster than pdsytrd on almost all matrices enough workspace is available to use the tailored codes. then, the processes which receive the answer will be (note that if an operation involves more than one vector, the processes which re each vector): then, the processes which receive the answer will be (note that if an operation involves more than one vector, the processes which re each vector): of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on finally aptr is the pointer to the first element of a. as lapack has a slightly different matrix format than scalapack the pointe of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form the node owning h(m,m) does not. this will occur on a border and can happen in no more than 3 locations per block assumin values: a buffer to send diagonally down and right, a buffer j = 1,...,minp. it uses and computes the function n(w), which is the count of eigenvalues of a symmetric tridiagonal matrix less than specifies the criterion for "convergence" of an interval. = 0 : when an interval is narrower than abstol, or tha it is considered to have "converged". the shift. pslapdct finds the number of eigenvalues of t less than or equal to sigma n (input) integer it contains the same values as bycol, but it is replicated across all processes rather than being distribute byall(i) = bycol( numroc(i,desc( nb_ ),myrow,0,nprow ) on the procs it contains the same values as byrow, but it is replicated across all processes rather than being distribute byall(i) = byrow( numroc(i,desc( mb_ ),mycol,0,npcol ) on the procs of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if range='v', the lower bound of the interval to be searched for eigenvalues. eigenvalues less than vl will not b orthogonality is similar to that obtained from sstein2). note : lwork must be no smaller than and should have the same input value on all processes. when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , pssyngst performs the same function as pshegst, but is based on rank 2k updates, which are faster and more scalable than pssyntrd is faster than pssytrd on almost all matrices enough workspace is available to use the tailored codes. of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on finally aptr is the pointer to the first element of a. as lapack has a slightly different matrix format than scalapack the pointe of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , when it is determined to lie in an interval [a,b] of width less than or equal t abstol + eps * max( |a|,|b| ) , pzhengst performs the same function as pzhegst, but is based on rank 2k updates, which are faster and more scalable than pzhentrd is faster than pzhetrd on almost all matrices enough workspace is available to use the tailored codes. the node owning h(m,m) does not. this will occur on a border and can happen in no more than 3 locations per block assumin values: a buffer to send diagonally down and right, a buffer scale the column norms by tscal if the maximum element in cnorm is greater than bignum/2 then, the processes which receive the answer will be (note that if an operation involves more than one vector, the processes which re each vector): of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on the following method uses more flops than necessary bu of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on of the matrix a. if the reciprocal of the condition number is less than machine precision, steps 4-6 are skipped 4. the system of equations is solved for x using the factored form of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on if this is the first group of processors, the receive comes from a different processor than otherwise of the divide and conquer algorithm as a task-parallel algorithm. this formula in words is: no processor may have more than on orthogonality is similar to that obtained from zstein2). note : lwork must be no smaller than and should have the same input value on all processes. on entry, the number of bulges to send through h ( >1 ). nbulge should be less than the maximum determined (jblk) on exit, the maximum number of bulges that can be sent on entry, the number of bulges to send through h ( >1 ). nbulge should be less than the maximum determined (jblk) on exit, the maximum number of bulges that can be sent |
| that that a. on exit, dl is overwritten by the (n-1) multipliers that dl (input) complex array, dimension (n-1) the (n-1) multipliers that define the matrix l from th eigenvalues i+1 to ihi have already converged. either l = ilo, or h(l,l-1) is negligible so that the matrix splits subsequent shifts in an effort to maximize the number of bulges that can be sent through (nbulge > 1) and the first shift is starting in the middle of an where l or u is the cholesky factor of a hermitian positive definite tridiagonal matrix a such that $ ( two*( c*oldrp-b )+safmin ) make sure that we are making progres skip the current step: the subdiagonal info is just noise. a. on exit, dl is overwritten by the (n-1) multipliers that dl (input) complex array, dimension (n-1) the (n-1) multipliers that define the matrix l from th subsequent shifts in an effort to maximize the number of bulges that can be sent through (nbulge > 1) and the first shift is starting in the middle of an dlasorte sorts eigenpairs so that real eigenpairs are together an since every 2nd subdiagonal is guaranteed to be zero. where l is the cholesky factor of a hermitian positive definite tridiagonal matrix a such that of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its or its conjugate-transpose, using a qr or lq factorization of sub( a ). it is assumed that sub( a ) has full rank the following options are provided: let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension r x c. locr( k ) denote distributed over the r processes of its process column. similarly, let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its only spot checks of the consistency of the eigenvalues across the different processes. because of this, it is possible that messages. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pchentrd is faster than pchetrd on almost all matrices, particularly small ones (i.e. n < 500 * sqrt(p) ), provided that let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its a(ia:ia+m-1,ja:ja+n-1) and sub( b ) denotes b(ib:ib+m-1,jb:jb+n-1). pclacp2 requires that only dimension of the matrix operands i pclacp3 is an auxiliary routine that copies from a global paralle the entire submatrix that is copied gets placed on one node or let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its where they are computed, to a scalapack standard block cyclic array, sorted so that the corresponding eigenvalues are sorted notes converged. either l = ilo or the global a(l,l-1) is negligible so that the matrix splits pclahrd reduces the first nb columns of a complex general n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that performed by an unitary similarity transformation q' * a * q. the i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. normf denotes the frobenius norm of a matrix (square root of sum of squares). note that max(abs(a(i,j))) is not a matrix norm notes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pclarfg generates a complex elementary reflector h of order n, such that h * sub( x ) = h * ( x(iax,jax) ) = ( alpha ), h' * h = i. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies that hessenberg. a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on the offdiagonals. pclase2 requires that only dimension of the matri let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pclasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero notes pclassq returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its scale x so that its components are less than or equal t let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its (with respect to the two-norm). sr and sc contain the scale factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri the diagonal. this choice of sr and sc puts the condition number let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its correspond to user specified eigenvalues. pcstein does not orthogonalize vectors that are on different processes. the exten eigenvectors that are to be orthogonalized are computed by the same let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension r x c would receive if k were distributed over the r processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its n-by-nrhs distributed matrix denoted by sub( b ). a check is made to verify that sub( a ) is nonsingular notes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the order of the unitary matrix q or p**h that is applied if vect = 'q', a(ia:*,ja:*) is assumed to have been an nq-by-k let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its or its transpose, using a qr or lq factorization of sub( a ). it is assumed that sub( a ) has full rank the following options are provided: let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension r x c. locr( k ) denote distributed over the r processes of its process column. similarly, let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its a(ia:ia+m-1,ja:ja+n-1) and sub( b ) denotes b(ib:ib+m-1,jb:jb+n-1). pdlacp2 requires that only dimension of the matrix operands i pdlacp3 is an auxiliary routine that copies from a global paralle the entire submatrix that is copied gets placed on one node or let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its mmax (input) integer the maximum number of intervals that may be generated. i quit with info = mmax+1. i.e., on output, all intervals [ intvl(2*i-1), intvl(2*i) ], i < kf, have converged. note that the input intervals may be reordered b where they are computed, to a scalapack standard block cyclic array, sorted so that the corresponding eigenvalues are sorted notes converged. either l = ilo or the global a(l,l-1) is negligible so that the matrix splits pdlahrd reduces the first nb columns of a real general n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below th nal similarity transformation q' * a * q. the routine returns the eps = relative machine precision sfmin = safe minimum, such that 1/sfmin does not overflo prec = eps*base i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. normf denotes the frobenius norm of a matrix (square root of sum of squares). note that max(abs(a(i,j))) is not a matrix norm notes entries are d(2),d(4),...,d(2*n-2). to avoid overflow, the matrix must be scaled so that its largest entry is no greate and for greatest accuracy, it should not be much smaller let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its it assumes that the input array, bycol, is distributed acros bycol. the output array, byall, will be identical on all processes it assumes that the input array, byrow, is distributed acros byrow. the output array, byall, will be identical on all processes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pdlarfg generates a real elementary reflector h of order n, such that h * sub( x ) = h * ( x(iax,jax) ) = ( alpha ), h' * h = i. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies that hessenberg. a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on the offdiagonals. pdlase2 requires that only dimension of the matri let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pdlasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero notes pdlassq returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the order of the orthogonal matrix q or p**t that is applied if vect = 'q', a(ia:*,ja:*) is assumed to have been an nq-by-k let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its (with respect to the two-norm). sr and sc contain the scale factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri the diagonal. this choice of sr and sc puts the condition number let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its note : it is assumed that the user is on an ieee machine. if the use to 1 (in slmake.inc). the features of ieee arithmetic that correspond to user specified eigenvalues. pdstein does not orthogonalize vectors that are on different processes. the exten eigenvectors that are to be orthogonalized are computed by the same no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pdsyntrd is faster than pdsytrd on almost all matrices, particularly small ones (i.e. n < 500 * sqrt(p) ), provided that let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its n-by-nrhs distributed matrix denoted by sub( b ). a check is made to verify that sub( a ) is nonsingular notes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its 1) opts is a concatenation of all of the character options to subroutine name, in the same order that they appear in th the value of the parameter specified by ispec. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its or its transpose, using a qr or lq factorization of sub( a ). it is assumed that sub( a ) has full rank the following options are provided: let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension r x c. locr( k ) denote distributed over the r processes of its process column. similarly, let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its a(ia:ia+m-1,ja:ja+n-1) and sub( b ) denotes b(ib:ib+m-1,jb:jb+n-1). pslacp2 requires that only dimension of the matrix operands i pslacp3 is an auxiliary routine that copies from a global paralle the entire submatrix that is copied gets placed on one node or let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its mmax (input) integer the maximum number of intervals that may be generated. i quit with info = mmax+1. i.e., on output, all intervals [ intvl(2*i-1), intvl(2*i) ], i < kf, have converged. note that the input intervals may be reordered b where they are computed, to a scalapack standard block cyclic array, sorted so that the corresponding eigenvalues are sorted notes converged. either l = ilo or the global a(l,l-1) is negligible so that the matrix splits pslahrd reduces the first nb columns of a real general n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below th nal similarity transformation q' * a * q. the routine returns the eps = relative machine precision sfmin = safe minimum, such that 1/sfmin does not overflo prec = eps*base i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. normf denotes the frobenius norm of a matrix (square root of sum of squares). note that max(abs(a(i,j))) is not a matrix norm notes entries are d(2),d(4),...,d(2*n-2). to avoid overflow, the matrix must be scaled so that its largest entry is no greate and for greatest accuracy, it should not be much smaller let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its it assumes that the input array, bycol, is distributed acros bycol. the output array, byall, will be identical on all processes it assumes that the input array, byrow, is distributed acros byrow. the output array, byall, will be identical on all processes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pslarfg generates a real elementary reflector h of order n, such that h * sub( x ) = h * ( x(iax,jax) ) = ( alpha ), h' * h = i. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies that hessenberg. a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on the offdiagonals. pslase2 requires that only dimension of the matri let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pslasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero notes pslassq returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the order of the orthogonal matrix q or p**t that is applied if vect = 'q', a(ia:*,ja:*) is assumed to have been an nq-by-k let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its (with respect to the two-norm). sr and sc contain the scale factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri the diagonal. this choice of sr and sc puts the condition number let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its note : it is assumed that the user is on an ieee machine. if the use to 1 (in slmake.inc). the features of ieee arithmetic that correspond to user specified eigenvalues. psstein does not orthogonalize vectors that are on different processes. the exten eigenvectors that are to be orthogonalized are computed by the same no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pssyntrd is faster than pssytrd on almost all matrices, particularly small ones (i.e. n < 500 * sqrt(p) ), provided that let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its n-by-nrhs distributed matrix denoted by sub( b ). a check is made to verify that sub( a ) is nonsingular notes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its or its conjugate-transpose, using a qr or lq factorization of sub( a ). it is assumed that sub( a ) has full rank the following options are provided: let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension r x c. locr( k ) denote distributed over the r processes of its process column. similarly, let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its only spot checks of the consistency of the eigenvalues across the different processes. because of this, it is possible that messages. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pzhentrd is faster than pzhetrd on almost all matrices, particularly small ones (i.e. n < 500 * sqrt(p) ), provided that let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its a(ia:ia+m-1,ja:ja+n-1) and sub( b ) denotes b(ib:ib+m-1,jb:jb+n-1). pzlacp2 requires that only dimension of the matrix operands i pzlacp3 is an auxiliary routine that copies from a global paralle the entire submatrix that is copied gets placed on one node or let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its where they are computed, to a scalapack standard block cyclic array, sorted so that the corresponding eigenvalues are sorted notes converged. either l = ilo or the global a(l,l-1) is negligible so that the matrix splits pzlahrd reduces the first nb columns of a complex general n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that performed by an unitary similarity transformation q' * a * q. the i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. normf denotes the frobenius norm of a matrix (square root of sum of squares). note that max(abs(a(i,j))) is not a matrix norm notes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pzlarfg generates a complex elementary reflector h of order n, such that h * sub( x ) = h * ( x(iax,jax) ) = ( alpha ), h' * h = i. let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies that hessenberg. a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on the offdiagonals. pzlase2 requires that only dimension of the matri let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its pzlasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero notes pzlassq returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its scale x so that its components are less than or equal t let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its of the factorization. note that permutations are performed on the matrix, so tha by lapack. convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its (with respect to the two-norm). sr and sc contain the scale factors, s(i) = 1/sqrt(a(i,i)), chosen so that the scaled distri the diagonal. this choice of sr and sc puts the condition number let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape ja (global input) integer the index in the global array a that points to the start o or a submatrix of a). convert descriptor into standard form for easy access to parameters, check that grid is of right shape correspond to user specified eigenvalues. pzstein does not orthogonalize vectors that are on different processes. the exten eigenvectors that are to be orthogonalized are computed by the same let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension r x c would receive if k were distributed over the r processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its n-by-nrhs distributed matrix denoted by sub( b ). a check is made to verify that sub( a ) is nonsingular notes let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is the order of the unitary matrix q or p**h that is applied if vect = 'q', a(ia:*,ja:*) is assumed to have been an nq-by-k let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its let k be the number of rows or columns of a distributed matrix, and assume that its process grid has dimension p x q would receive if k were distributed over the p processes of its a. on exit, dl is overwritten by the (n-1) multipliers that dl (input) complex array, dimension (n-1) the (n-1) multipliers that define the matrix l from th subsequent shifts in an effort to maximize the number of bulges that can be sent through (nbulge > 1) and the first shift is starting in the middle of an slasorte sorts eigenpairs so that real eigenpairs are together an since every 2nd subdiagonal is guaranteed to be zero. where l is the cholesky factor of a hermitian positive definite tridiagonal matrix a such that a. on exit, dl is overwritten by the (n-1) multipliers that dl (input) complex array, dimension (n-1) the (n-1) multipliers that define the matrix l from th eigenvalues i+1 to ihi have already converged. either l = ilo, or h(l,l-1) is negligible so that the matrix splits subsequent shifts in an effort to maximize the number of bulges that can be sent through (nbulge > 1) and the first shift is starting in the middle of an where l or u is the cholesky factor of a hermitian positive definite tridiagonal matrix a such that $ ( two*( c*oldrp-b )+safmin ) make sure that we are making progres skip the current step: the subdiagonal info is just noise. |
| the the ccombamax1 finds the element having maximum real part absolut this is the unblocked version of the algorithm, calling level 2 blas arguments kv is the number of superdiagonals in the factor the factorization has the for where l is a product of unit lower bidiagonal cdttrsv solves one of the systems of equation u * x = b, u**t * x = b, or u**h * x = b, set machine-dependent constants for the stopping criterion see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulge clamsh should only be called when there are multiple shifts/bulges clanv2 computes the schur factorization of a complex 2-by- claref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei cpttrsv solves one of the triangular system u * x = b, or u**h * x = b, skip the current step: the subdiagonal info is just noise ctrmvt performs the matrix-vector operation x := conjg( t' ) *y, and w := t *z, this is the unblocked version of the algorithm, calling level 2 blas arguments kv is the number of superdiagonals in the factor the factorization has the for where l is a product of unit lower bidiagonal ddttrsv solves one of the systems of equation u * x = b, u**t * x = b, or u**h * x = b, see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulge dlamsh should only be called when there are multiple shifts/bulges test the input paramters dlaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei dlasorte sorts eigenpairs so that real eigenpairs are together an since every 2nd subdiagonal is guaranteed to be zero. test the input paramters dpttrsv solves one of the triangular system where l is the cholesky factor of a hermitian positive test the input parameters test the input parameters dtrmvt performs the matrix-vector operation x := t' *y, and w := t *z, is used to factor a reordering of the matrix into l u see pcdbtrf and pcdbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter is used to factor a reordering of the matrix into l u see pcdttrf and pcdttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter is used to factor a reordering of the matrix into p l u see pcgbtrf and pcgbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pcgecon estimates the reciprocal of the condition number of a genera 1-norm or the infinity-norm, using the lu factorization computed by m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) and reduce its condition number. r returns the row scale factors and each row and column of the distributed matrix b with elements each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the following options are provided 1. if trans = 'n' and m >= n: find the least squares solution of each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pcgerfs improves the computed solution to a system of linea the solutions. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pcgesv computes the solution to a complex system of linear equation sub( a ) * x = sub( b ), pcgesvd computes the singular value decomposition (svd) of a singular vectors. the svd is written as pcgesvx uses the lu factorization to compute the solution to the factorization has the form sub( a ) = p * l * u, where p is elements (lower trapezoidal if m > n), and u is upper triangular the factorization has the form sub( a ) = p * l * u, where p is ments (lower trapezoidal if m > n), and u is upper triangular pcgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted with a general n-by-n distributed matrix sub( a ) using the l sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1), op( a ) = a, a**t or a**h where q is an n-by-n unitary matrix, z is a p-by-p unitary matrix, and r and t assume one of the forms if n >= m, r = ( r11 ) m , or if n < m, r = ( r11 r12 ) n, where q is an n-by-n unitary matrix, z is a p-by-p unitary matrix, and r and t assume one of the forms if m <= n, r = ( 0 r12 ) m, or if m > n, r = ( r11 ) m-n, pcheev computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix a by calling the recommended sequenc pcheevd computes all the eigenvalues and eigenvectors of a hermitia pcheevx computes selected eigenvalues and, optionally, eigenvectors of a complex hermitian matrix a by calling the recommended sequenc specifying a range of values or a range of indices for the desired in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an pchegvx computes all the eigenvalues, and optionally of a complex generalized hermitian-definite eigenproblem, of the form pchengst performs the same function as pchegst, but is based o triangular solves (the basis of pchengst). support for uplo='u' is limited to calling the old, slow, pchetr each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. pclabrd reduces the first nb rows and columns of a complex genera or lower bidiagonal form by an unitary transformation q' * a * p, and each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pclacon estimates the 1-norm of a square, complex distributed matri products. x and v are aligned with the distributed matrix a, this pclaconsb looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift qr iteratio subdiagonal negligible. pclacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes array into a local replicated array or vise versa. notice that the entire submatrix that is copied gets placed on one node o can receive, or just one row or column of nodes. pclacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pclaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. determine the number of columns we have so we can check workspac pclahrd reduces the first nb columns of a complex genera elements below the k-th subdiagonal are zero. the reduction is pclamr1d has not been tested except withint the contect o pclange returns the value of the one norm, or the frobenius norm distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1). if the matrix is hermitian, we address only a triangular portio can be obtained by adding along row i and column i of the the gather the intermediate results to process (0,0) if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the gather the intermediate results to process (0,0) pclapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pclapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pclaqge equilibrates a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) using the row and scalin pclaqsy equilibrates a symmetric distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using the scaling factors in th perform the local computation within a process colum transpose q**h to a complex m-by-n distributed matrix sub( c ) denoting c(ic:ic+m-1,jc:jc+n-1), from the left or the right notes perform the local computation within a process colum complex distributed vector x(ix:ix+n-2,jx) if incx = 1 and x(ix,jx:jx+n-2) if incx = descx(m_). h is represented in the for h = i - tau * ( 1 ) * ( 1 v' ) , pclarft forms the triangular factor t of a complex block reflector perform the local computation within a process colum transpose q**h to a complex m-by-n distributed matrix sub( c ) denoting c(ic:ic+m-1,jc:jc+n-1), from the left or the right q is a product of k elementary reflectors as returned by pctzrzf. perform the local computation within a process colum pclarzt forms the triangular factor t of a complex block reflecto reflectors as returned by pctzrzf. pclascl multiplies the m-by-n complex distributed matrix sub( a is done without over/underflow as long as the final result pclase2 initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th operand is distributed. pclaset initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th pclasmsub looks for a small subdiagonal element from the botto pclassq returns the values scl and smsq such tha ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, pclaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pclatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. tridiagonal form by an unitary similarity transformation q' * sub( a ) * q, and returns the matrices v and w which ar pclatrz reduces the m-by-n ( m<=n ) complex upper trapezoida to upper triangular form by means of unitary transformations. test the input parameters pclauu2 computes the product u * u' or l' * l, where the triangula the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pclauum computes the product u * u' or l' * l, where the triangula the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pclawil gets the transform given by h44,h33, & h43h34 into pcmax1 computes the global index of the maximum element in absolut in indx and the value is returned in amax, cholesky factorization is used to factor a reordering of the matrix into l l' see pcpbtrf and pcpbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter pcpocon estimates the reciprocal of the condition number (in th using the cholesky factorization a = u**h*u or a = l*l**h computed by sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on pcporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the pcposv computes the solution to a complex system of linear equation sub( a ) * x = sub( b ), pcposvx uses the cholesky factorization a = u**h*u or a = l*l**h t pcpotf2 computes the cholesky factorization of a complex hermitia pcpotrf computes the cholesky factorization of an n-by-n comple a(ia:ia+n-1, ja:ja+n-1). pcpotri computes the inverse of a complex hermitian positive definit cholesky factorization sub( a ) = u**h*u or l*l**h computed by where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n hermitian positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). cholesky factorization is used to factor a reordering of the matrix into l l' see pcpttrf and pcpttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter pcsrscl multiplies an n-element complex distributed vector sub( x ) by the real scalar 1/a. this is done without overflow o underflow. pcstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pcstein does not pctrcon estimates the reciprocal of the condition number of 1-norm or the infinity-norm. pctrevc computes some or all of the right and/or left eigenvectors o pctrrfs provides error bounds and backward error estimates for the coefficient matrix. pctrti2 computes the inverse of a complex upper or lower triangula contained in one and only one process memory space (local operation). pctrtri computes the inverse of a upper or lower triangula pctrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ) or pctzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matri of unitary transformations. a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k)' . . . h(2)' h(1)' a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k)' . . . h(2)' h(1)' a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde pcungr2 generates an m-by-n complex distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the pcungrq generates an m-by-n complex distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the pcunm2l overwrites the general complex m-by-n distributed matri pcunm2r overwrites the general complex m-by-n distributed matri if vect = 'q', pcunmbr overwrites the general complex distribute pcunmhr overwrites the general complex m-by-n distributed matri pcunml2 overwrites the general complex m-by-n distributed matri pcunmlq overwrites the general complex m-by-n distributed matri pcunmql overwrites the general complex m-by-n distributed matri pcunmqr overwrites the general complex m-by-n distributed matri pcunmr2 overwrites the general complex m-by-n distributed matri pcunmr3 overwrites the general complex m-by-n distributed matri pcunmrq overwrites the general complex m-by-n distributed matri pcunmrz overwrites the general complex m-by-n distributed matri pcunmtr overwrites the general complex m-by-n distributed matri is used to factor a reordering of the matrix into l u see pddbtrf and pddbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter is used to factor a reordering of the matrix into l u see pddttrf and pddttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter is used to factor a reordering of the matrix into p l u see pdgbtrf and pdgbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pdgecon estimates the reciprocal of the condition number of a genera or the infinity-norm, using the lu factorization computed by pdgetrf. m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) and reduce its condition number. r returns the row scale factors and each row and column of the distributed matrix b with elements each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the following options are provided 1. if trans = 'n' and m >= n: find the least squares solution of each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pdgerfs improves the computed solution to a system of linea the solutions. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pdgesv computes the solution to a real system of linear equation sub( a ) * x = sub( b ), pdgesvd computes the singular value decomposition (svd) of a singular vectors. the svd is written as pdgesvx uses the lu factorization to compute the solution to a rea the factorization has the form sub( a ) = p * l * u, where p is elements (lower trapezoidal if m > n), and u is upper triangular the factorization has the form sub( a ) = p * l * u, where p is ments (lower trapezoidal if m > n), and u is upper triangular pdgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted with a general n-by-n distributed matrix sub( a ) using the l sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1), op( a ) = a or a**t and where q is an n-by-n orthogonal matrix, z is a p-by-p orthogonal matrix, and r and t assume one of the forms if n >= m, r = ( r11 ) m , or if n < m, r = ( r11 r12 ) n, where q is an n-by-n orthogonal matrix, z is a p-by-p orthogonal matrix, and r and t assume one of the forms if m <= n, r = ( 0 r12 ) m, or if m > n, r = ( r11 ) m-n, pdlabad takes as input the values computed by pdlamch for underflo the log of large is sufficiently large. this subroutine is intended pdlabrd reduces the first nb rows and columns of a real genera or lower bidiagonal form by an orthogonal transformation q' * a * p, pdlacon estimates the 1-norm of a square, real distributed matrix a x and v are aligned with the distributed matrix a, this information pdlaconsb looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift qr iteratio subdiagonal negligible. pdlacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes array into a local replicated array or vise versa. notice that the entire submatrix that is copied gets placed on one node o can receive, or just one row or column of nodes. pdlacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pdlaebz contains the iteration loop which computes the eigenvalue j = 1,...,minp. it uses and computes the function n(w), which is pdlaecv checks if the input intervals [ intvl(2*i-1), intvl(2*i) ] pdlaecv modifies kf to be the index of the last converged interval, pdlaed0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method pdlaed1 computes the updated eigensystem of a diagona in parallel. pdlaed2 sorts the two sets of eigenvalues together into a singl there are two ways in which deflation can occur: when two or more pdlaed3 finds the roots of the secular equation, as defined by th appropriate calls to slaed4 form z1 which consist of the last row of q pdlaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. determine the number of columns we have so we can check workspac pdlahrd reduces the first nb columns of a real general n-by-(n-k+1 k-th subdiagonal are zero. the reduction is performed by an orthogo- ictxt (global input) integer the blacs context handle in which the computation take pdlamr1d has not been tested except withint the contect o pdlange returns the value of the one norm, or the frobenius norm distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1). gather the intermediate results to process (0,0) if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the gather the intermediate results to process (0,0) pdlapdct counts the number of negative eigenvalues of (t - sigma i) the innermost loop to avoid overflow and determine the sign of a pdlapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pdlapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pdlaqge equilibrates a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) using the row and scalin pdlaqsy equilibrates a symmetric distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using the scaling factors in th it assumes that the input array, bycol, is distributed acros bycol. the output array, byall, will be identical on all processes it assumes that the input array, byrow, is distributed acros byrow. the output array, byall, will be identical on all processes perform the local computation within a process colum real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1) from the left or the right notes distributed vector x(ix:ix+n-2,jx) if incx = 1 and x(ix,jx:jx+n-2) if incx = descx(m_). h is represented in the for h = i - tau * ( 1 ) * ( 1 v' ) , pdlarft forms the triangular factor t of a real block reflector perform the local computation within a process colum a real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1) from the left or the right q is a product of k elementary reflectors as returned by pdtzrzf. pdlarzt forms the triangular factor t of a real block reflecto reflectors as returned by pdtzrzf. pdlascl multiplies the m-by-n real distributed matrix sub( a is done without over/underflow as long as the final result pdlase2 initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th operand is distributed. pdlaset initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th pdlasmsub looks for a small subdiagonal element from the botto pdlasrt sort the numbers in d in increasing order and th pdlassq returns the values scl and smsq such tha ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, pdlaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pdlatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. form by an orthogonal similarity transformation q' * sub( a ) * q, and returns the matrices v and w which are needed to apply th pdlatrz reduces the m-by-n ( m<=n ) real upper trapezoidal matri upper triangular form by means of orthogonal transformations. pdlauu2 computes the product u * u' or l' * l, where the triangula the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pdlauum computes the product u * u' or l' * l, where the triangula the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pdlawil gets the transform given by h44,h33, & h43h34 into a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde pdorgr2 generates an m-by-n real distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the pdorgrq generates an m-by-n real distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the pdorm2l overwrites the general real m-by-n distributed matri pdorm2r overwrites the general real m-by-n distributed matri if vect = 'q', pdormbr overwrites the general real distributed m-by- pdormhr overwrites the general real m-by-n distributed matri pdorml2 overwrites the general real m-by-n distributed matri pdormlq overwrites the general real m-by-n distributed matri pdormql overwrites the general real m-by-n distributed matri pdormqr overwrites the general real m-by-n distributed matri pdormr2 overwrites the general real m-by-n distributed matri pdormr3 overwrites the general real m-by-n distributed matri pdormrq overwrites the general real m-by-n distributed matri pdormrz overwrites the general real m-by-n distributed matri pdormtr overwrites the general real m-by-n distributed matri cholesky factorization is used to factor a reordering of the matrix into l l' see pdpbtrf and pdpbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter pdpocon estimates the reciprocal of the condition number (in th using the cholesky factorization a = u**t*u or a = l*l**t computed by sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on pdporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the pdposv computes the solution to a real system of linear equation sub( a ) * x = sub( b ), pdposvx uses the cholesky factorization a = u**t*u or a = l*l**t t pdpotf2 computes the cholesky factorization of a real symmetri pdpotrf computes the cholesky factorization of an n-by-n rea a(ia:ia+n-1, ja:ja+n-1). pdpotri computes the inverse of a real symmetric positive definit cholesky factorization sub( a ) = u**t*u or l*l**t computed by where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n symmetric positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). cholesky factorization is used to factor a reordering of the matrix into l l' see pdpttrf and pdpttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter pdrscl multiplies an n-element real distributed vector sub( x ) by the real scalar 1/a. this is done without overflow or underflow a pdstebz computes the eigenvalues of a symmetric tridiagonal matrix i the interval [vl, vu], or the eigenvalues indexed il through iu. a pdstedc computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix in parallel, using the divide an pdstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pdstein does not pdsyev computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix a by calling the recommended sequenc pdsyevd computes all the eigenvalues and eigenvector of scalapack routines. pdsyevx computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix a by calling the recommended sequenc specifying a range of values or a range of indices for the desired in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an pdsygvx computes all the eigenvalues, and optionally of a real generalized sy-definite eigenproblem, of the form pdsyngst performs the same function as pdhegst, but is based o triangular solves (the basis of pdsyngst). support for uplo='u' is limited to calling the old, slow, pdsytr each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. pdtrcon estimates the reciprocal of the condition number of 1-norm or the infinity-norm. pdtrrfs provides error bounds and backward error estimates for the coefficient matrix. pdtrti2 computes the inverse of a real upper or lower triangula contained in one and only one process memory space (local operation). pdtrtri computes the inverse of a upper or lower triangula pdtrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ), pdtzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matri of orthogonal transformations. pdzsum1 returns the sum of absolute values of a comple pjlaenv is called from the scalapack symmetric and hermitia problem-dependent parameters for the local environment. see ispec pscsum1 returns the sum of absolute values of a comple is used to factor a reordering of the matrix into l u see psdbtrf and psdbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter is used to factor a reordering of the matrix into l u see psdttrf and psdttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter is used to factor a reordering of the matrix into p l u see psgbtrf and psgbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. psgecon estimates the reciprocal of the condition number of a genera or the infinity-norm, using the lu factorization computed by psgetrf. m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) and reduce its condition number. r returns the row scale factors and each row and column of the distributed matrix b with elements each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the following options are provided 1. if trans = 'n' and m >= n: find the least squares solution of each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. psgerfs improves the computed solution to a system of linea the solutions. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. psgesv computes the solution to a real system of linear equation sub( a ) * x = sub( b ), psgesvd computes the singular value decomposition (svd) of a singular vectors. the svd is written as psgesvx uses the lu factorization to compute the solution to a rea the factorization has the form sub( a ) = p * l * u, where p is elements (lower trapezoidal if m > n), and u is upper triangular the factorization has the form sub( a ) = p * l * u, where p is ments (lower trapezoidal if m > n), and u is upper triangular psgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted with a general n-by-n distributed matrix sub( a ) using the l sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1), op( a ) = a or a**t and where q is an n-by-n orthogonal matrix, z is a p-by-p orthogonal matrix, and r and t assume one of the forms if n >= m, r = ( r11 ) m , or if n < m, r = ( r11 r12 ) n, where q is an n-by-n orthogonal matrix, z is a p-by-p orthogonal matrix, and r and t assume one of the forms if m <= n, r = ( 0 r12 ) m, or if m > n, r = ( r11 ) m-n, pslabad takes as input the values computed by pslamch for underflo the log of large is sufficiently large. this subroutine is intended pslabrd reduces the first nb rows and columns of a real genera or lower bidiagonal form by an orthogonal transformation q' * a * p, pslacon estimates the 1-norm of a square, real distributed matrix a x and v are aligned with the distributed matrix a, this information pslaconsb looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift qr iteratio subdiagonal negligible. pslacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes array into a local replicated array or vise versa. notice that the entire submatrix that is copied gets placed on one node o can receive, or just one row or column of nodes. pslacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pslaebz contains the iteration loop which computes the eigenvalue j = 1,...,minp. it uses and computes the function n(w), which is pslaecv checks if the input intervals [ intvl(2*i-1), intvl(2*i) ] pslaecv modifies kf to be the index of the last converged interval, pslaed0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method pslaed1 computes the updated eigensystem of a diagona in parallel. pslaed2 sorts the two sets of eigenvalues together into a singl there are two ways in which deflation can occur: when two or more pslaed3 finds the roots of the secular equation, as defined by th appropriate calls to slaed4 form z1 which consist of the last row of q pslaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. determine the number of columns we have so we can check workspac pslahrd reduces the first nb columns of a real general n-by-(n-k+1 k-th subdiagonal are zero. the reduction is performed by an orthogo- ictxt (global input) integer the blacs context handle in which the computation take pslamr1d has not been tested except withint the contect o pslange returns the value of the one norm, or the frobenius norm distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1). gather the intermediate results to process (0,0) if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the gather the intermediate results to process (0,0) pslapdct counts the number of negative eigenvalues of (t - sigma i) the innermost loop to avoid overflow and determine the sign of a pslapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pslapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pslaqge equilibrates a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) using the row and scalin pslaqsy equilibrates a symmetric distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using the scaling factors in th it assumes that the input array, bycol, is distributed acros bycol. the output array, byall, will be identical on all processes it assumes that the input array, byrow, is distributed acros byrow. the output array, byall, will be identical on all processes perform the local computation within a process colum real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1) from the left or the right notes distributed vector x(ix:ix+n-2,jx) if incx = 1 and x(ix,jx:jx+n-2) if incx = descx(m_). h is represented in the for h = i - tau * ( 1 ) * ( 1 v' ) , pslarft forms the triangular factor t of a real block reflector perform the local computation within a process colum a real distributed m-by-n matrix sub( c ) = c(ic:ic+m-1,jc:jc+n-1) from the left or the right q is a product of k elementary reflectors as returned by pstzrzf. pslarzt forms the triangular factor t of a real block reflecto reflectors as returned by pstzrzf. pslascl multiplies the m-by-n real distributed matrix sub( a is done without over/underflow as long as the final result pslase2 initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th operand is distributed. pslaset initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th pslasmsub looks for a small subdiagonal element from the botto pslasrt sort the numbers in d in increasing order and th pslassq returns the values scl and smsq such tha ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, pslaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pslatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. form by an orthogonal similarity transformation q' * sub( a ) * q, and returns the matrices v and w which are needed to apply th pslatrz reduces the m-by-n ( m<=n ) real upper trapezoidal matri upper triangular form by means of orthogonal transformations. pslauu2 computes the product u * u' or l' * l, where the triangula the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pslauum computes the product u * u' or l' * l, where the triangula the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pslawil gets the transform given by h44,h33, & h43h34 into a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde psorgr2 generates an m-by-n real distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the psorgrq generates an m-by-n real distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the psorm2l overwrites the general real m-by-n distributed matri psorm2r overwrites the general real m-by-n distributed matri if vect = 'q', psormbr overwrites the general real distributed m-by- psormhr overwrites the general real m-by-n distributed matri psorml2 overwrites the general real m-by-n distributed matri psormlq overwrites the general real m-by-n distributed matri psormql overwrites the general real m-by-n distributed matri psormqr overwrites the general real m-by-n distributed matri psormr2 overwrites the general real m-by-n distributed matri psormr3 overwrites the general real m-by-n distributed matri psormrq overwrites the general real m-by-n distributed matri psormrz overwrites the general real m-by-n distributed matri psormtr overwrites the general real m-by-n distributed matri cholesky factorization is used to factor a reordering of the matrix into l l' see pspbtrf and pspbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter pspocon estimates the reciprocal of the condition number (in th using the cholesky factorization a = u**t*u or a = l*l**t computed by sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on psporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the psposv computes the solution to a real system of linear equation sub( a ) * x = sub( b ), psposvx uses the cholesky factorization a = u**t*u or a = l*l**t t pspotf2 computes the cholesky factorization of a real symmetri pspotrf computes the cholesky factorization of an n-by-n rea a(ia:ia+n-1, ja:ja+n-1). pspotri computes the inverse of a real symmetric positive definit cholesky factorization sub( a ) = u**t*u or l*l**t computed by where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n symmetric positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). cholesky factorization is used to factor a reordering of the matrix into l l' see pspttrf and pspttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n real test the input parameter psrscl multiplies an n-element real distributed vector sub( x ) by the real scalar 1/a. this is done without overflow or underflow a psstebz computes the eigenvalues of a symmetric tridiagonal matrix i the interval [vl, vu], or the eigenvalues indexed il through iu. a psstedc computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix in parallel, using the divide an psstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. psstein does not pssyev computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix a by calling the recommended sequenc pssyevd computes all the eigenvalues and eigenvector of scalapack routines. pssyevx computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix a by calling the recommended sequenc specifying a range of values or a range of indices for the desired in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an pssygvx computes all the eigenvalues, and optionally of a real generalized sy-definite eigenproblem, of the form pssyngst performs the same function as pshegst, but is based o triangular solves (the basis of pssyngst). support for uplo='u' is limited to calling the old, slow, pssytr each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. pstrcon estimates the reciprocal of the condition number of 1-norm or the infinity-norm. pstrrfs provides error bounds and backward error estimates for the coefficient matrix. pstrti2 computes the inverse of a real upper or lower triangula contained in one and only one process memory space (local operation). pstrtri computes the inverse of a upper or lower triangula pstrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ), pstzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matri of orthogonal transformations. is used to factor a reordering of the matrix into l u see pzdbtrf and pzdbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter pzdrscl multiplies an n-element complex distributed vector sub( x ) by the real scalar 1/a. this is done without overflow o underflow. is used to factor a reordering of the matrix into l u see pzdttrf and pzdttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter is used to factor a reordering of the matrix into p l u see pzgbtrf and pzgbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pzgecon estimates the reciprocal of the condition number of a genera 1-norm or the infinity-norm, using the lu factorization computed by m-by-n distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja:ja+n-1) and reduce its condition number. r returns the row scale factors and each row and column of the distributed matrix b with elements each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the following options are provided 1. if trans = 'n' and m >= n: find the least squares solution of each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pzgerfs improves the computed solution to a system of linea the solutions. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pzgesv computes the solution to a complex system of linear equation sub( a ) * x = sub( b ), pzgesvd computes the singular value decomposition (svd) of a singular vectors. the svd is written as pzgesvx uses the lu factorization to compute the solution to the factorization has the form sub( a ) = p * l * u, where p is elements (lower trapezoidal if m > n), and u is upper triangular the factorization has the form sub( a ) = p * l * u, where p is ments (lower trapezoidal if m > n), and u is upper triangular pzgetri computes the inverse of a distributed matrix using the l computes the inverse of sub( a ) = a(ia:ia+n-1,ja:ja+n-1) denoted with a general n-by-n distributed matrix sub( a ) using the l sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1), op( a ) = a, a**t or a**h where q is an n-by-n unitary matrix, z is a p-by-p unitary matrix, and r and t assume one of the forms if n >= m, r = ( r11 ) m , or if n < m, r = ( r11 r12 ) n, where q is an n-by-n unitary matrix, z is a p-by-p unitary matrix, and r and t assume one of the forms if m <= n, r = ( 0 r12 ) m, or if m > n, r = ( r11 ) m-n, pzheev computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix a by calling the recommended sequenc pzheevd computes all the eigenvalues and eigenvectors of a hermitia pzheevx computes selected eigenvalues and, optionally, eigenvectors of a complex hermitian matrix a by calling the recommended sequenc specifying a range of values or a range of indices for the desired in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an in the following sub( a ) denotes a( ia:ia+n-1, ja:ja+n-1 ) an pzhegvx computes all the eigenvalues, and optionally of a complex generalized hermitian-definite eigenproblem, of the form pzhengst performs the same function as pzhegst, but is based o triangular solves (the basis of pzhengst). support for uplo='u' is limited to calling the old, slow, pzhetr each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. pzlabrd reduces the first nb rows and columns of a complex genera or lower bidiagonal form by an unitary transformation q' * a * p, and each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pzlacon estimates the 1-norm of a square, complex distributed matri products. x and v are aligned with the distributed matrix a, this pzlaconsb looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift qr iteratio subdiagonal negligible. pzlacp2 copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes array into a local replicated array or vise versa. notice that the entire submatrix that is copied gets placed on one node o can receive, or just one row or column of nodes. pzlacpy copies all or part of a distributed matrix a to anothe performs a local copy sub( a ) := sub( b ), where sub( a ) denotes pzlaevswp moves the eigenvectors (potentially unsorted) fro array, sorted so that the corresponding eigenvalues are sorted. determine the number of columns we have so we can check workspac pzlahrd reduces the first nb columns of a complex genera elements below the k-th subdiagonal are zero. the reduction is pzlamr1d has not been tested except withint the contect o pzlange returns the value of the one norm, or the frobenius norm distributed matrix sub( a ) = a(ia:ia+m-1, ja:ja+n-1). if the matrix is hermitian, we address only a triangular portio can be obtained by adding along row i and column i of the the gather the intermediate results to process (0,0) if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the gather the intermediate results to process (0,0) pzlapiv applies either p (permutation matrix indicated by ipiv sub( a ) = a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pzlapv2 applies either p (permutation matrix indicated by ipiv a(ia:ia+m-1,ja:ja+n-1), resulting in row or column pivoting. the pzlaqge equilibrates a general m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) using the row and scalin pzlaqsy equilibrates a symmetric distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) using the scaling factors in th perform the local computation within a process colum transpose q**h to a complex m-by-n distributed matrix sub( c ) denoting c(ic:ic+m-1,jc:jc+n-1), from the left or the right notes perform the local computation within a process colum complex distributed vector x(ix:ix+n-2,jx) if incx = 1 and x(ix,jx:jx+n-2) if incx = descx(m_). h is represented in the for h = i - tau * ( 1 ) * ( 1 v' ) , pzlarft forms the triangular factor t of a complex block reflector perform the local computation within a process colum transpose q**h to a complex m-by-n distributed matrix sub( c ) denoting c(ic:ic+m-1,jc:jc+n-1), from the left or the right q is a product of k elementary reflectors as returned by pztzrzf. perform the local computation within a process colum pzlarzt forms the triangular factor t of a complex block reflecto reflectors as returned by pztzrzf. pzlascl multiplies the m-by-n complex distributed matrix sub( a is done without over/underflow as long as the final result pzlase2 initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th operand is distributed. pzlaset initializes an m-by-n distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) to beta on the diagonal and alpha on th pzlasmsub looks for a small subdiagonal element from the botto pzlassq returns the values scl and smsq such tha ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, pzlaswp performs a series of row or column interchanges on the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). on sub( a ). this routine assumes that the pivoting information has pzlatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. tridiagonal form by an unitary similarity transformation q' * sub( a ) * q, and returns the matrices v and w which ar pzlatrz reduces the m-by-n ( m<=n ) complex upper trapezoida to upper triangular form by means of unitary transformations. test the input parameters pzlauu2 computes the product u * u' or l' * l, where the triangula the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pzlauum computes the product u * u' or l' * l, where the triangula the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pzlawil gets the transform given by h44,h33, & h43h34 into pzmax1 computes the global index of the maximum element in absolut in indx and the value is returned in amax, cholesky factorization is used to factor a reordering of the matrix into l l' see pzpbtrf and pzpbtrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter pzpocon estimates the reciprocal of the condition number (in th using the cholesky factorization a = u**h*u or a = l*l**h computed by sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on pzporfs improves the computed solution to a system of linea and provides error bounds and backward error estimates for the pzposv computes the solution to a complex system of linear equation sub( a ) * x = sub( b ), pzposvx uses the cholesky factorization a = u**h*u or a = l*l**h t pzpotf2 computes the cholesky factorization of a complex hermitia pzpotrf computes the cholesky factorization of an n-by-n comple a(ia:ia+n-1, ja:ja+n-1). pzpotri computes the inverse of a complex hermitian positive definit cholesky factorization sub( a ) = u**h*u or l*l**h computed by where sub( a ) denotes a(ia:ia+n-1,ja:ja+n-1) and is a n-by-n hermitian positive definite distributed matrix using the cholesk sub( b ) denotes the distributed matrix b(ib:ib+n-1,jb:jb+nrhs-1). cholesky factorization is used to factor a reordering of the matrix into l l' see pzpttrf and pzpttrs for details. test the input parameter where a(1:n, ja:ja+n-1) is the matrix used to produce the factor a(1:n, ja:ja+n-1) is an n-by-n complex test the input parameter pzstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pzstein does not pztrcon estimates the reciprocal of the condition number of 1-norm or the infinity-norm. pztrevc computes some or all of the right and/or left eigenvectors o pztrrfs provides error bounds and backward error estimates for the coefficient matrix. pztrti2 computes the inverse of a complex upper or lower triangula contained in one and only one process memory space (local operation). pztrtri computes the inverse of a upper or lower triangula pztrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ) or pztzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matri of unitary transformations. a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k)' . . . h(2)' h(1)' a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order q = h(k)' . . . h(2)' h(1)' a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order q = h(k) . . . h(2) h(1) a(ia:ia+m-1,ja:ja+n-1) with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of orde pzungr2 generates an m-by-n complex distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the pzungrq generates an m-by-n complex distributed matrix q denoting a(ia:ia+m-1,ja:ja+n-1) with orthonormal rows, which is defined as the pzunm2l overwrites the general complex m-by-n distributed matri pzunm2r overwrites the general complex m-by-n distributed matri if vect = 'q', pzunmbr overwrites the general complex distribute pzunmhr overwrites the general complex m-by-n distributed matri pzunml2 overwrites the general complex m-by-n distributed matri pzunmlq overwrites the general complex m-by-n distributed matri pzunmql overwrites the general complex m-by-n distributed matri pzunmqr overwrites the general complex m-by-n distributed matri pzunmr2 overwrites the general complex m-by-n distributed matri pzunmr3 overwrites the general complex m-by-n distributed matri pzunmrq overwrites the general complex m-by-n distributed matri pzunmrz overwrites the general complex m-by-n distributed matri pzunmtr overwrites the general complex m-by-n distributed matri this is the unblocked version of the algorithm, calling level 2 blas arguments kv is the number of superdiagonals in the factor the factorization has the for where l is a product of unit lower bidiagonal sdttrsv solves one of the systems of equation u * x = b, u**t * x = b, or u**h * x = b, see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulge slamsh should only be called when there are multiple shifts/bulges test the input paramters slaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei slasorte sorts eigenpairs so that real eigenpairs are together an since every 2nd subdiagonal is guaranteed to be zero. test the input paramters spttrsv solves one of the triangular system where l is the cholesky factor of a hermitian positive test the input parameters test the input parameters strmvt performs the matrix-vector operation x := t' *y, and w := t *z, zcombamax1 finds the element having maximum real part absolut this is the unblocked version of the algorithm, calling level 2 blas arguments kv is the number of superdiagonals in the factor the factorization has the for where l is a product of unit lower bidiagonal zdttrsv solves one of the systems of equation u * x = b, u**t * x = b, or u**h * x = b, set machine-dependent constants for the stopping criterion see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulge zlamsh should only be called when there are multiple shifts/bulges zlanv2 computes the schur factorization of a complex 2-by- zlaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei zpttrsv solves one of the triangular system u * x = b, or u**h * x = b, skip the current step: the subdiagonal info is just noise ztrmvt performs the matrix-vector operation x := conjg( t' ) *y, and w := t *z, |
| Their Their claref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either Their dlaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either Their > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store send e-mail to scalapack@cs.utk.edu > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store if (mod(info/2,2).ne.0),then eigenvectors corresponding two consecutive small subdiagonal elements will stall convergence of a double shift if Their product is smal necessary to scan the "tridiagonal portion of the matrix." in set all values for bulges. all bulges are stored in intermediate steps as loops over ki. Their current "task however, because there are many bulges, k1(ki) & k2(ki) might > 0 : if mod(info,m+1) = i, then i eigenvectors failed to converge in maxits iterations. Their indices ar if info/(m+1) = i, then eigenvectors corresponding to select, stored consecutively in the columns of vl, in the same order as Their if side = 'r', vl is not referenced. two consecutive small subdiagonal elements will stall convergence of a double shift if Their product is smal necessary to scan the "tridiagonal portion of the matrix." in set all values for bulges. all bulges are stored in intermediate steps as loops over ki. Their current "task however, because there are many bulges, k1(ki) & k2(ki) might order (global input) character
specifies the order in which the eigenvalues and Their bloc
= 'b': ("by block") the eigenvalues will be grouped by
> 0 : if mod(info,m+1) = i, then i eigenvectors failed to converge in maxits iterations. Their indices ar if info/(m+1) = i, then eigenvectors corresponding to > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store send e-mail to scalapack@cs.utk.edu > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store if (mod(info/2,2).ne.0),then eigenvectors corresponding computers. users are encouraged to modify this subroutine to set the tuning parameters for Their particular machine using the optio two consecutive small subdiagonal elements will stall convergence of a double shift if Their product is smal necessary to scan the "tridiagonal portion of the matrix." in set all values for bulges. all bulges are stored in intermediate steps as loops over ki. Their current "task however, because there are many bulges, k1(ki) & k2(ki) might order (global input) character
specifies the order in which the eigenvalues and Their bloc
= 'b': ("by block") the eigenvalues will be grouped by
> 0 : if mod(info,m+1) = i, then i eigenvectors failed to converge in maxits iterations. Their indices ar if info/(m+1) = i, then eigenvectors corresponding to > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store send e-mail to scalapack@cs.utk.edu > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store if (mod(info/2,2).ne.0),then eigenvectors corresponding > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store send e-mail to scalapack@cs.utk.edu > 0: if (mod(info,2).ne.0), then one or more eigenvectors failed to converge. Their indices are store if (mod(info/2,2).ne.0),then eigenvectors corresponding two consecutive small subdiagonal elements will stall convergence of a double shift if Their product is smal necessary to scan the "tridiagonal portion of the matrix." in set all values for bulges. all bulges are stored in intermediate steps as loops over ki. Their current "task however, because there are many bulges, k1(ki) & k2(ki) might > 0 : if mod(info,m+1) = i, then i eigenvectors failed to converge in maxits iterations. Their indices ar if info/(m+1) = i, then eigenvectors corresponding to select, stored consecutively in the columns of vl, in the same order as Their if side = 'r', vl is not referenced. slaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either Their zlaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either Their |
| them them only the eliminations of unknowns > ln-bw have an effect on the last bw columns. loop over them.. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. = 'b': compute all right and/or left eigenvectors, and backtransform them using the input matrice = 's': compute selected right and/or left eigenvectors, only the eliminations of unknowns > ln-bw have an effect on the last bw columns. loop over them.. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. only the eliminations of unknowns > ln-bw have an effect on the last bw columns. loop over them.. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. only the eliminations of unknowns > ln-bw have an effect on the last bw columns. loop over them.. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. space to hold the eigenvectors in z (m .le. descz(n_)) and sufficient workspace to compute them. (see lwork below. computation unless range .eq. 'v'. = 'b': compute all right and/or left eigenvectors, and backtransform them using the input matrice = 's': compute selected right and/or left eigenvectors, |
| then then wantz (global input) logical if .true., then apply any column reflections to z as well if eigenvectors are desired, then save rotations wantz (global input) logical if .true., then apply any column reflections to z as well if eigenvectors are desired, then save rotations < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these lwork >= ltau + max( lwf, lws ) where if m >= n, then lwf = nb_a * ( mpa0 + nqa0 + nb_a ) if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these tation matrix, l is unit lower triangular, and u is upper triangular. l and u are stored in sub( a ). the factored form of sub( a ) is then if lwork = -1, then lwork is global input and a workspac size for the work array. the required workspace is returned = 'e': the matrix a(ia:ia+n-1,ja:ja+n-1) will be equili- brated if necessary, then copied t < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. pcgetri computes the inverse of a distributed matrix using the lu factorization computed by pcgetrf. this method inverts u and then inva by solving the system inva*l = inv(u) for inva. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these local dimension (lld_z, locc(jz+n-1)) if jobz = 'v', then on normal exit the first m columns of corresponding to the selected eigenvalues. if lwork = -1, then lwork is global input and a workspac work arrays. each of these values is returned in the first where eps is the machine precision. if abstol is less than or equal to zero, then eps*norm(t) will be used in its place obtained by reducing a to tridiagonal form. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. on exit, if jobz = 'v', then if info = 0, sub( a ) contain are normalized as follows: if lwork = -1, then lwork is global input and a workspac optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. by using rev 0 & 1, data can be sent out and returned again. if rev=0, then ii is destination row index for the node(s if ii>=0,jj>=0, then node (ii,jj) receives the data rules: if mod(k1(ki)-1,hbl) < hbl-2 then mod(k2(ki)-1,hbl)<hbl- k2(ki)-k1(ki) <= rotn ipiv must always be a distributed vector (not a matrix). thus: if( rowpiv .eq. 'c' ) then else if the elements of sub( x ) are all zero and x(iax,jax) is real, then tau = 0 and h is taken to be the unit matrix otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. the value of sumsq is assumed to be at least unity and the value of ssq will then satisf 1.0 .le. ssq .le. ( sumsq + 2*n ). if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, being operated on. let x be a generic term for the input vector(s). then, the processes which receive the answer will be (note that i ceive the result will be the union of the following calculation for < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these where u is an upper triangular matrix and l is a lower triangular matrix. the factored form of sub( a ) is then used to solve th = 'n': the matrix a will be copied to af and factored. = 'e': the matrix a will be equilibrated if necessary, then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. process. pcstein decides on the allocation of work among the processes and then calls sstein2 (modified lapack routine) on eac expected orthogonalization may not be done. the norm of a(ia:ia+n-1,ja:ja+n-1) is computed and an estimate is obtained for norm(inv(a(ia:ia+n-1,ja:ja+n-1))), then the reciproca rcond = 1 / ( norm( a(ia:ia+n-1,ja:ja+n-1) ) * matrix. if t was obtained from the schur factorization of an original matrix a = q*t*q', then q*x and q*y are the matrices o if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these lwork >= ltau + max( lwf, lws ) where if m >= n, then lwf = nb_a * ( mpa0 + nqa0 + nb_a ) if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these tation matrix, l is unit lower triangular, and u is upper triangular. l and u are stored in sub( a ). the factored form of sub( a ) is then if lwork = -1, then lwork is global input and a workspac size for the work array. the required workspace is returned = 'e': the matrix a(ia:ia+n-1,ja:ja+n-1) will be equili- brated if necessary, then copied t < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. pdgetri computes the inverse of a distributed matrix using the lu factorization computed by pdgetrf. this method inverts u and then inva by solving the system inva*l = inv(u) for inva. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. by using rev 0 & 1, data can be sent out and returned again. if rev=0, then ii is destination row index for the node(s if ii>=0,jj>=0, then node (ii,jj) receives the data the maximum number of intervals that may be generated. if more than mmax intervals are generated, then pdlaebz wil = 0 : when an interval is narrower than abstol, or than reltol times the larger (in magnitude) endpoint, then = 1 : when an interval is narrower than abstol, or than < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. pdlaed2 sorts the two sets of eigenvalues together into a single sorted set. then it tries to deflate the size of the problem eigenvalues are close together or if there is a tiny entry in the rules: if mod(k1(ki)-1,hbl) < hbl-2 then mod(k2(ki)-1,hbl)<hbl- if mod(k1(ki)-1,hbl) = hbl-1 then mod(k2(ki)-1,hbl)=hbl-1 ipiv must always be a distributed vector (not a matrix). thus: if( rowpiv .eq. 'c' ) then else if the elements of sub( x ) are all zero, then tau = 0 and h i < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these where u is an upper triangular matrix and l is a lower triangular matrix. the factored form of sub( a ) is then used to solve th = 'n': the matrix a will be copied to af and factored. = 'e': the matrix a will be equilibrated if necessary, then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. determined to lie in an interval whose width is abstol or less. if abstol is less than or equal to zero, then ulp*|t eigenvalues will be computed most accurately when abstol is < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. process. pdstein decides on the allocation of work among the processes and then calls dstein2 (modified lapack routine) on eac expected orthogonalization may not be done. local dimension ( lld_z, locc(jz+n-1) ) if jobz = 'v', then on normal exit the first m columns of corresponding to the selected eigenvalues. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. where eps is the machine precision. if abstol is less than or equal to zero, then eps*norm(t) will be used in its place obtained by reducing a to tridiagonal form. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. on exit, if jobz = 'v', then if info = 0, sub( a ) contain are normalized as follows: if lwork = -1, then lwork is global input and a workspac optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. the norm of a(ia:ia+n-1,ja:ja+n-1) is computed and an estimate is obtained for norm(inv(a(ia:ia+n-1,ja:ja+n-1))), then the reciproca rcond = 1 / ( norm( a(ia:ia+n-1,ja:ja+n-1) ) * if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these being operated on. let x be a generic term for the input vector(s). then, the processes which receive the answer will be (note that i ceive the result will be the union of the following calculation for being operated on. let x be a generic term for the input vector(s). then, the processes which receive the answer will be (note that i ceive the result will be the union of the following calculation for < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these lwork >= ltau + max( lwf, lws ) where if m >= n, then lwf = nb_a * ( mpa0 + nqa0 + nb_a ) if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these tation matrix, l is unit lower triangular, and u is upper triangular. l and u are stored in sub( a ). the factored form of sub( a ) is then if lwork = -1, then lwork is global input and a workspac size for the work array. the required workspace is returned = 'e': the matrix a(ia:ia+n-1,ja:ja+n-1) will be equili- brated if necessary, then copied t < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. psgetri computes the inverse of a distributed matrix using the lu factorization computed by psgetrf. this method inverts u and then inva by solving the system inva*l = inv(u) for inva. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. by using rev 0 & 1, data can be sent out and returned again. if rev=0, then ii is destination row index for the node(s if ii>=0,jj>=0, then node (ii,jj) receives the data the maximum number of intervals that may be generated. if more than mmax intervals are generated, then pslaebz wil = 0 : when an interval is narrower than abstol, or than reltol times the larger (in magnitude) endpoint, then = 1 : when an interval is narrower than abstol, or than < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. pslaed2 sorts the two sets of eigenvalues together into a single sorted set. then it tries to deflate the size of the problem eigenvalues are close together or if there is a tiny entry in the rules: if mod(k1(ki)-1,hbl) < hbl-2 then mod(k2(ki)-1,hbl)<hbl- if mod(k1(ki)-1,hbl) = hbl-1 then mod(k2(ki)-1,hbl)=hbl-1 ipiv must always be a distributed vector (not a matrix). thus: if( rowpiv .eq. 'c' ) then else if the elements of sub( x ) are all zero, then tau = 0 and h i < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these where u is an upper triangular matrix and l is a lower triangular matrix. the factored form of sub( a ) is then used to solve th = 'n': the matrix a will be copied to af and factored. = 'e': the matrix a will be equilibrated if necessary, then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. determined to lie in an interval whose width is abstol or less. if abstol is less than or equal to zero, then ulp*|t eigenvalues will be computed most accurately when abstol is < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. process. psstein decides on the allocation of work among the processes and then calls sstein2 (modified lapack routine) on eac expected orthogonalization may not be done. local dimension ( lld_z, locc(jz+n-1) ) if jobz = 'v', then on normal exit the first m columns of corresponding to the selected eigenvalues. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. where eps is the machine precision. if abstol is less than or equal to zero, then eps*norm(t) will be used in its place obtained by reducing a to tridiagonal form. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. on exit, if jobz = 'v', then if info = 0, sub( a ) contain are normalized as follows: if lwork = -1, then lwork is global input and a workspac optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. the norm of a(ia:ia+n-1,ja:ja+n-1) is computed and an estimate is obtained for norm(inv(a(ia:ia+n-1,ja:ja+n-1))), then the reciproca rcond = 1 / ( norm( a(ia:ia+n-1,ja:ja+n-1) ) * if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these lwork >= ltau + max( lwf, lws ) where if m >= n, then lwf = nb_a * ( mpa0 + nqa0 + nb_a ) if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these tation matrix, l is unit lower triangular, and u is upper triangular. l and u are stored in sub( a ). the factored form of sub( a ) is then if lwork = -1, then lwork is global input and a workspac size for the work array. the required workspace is returned = 'e': the matrix a(ia:ia+n-1,ja:ja+n-1) will be equili- brated if necessary, then copied t < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. pzgetri computes the inverse of a distributed matrix using the lu factorization computed by pzgetrf. this method inverts u and then inva by solving the system inva*l = inv(u) for inva. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these local dimension (lld_z, locc(jz+n-1)) if jobz = 'v', then on normal exit the first m columns of corresponding to the selected eigenvalues. if lwork = -1, then lwork is global input and a workspac work arrays. each of these values is returned in the first where eps is the machine precision. if abstol is less than or equal to zero, then eps*norm(t) will be used in its place obtained by reducing a to tridiagonal form. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. on exit, if jobz = 'v', then if info = 0, sub( a ) contain are normalized as follows: if lwork = -1, then lwork is global input and a workspac optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. by using rev 0 & 1, data can be sent out and returned again. if rev=0, then ii is destination row index for the node(s if ii>=0,jj>=0, then node (ii,jj) receives the data rules: if mod(k1(ki)-1,hbl) < hbl-2 then mod(k2(ki)-1,hbl)<hbl- k2(ki)-k1(ki) <= rotn ipiv must always be a distributed vector (not a matrix). thus: if( rowpiv .eq. 'c' ) then else if the elements of sub( x ) are all zero and x(iax,jax) is real, then tau = 0 and h is taken to be the unit matrix otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. the value of sumsq is assumed to be at least unity and the value of ssq will then satisf 1.0 .le. ssq .le. ( sumsq + 2*n ). if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, being operated on. let x be a generic term for the input vector(s). then, the processes which receive the answer will be (note that i ceive the result will be the union of the following calculation for < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. first copy and multiply it into temporary storage, then use it on rh if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these where u is an upper triangular matrix and l is a lower triangular matrix. the factored form of sub( a ) is then used to solve th = 'n': the matrix a will be copied to af and factored. = 'e': the matrix a will be equilibrated if necessary, then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. end of "if (info.eq.0) then < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. process. pzstein decides on the allocation of work among the processes and then calls dstein2 (modified lapack routine) on eac expected orthogonalization may not be done. the norm of a(ia:ia+n-1,ja:ja+n-1) is computed and an estimate is obtained for norm(inv(a(ia:ia+n-1,ja:ja+n-1))), then the reciproca rcond = 1 / ( norm( a(ia:ia+n-1,ja:ja+n-1) ) * matrix. if t was obtained from the schur factorization of an original matrix a = q*t*q', then q*x and q*y are the matrices o if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. < 0: if the i-th argument is an array and the j-entry had an illegal value, then info = -(i*100+j), if the i-t info = -i. if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these if lwork = -1, then lwork is global input and a workspac and optimal size for all work arrays. each of these wantz (global input) logical if .true., then apply any column reflections to z as well if eigenvectors are desired, then save rotations wantz (global input) logical if .true., then apply any column reflections to z as well if eigenvectors are desired, then save rotations |
| theoretically theoretically to the number of blocks) the eigenvalue w(i) belongs to. note: in the (theoretically impossible) event that bisectio to 1 and the ones for which it did not are identified by a to the number of blocks) the eigenvalue w(i) belongs to. note: in the (theoretically impossible) event that bisectio to 1 and the ones for which it did not are identified by a |
| there there that can be sent through. clamsh should only be called when there are multiple shifts/bulge unreduced hessenberg matrix because of two or more consecutive that can be sent through. dlamsh should only be called when there are multiple shifts/bulge unreduced hessenberg matrix because of two or more consecutive small want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th difference between truea and a at the point that mvr2 is called, so we will start there let truea be the value that a would and can happen in no more than 3 locations per block assuming square blocks. there are 5 buffers that each node stores thes to send up, a buffer to send left, a buffer to send diagonally over the global m to i-1 values is always k1(ki) to k2(ki). however, because there are many bulges, k1(ki) & k2(ki) migh finishing up. even if rotn=1, in order to minimize border want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th and can happen in no more than 3 locations per block assuming square blocks. there are 5 buffers that each node stores thes to send up, a buffer to send left, a buffer to send diagonally the first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero i secular equation problem is reduced by one. this stage is sorted set. then it tries to deflate the size of the problem. there are two ways in which deflation can occur: when two or mor z vector. for each such occurrence the order of the related secular over the global m to i-1 values is always k1(ki) to k2(ki). however, because there are many bulges, k1(ki) & k2(ki) migh finishing up. want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th which is less accurate than pdlamch says. = 2 : there is a mismatch between the number o = 3 : range='i', and the gershgorin interval initially difference between truea and a at the point that mvr2 is called, so we will start there let truea be the value that a would data layout blocking factor as the algorithmic blocking factor - hence there is no need or opportunity to set the algorithmic o want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th and can happen in no more than 3 locations per block assuming square blocks. there are 5 buffers that each node stores thes to send up, a buffer to send left, a buffer to send diagonally the first stage consists of deflating the size of the problem when there are multiple eigenvalues or if there is a zero i secular equation problem is reduced by one. this stage is sorted set. then it tries to deflate the size of the problem. there are two ways in which deflation can occur: when two or mor z vector. for each such occurrence the order of the related secular over the global m to i-1 values is always k1(ki) to k2(ki). however, because there are many bulges, k1(ki) & k2(ki) migh finishing up. want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th which is less accurate than pslamch says. = 2 : there is a mismatch between the number o = 3 : range='i', and the gershgorin interval initially difference between truea and a at the point that mvr2 is called, so we will start there let truea be the value that a would want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th difference between truea and a at the point that mvr2 is called, so we will start there let truea be the value that a would and can happen in no more than 3 locations per block assuming square blocks. there are 5 buffers that each node stores thes to send up, a buffer to send left, a buffer to send diagonally over the global m to i-1 values is always k1(ki) to k2(ki). however, because there are many bulges, k1(ki) & k2(ki) migh finishing up. even if rotn=1, in order to minimize border want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th want to find errors with min( ), so if no error, set it to a big number. if there already is an error, multiply by the th that can be sent through. slamsh should only be called when there are multiple shifts/bulge unreduced hessenberg matrix because of two or more consecutive small that can be sent through. zlamsh should only be called when there are multiple shifts/bulge unreduced hessenberg matrix because of two or more consecutive |
| Therefore Therefore not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pcheevx will compute the not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pchegvx will compute the if n = 1, m_x = 1 and incx = 1, then one can't determine if a process row or process column owns the vector operand, Therefore only th not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pdsyevx will compute the not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pdsygvx will compute the if n = 1, m_x = 1 and incx = 1, then one can't determine if a process row or process column owns the vector operand, Therefore only th if n = 1, m_x = 1 and incx = 1, then one can't determine if a process row or process column owns the vector operand, Therefore only th not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pssyevx will compute the not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pssygvx will compute the not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pzheevx will compute the not know how many eigenvectors are requested until the eigenvalues are computed. Therefore, when range='v compute the eigenvalues, pzhegvx will compute the if n = 1, m_x = 1 and incx = 1, then one can't determine if a process row or process column owns the vector operand, Therefore only th |
| these these lihiz (local input) integer these serve the same purpose as itmp1,itmp2 but for lihiz (local input) integer these serve the same purpose as itmp1,itmp2 but for the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a r(i) and c(j) are restricted to be between smlnum = smallest safe number and bignum = largest safe number. use of these scalin sub( a ) but works well in practice. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a query is assumed; the routine calculates the size for all work arrays. each of these values is returned in the firs is issued by pxerbla. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a at present, ia, ja, mb and nb are restricted to those values allowed by pchetrd to keep the interface simple. these restrictions ar locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locq( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a each of these three parts are further subdivided into a.) work at the start of a border when locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a r(i) and c(j) are restricted to be between smlnum = smallest safe number and bignum = largest safe number. use of these scalin sub( a ) but works well in practice. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a pdlabad takes as input the values computed by pdlamch for underflow and overflow, and returns the square root of each of these values i to identify machines with a large exponent range, such as the crays, locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a contains the diagonals and the squares of the off-diagonal elements of the tridiagonal matrix t. these elements ar performance. the diagonal entries of t are in the entries locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a each of these three parts are further subdivided into a.) work at the start of a border when locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a contains the diagonals and the squares of the off-diagonal elements of the tridiagonal matrix t. these elements ar performance. the diagonal entries of t are in the entries locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a query is assumed; the routine only calculates the minimum and optimal size for all work arrays. each of these work array, and no error message is issued by pxerbla. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a at present, ia, ja, mb and nb are restricted to those values allowed by pdsytrd to keep the interface simple. these restrictions ar locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locq( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a n4 (global input) integer problem dimensions for the subroutine name; these may not al locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a r(i) and c(j) are restricted to be between smlnum = smallest safe number and bignum = largest safe number. use of these scalin sub( a ) but works well in practice. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a pslabad takes as input the values computed by pslamch for underflow and overflow, and returns the square root of each of these values i to identify machines with a large exponent range, such as the crays, locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a contains the diagonals and the squares of the off-diagonal elements of the tridiagonal matrix t. these elements ar performance. the diagonal entries of t are in the entries locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a each of these three parts are further subdivided into a.) work at the start of a border when locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a contains the diagonals and the squares of the off-diagonal elements of the tridiagonal matrix t. these elements ar performance. the diagonal entries of t are in the entries locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a query is assumed; the routine only calculates the minimum and optimal size for all work arrays. each of these work array, and no error message is issued by pxerbla. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a at present, ia, ja, mb and nb are restricted to those values allowed by pssytrd to keep the interface simple. these restrictions ar locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locq( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a r(i) and c(j) are restricted to be between smlnum = smallest safe number and bignum = largest safe number. use of these scalin sub( a ) but works well in practice. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a query is assumed; the routine calculates the size for all work arrays. each of these values is returned in the firs is issued by pxerbla. locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a at present, ia, ja, mb and nb are restricted to those values allowed by pzhetrd to keep the interface simple. these restrictions ar locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locq( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a each of these three parts are further subdivided into a.) work at the start of a border when locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. the following are restrictions on the input parameters. some of these may reflect fundamental technical limitations. these are alignment restrictions that may or may not be remove locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a lihiz (local input) integer these serve the same purpose as itmp1,itmp2 but for lihiz (local input) integer these serve the same purpose as itmp1,itmp2 but for |
| they they on entry, the elements of the input matrix. on exit, they are overwritten by the elements of th one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 liip1 and ltlip1) is subtle. within the current processor column (i.e. mycol .eq. curcol) they are the same. however above the diagonal, on these processors, ltli = lii+1. the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. pclaevswp moves the eigenvectors (potentially unsorted) from where they are computed, to a scalapack standard block cycli irsc0 : pointer to part of work used to store the rowsums while they are stored along a process colum they have been transposed to be along a process row irsc0 : pointer to part of work used to store the rowsums while they are stored along a process colum they have been transposed to be along a process row one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. pdlaevswp moves the eigenvectors (potentially unsorted) from where they are computed, to a scalapack standard block cycli sort the eigenpairs so that they are in twos for doubl irsc0 : pointer to part of work used to store the rowsums while they are stored along a process colum they have been transposed to be along a process row one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 liip1 and ltlip1) is subtle. within the current processor column (i.e. mycol .eq. curcol) they are the same. however above the diagonal, on these processors, ltli = lii+1. 1) opts is a concatenation of all of the character options to subroutine name, in the same order that they appear in th the value of the parameter specified by ispec. one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. pslaevswp moves the eigenvectors (potentially unsorted) from where they are computed, to a scalapack standard block cycli sort the eigenpairs so that they are in twos for doubl irsc0 : pointer to part of work used to store the rowsums while they are stored along a process colum they have been transposed to be along a process row one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 liip1 and ltlip1) is subtle. within the current processor column (i.e. mycol .eq. curcol) they are the same. however above the diagonal, on these processors, ltli = lii+1. one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 liip1 and ltlip1) is subtle. within the current processor column (i.e. mycol .eq. curcol) they are the same. however above the diagonal, on these processors, ltli = lii+1. the values are stored, if there are any values that a node needs, they will be sent and received. then the next majo small subdiagonals. pzlaevswp moves the eigenvectors (potentially unsorted) from where they are computed, to a scalapack standard block cycli irsc0 : pointer to part of work used to store the rowsums while they are stored along a process colum they have been transposed to be along a process row irsc0 : pointer to part of work used to store the rowsums while they are stored along a process colum they have been transposed to be along a process row one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 one-dimensional descriptors are a new addition to scalapack since version 1.0. they simplify and shorten the descriptor for 1 on entry, the elements of the input matrix. on exit, they are overwritten by the elements of th |
| things things this is set if the input matrix had an odd number of real eigenvalues and things couldn't be paired or if the inpu 0 indicates successful completion. this is set if the input matrix had an odd number of real eigenvalues and things couldn't be paired or if the inpu 0 indicates successful completion. |
| third third elements only at and above n1, the second contains non-zero elements only below n1, and the third is dense indxp (workspace) integer array, dimension (n) elements only at and above n1, the second contains non-zero elements only below n1, and the third is dense indxp (workspace) integer array, dimension (n) |
| this this this is the unblocked version of the algorithm, calling level 2 blas arguments determine the block size for this environmen determine the effect of starting the double-shift qr iteration at row m, and see if this would make h(m,m-1 go through, n should be at least 4*nbulge+2. otherwise, nbulge may be reduced by this routine ulp (local input) real on entry, the second matrix to receive column reflections. this is changed only if wantz is set ldz (local input) integer this is the lookahead loop, going until we hav this is the unblocked version of the algorithm, calling level 2 blas arguments determine the block size for this environmen go through, n should be at least 4*nbulge+2. otherwise, nbulge may be reduced by this routine ulp (local input) double precision on entry, the second matrix to receive column reflections. this is changed only if wantz is set ldz (local input) integer dlasorte sorts eigenpairs so that real eigenpairs are together and complex are together. this way one can employ 2x2 shifts easil this routine does no parallel work. lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation must be of size >= desca( nb_ ). on exit, this array contains information containing th receive cont. to diagonal block that is stored on this proc must be of size >= desca( nb_ ). on exit, this array contains information containing th do until this proc is needed to modify other procs' equation lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the in this case the loop over the levels will not b lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the right-looking parallel level 2 blas version of th this is the right-looking parallel level 3 blas version of th pcgetri computes the inverse of a distributed matrix using the lu factorization computed by pcgetrf. this method inverts u and the inva by solving the system inva*l = inv(u) for inva. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. only spot checks of the consistency of the eigenvalues across the different processes. because of this, it is possible that messages. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. this is an auxiliary routine called by pcgebrd notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. a. reverse communication is used for evaluating matrix-vector products. x and v are aligned with the distributed matrix a, this seeing the effect of starting a double shift qr iteration given by h44, h33, & h43h34 and see if this would make each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. look for two consecutive small subdiagonal elements: pclaconsb is the routine that does this this is an auxiliary routine called by pcgehrd. in the followin i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. triangular matrix, stopping/starting at the diagonal, which is the point of reflection. the pictures below demonstrate this refered to as rowsums, and the column sums shown by | are refered triangular matrix, stopping/starting at the diagonal, which is the point of reflection. the pictures below demonstrate this refered to as rowsums, and the column sums shown by | are refered or a column. the pivot vector should be aligned with the distributed matrix a. this routine will transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pclascl multiplies the m-by-n complex distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) by the real scalar cto/cfrom. this cto * a(i,j) / cfrom does not over/underflow. type specifies that each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is an auxiliary routine called by pchetrd notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the unblocked form of the algorithm, calling level 2 blas on should be strictly local to one process. this is the blocked form of the algorithm, calling level 3 pblas notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on the diagonal. this choice of sr and sc puts the condition numbe over all possible diagonal scalings. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). since there is no element-by-element vector multiplication in the blas, this loop must be hardwired in without a blas cal matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). do until this proc is needed to modify other procs' equation pcsrscl multiplies an n-element complex distributed vector sub( x ) by the real scalar 1/a. this is done without overflow o underflow. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the solution matrix x must be computed by pctrtrs or some other means before entering this routine. pctrrfs does not do iterativ pctrti2 computes the inverse of a complex upper or lower triangular block matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). this matrix should b each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation must be of size >= desca( nb_ ). on exit, this array contains information containing th receive cont. to diagonal block that is stored on this proc must be of size >= desca( nb_ ). on exit, this array contains information containing th do until this proc is needed to modify other procs' equation lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the in this case the loop over the levels will not b lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the right-looking parallel level 2 blas version of th this is the right-looking parallel level 3 blas version of th pdgetri computes the inverse of a distributed matrix using the lu factorization computed by pdgetrf. this method inverts u and the inva by solving the system inva*l = inv(u) for inva. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. and overflow, and returns the square root of each of these values if the log of large is sufficiently large. this subroutine is intende and redefine the underflow and overflow limits to be the square roots this is an auxiliary routine called by pdgebrd notes reverse communication is used for evaluating matrix-vector products. x and v are aligned with the distributed matrix a, this informatio seeing the effect of starting a double shift qr iteration given by h44, h33, & h43h34 and see if this would make each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is a scalapack internal subroutine and arguments are no this is a scalapack internal procedure and arguments are not checke the z vector. for each such occurence the dimension of the secular equation problem is reduced by one. this stage i this code makes very mild assumptions about floating poin add/subtract, or on those binary machines without guard digits each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. look for two consecutive small subdiagonal elements: pdlaconsb is the routine that does this this is an auxiliary routine called by pdgehrd. in the followin i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. triangular matrix, stopping/starting at the diagonal, which is the point of reflection. the pictures below demonstrate this refered to as rowsums, and the column sums shown by | are refered pdlapdct counts the number of negative eigenvalues of (t - sigma i). this implementation of the sturm sequence loop has conditionals i floating point number. pdlapdct will be referred to as the "paranoid" or a column. the pivot vector should be aligned with the distributed matrix a. this routine will transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pdlascl multiplies the m-by-n real distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) by the real scalar cto/cfrom. this cto * a(i,j) / cfrom does not over/underflow. type specifies that each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. q (local input) double precision pointer into the local memory to an array of dimension (lld_q, locc(jq+n-1) ). this arra to be copied from. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is an auxiliary routine called by pdsytrd notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the unblocked form of the algorithm, calling level 2 blas on should be strictly local to one process. this is the blocked form of the algorithm, calling level 3 pblas notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on the diagonal. this choice of sr and sc puts the condition numbe over all possible diagonal scalings. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). since there is no element-by-element vector multiplication in the blas, this loop must be hardwired in without a blas cal matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). do until this proc is needed to modify other procs' equation pdrscl multiplies an n-element real distributed vector sub( x ) by the real scalar 1/a. this is done without overflow or underflow a be as accurate as the absolute and relative tolerances. this is generally caused by arithmeti = 2 : there is a mismatch between the number of this code makes very mild assumptions about floating poin add/subtract, or on those binary machines without guard digits each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the solution matrix x must be computed by pdtrtrs or some other means before entering this routine. pdtrrfs does not do iterativ pdtrti2 computes the inverse of a real upper or lower triangular block matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). this matrix should b each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the serial version of this routine was originally contributed b this version provides a set of parameters which should give good computers. users are encouraged to modify this subroutine to set the serial version of this routine was originally contributed b lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation must be of size >= desca( nb_ ). on exit, this array contains information containing th receive cont. to diagonal block that is stored on this proc must be of size >= desca( nb_ ). on exit, this array contains information containing th do until this proc is needed to modify other procs' equation lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the in this case the loop over the levels will not b lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the right-looking parallel level 2 blas version of th this is the right-looking parallel level 3 blas version of th psgetri computes the inverse of a distributed matrix using the lu factorization computed by psgetrf. this method inverts u and the inva by solving the system inva*l = inv(u) for inva. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. and overflow, and returns the square root of each of these values if the log of large is sufficiently large. this subroutine is intende and redefine the underflow and overflow limits to be the square roots this is an auxiliary routine called by psgebrd notes reverse communication is used for evaluating matrix-vector products. x and v are aligned with the distributed matrix a, this informatio seeing the effect of starting a double shift qr iteration given by h44, h33, & h43h34 and see if this would make each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is a scalapack internal subroutine and arguments are no this is a scalapack internal procedure and arguments are not checke the z vector. for each such occurence the dimension of the secular equation problem is reduced by one. this stage i this code makes very mild assumptions about floating poin add/subtract, or on those binary machines without guard digits each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. look for two consecutive small subdiagonal elements: pslaconsb is the routine that does this this is an auxiliary routine called by psgehrd. in the followin i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. triangular matrix, stopping/starting at the diagonal, which is the point of reflection. the pictures below demonstrate this refered to as rowsums, and the column sums shown by | are refered pslapdct counts the number of negative eigenvalues of (t - sigma i). this implementation of the sturm sequence loop has conditionals i floating point number. pslapdct will be referred to as the "paranoid" or a column. the pivot vector should be aligned with the distributed matrix a. this routine will transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pslascl multiplies the m-by-n real distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) by the real scalar cto/cfrom. this cto * a(i,j) / cfrom does not over/underflow. type specifies that each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. q (local input) real pointer into the local memory to an array of dimension (lld_q, locc(jq+n-1) ). this arra to be copied from. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is an auxiliary routine called by pssytrd notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the unblocked form of the algorithm, calling level 2 blas on should be strictly local to one process. this is the blocked form of the algorithm, calling level 3 pblas notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on the diagonal. this choice of sr and sc puts the condition numbe over all possible diagonal scalings. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). since there is no element-by-element vector multiplication in the blas, this loop must be hardwired in without a blas cal matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). do until this proc is needed to modify other procs' equation psrscl multiplies an n-element real distributed vector sub( x ) by the real scalar 1/a. this is done without overflow or underflow a be as accurate as the absolute and relative tolerances. this is generally caused by arithmeti = 2 : there is a mismatch between the number of this code makes very mild assumptions about floating poin add/subtract, or on those binary machines without guard digits each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. no checks for consistency of the eigenvalues or eigenvectors across the different processes. because of this, it is possible that messages. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the solution matrix x must be computed by pstrtrs or some other means before entering this routine. pstrrfs does not do iterativ pstrti2 computes the inverse of a real upper or lower triangular block matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). this matrix should b each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bwl+bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation pzdrscl multiplies an n-element complex distributed vector sub( x ) by the real scalar 1/a. this is done without overflow o underflow. must be of size >= desca( nb_ ). on exit, this array contains information containing th receive cont. to diagonal block that is stored on this proc must be of size >= desca( nb_ ). on exit, this array contains information containing th do until this proc is needed to modify other procs' equation lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the in this case the loop over the levels will not b lld_a >=(2*bwl+2*bwu+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the right-looking parallel level 2 blas version of th this is the right-looking parallel level 3 blas version of th pzgetri computes the inverse of a distributed matrix using the lu factorization computed by pzgetrf. this method inverts u and the inva by solving the system inva*l = inv(u) for inva. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. only spot checks of the consistency of the eigenvalues across the different processes. because of this, it is possible that messages. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis process and memory location. this is an auxiliary routine called by pzgebrd notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. a. reverse communication is used for evaluating matrix-vector products. x and v are aligned with the distributed matrix a, this seeing the effect of starting a double shift qr iteration given by h44, h33, & h43h34 and see if this would make each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. look for two consecutive small subdiagonal elements: pzlaconsb is the routine that does this this is an auxiliary routine called by pzgehrd. in the followin i am not sure that this works correctly when ib and jb are not equa with 1 used in its place. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. triangular matrix, stopping/starting at the diagonal, which is the point of reflection. the pictures below demonstrate this refered to as rowsums, and the column sums shown by | are refered triangular matrix, stopping/starting at the diagonal, which is the point of reflection. the pictures below demonstrate this refered to as rowsums, and the column sums shown by | are refered or a column. the pivot vector should be aligned with the distributed matrix a. this routine will transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. pzlascl multiplies the m-by-n complex distributed matrix sub( a ) denoting a(ia:ia+m-1,ja:ja+n-1) by the real scalar cto/cfrom. this cto * a(i,j) / cfrom does not over/underflow. type specifies that each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. interchange is initiated for each of rows or columns k1 trough k2 of sub( a ). this routine assumes that the pivoting information ha also note that this routine will only work for k1-k2 being in the each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is an auxiliary routine called by pzhetrd notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the unblocked form of the algorithm, calling level 2 blas on should be strictly local to one process. this is the blocked form of the algorithm, calling level 3 pblas notes each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th used in lapack. please see the notes below and the receive cont. to diagonal block that is stored on this proc lld_a >=(bw+1) (stored in desca). on entry, this array contains the local pieces of th l^t a(1:n, ja:ja+n-1). do until this proc is needed to modify other procs' equation each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on the diagonal. this choice of sr and sc puts the condition numbe over all possible diagonal scalings. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). since there is no element-by-element vector multiplication in the blas, this loop must be hardwired in without a blas cal matrix. on exit, this array contains information containing th must be of size >= desca( nb_ ). do until this proc is needed to modify other procs' equation each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. the solution matrix x must be computed by pztrtrs or some other means before entering this routine. pztrrfs does not do iterativ pztrti2 computes the inverse of a complex upper or lower triangular block matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). this matrix should b each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. each global data object is described by an associated description vector. this vector stores the information required to establis and memory location. this is the unblocked version of the algorithm, calling level 2 blas arguments determine the block size for this environmen go through, n should be at least 4*nbulge+2. otherwise, nbulge may be reduced by this routine ulp (local input) real on entry, the second matrix to receive column reflections. this is changed only if wantz is set ldz (local input) integer slasorte sorts eigenpairs so that real eigenpairs are together and complex are together. this way one can employ 2x2 shifts easil this routine does no parallel work. this is the unblocked version of the algorithm, calling level 2 blas arguments determine the block size for this environmen determine the effect of starting the double-shift qr iteration at row m, and see if this would make h(m,m-1 go through, n should be at least 4*nbulge+2. otherwise, nbulge may be reduced by this routine ulp (local input) double precision on entry, the second matrix to receive column reflections. this is changed only if wantz is set ldz (local input) integer this is the lookahead loop, going until we hav |
| those those note that permutations are performed on the matrix, so that the factors returned are different from those returne note that permutations are performed on the matrix, so that the factors returned are different from those returne the tailored codes place no restrictions on ia, ja, mb or nb. at present, ia, ja, mb and nb are restricted to those values allowe documented below. (search for "restrictions".) note: ltnm0 == ltnm1 on all processors except the diagonal processors, i.e. those where mycol == myrow invariants: or 'c' and pivroc='r' or 'r', the last piece of this array of size mb_a (resp. nb_a) is used as workspace. in those cases note that permutations are performed on the matrix, so that the factors returned are different from those returne eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from psstebz is expected here). note that permutations are performed on the matrix, so that the factors returned are different from those returne note that permutations are performed on the matrix, so that the factors returned are different from those returne on exit, d contains the trailing (n-k) updated eigenvalues (those which were deflated) sorted into increasing order drow (global input) integer arithmetic. it will work on machines with a guard digit in add/subtract, or on those binary machines without guard digit it could conceivably fail on hexadecimal or decimal machines or 'c' and pivroc='r' or 'r', the last piece of this array of size mb_a (resp. nb_a) is used as workspace. in those cases note that permutations are performed on the matrix, so that the factors returned are different from those returne arithmetic. it will work on machines with a guard digit in add/subtract, or on those binary machines without guard digit it could conceivably fail on hexadecimal or decimal machines eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from pdstebz is expected here). the tailored codes place no restrictions on ia, ja, mb or nb. at present, ia, ja, mb and nb are restricted to those values allowe documented below. (search for "restrictions".) note: ltnm0 == ltnm1 on all processors except the diagonal processors, i.e. those where mycol == myrow invariants: note that permutations are performed on the matrix, so that the factors returned are different from those returne note that permutations are performed on the matrix, so that the factors returned are different from those returne on exit, d contains the trailing (n-k) updated eigenvalues (those which were deflated) sorted into increasing order drow (global input) integer arithmetic. it will work on machines with a guard digit in add/subtract, or on those binary machines without guard digit it could conceivably fail on hexadecimal or decimal machines or 'c' and pivroc='r' or 'r', the last piece of this array of size mb_a (resp. nb_a) is used as workspace. in those cases note that permutations are performed on the matrix, so that the factors returned are different from those returne arithmetic. it will work on machines with a guard digit in add/subtract, or on those binary machines without guard digit it could conceivably fail on hexadecimal or decimal machines eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from psstebz is expected here). the tailored codes place no restrictions on ia, ja, mb or nb. at present, ia, ja, mb and nb are restricted to those values allowe documented below. (search for "restrictions".) note: ltnm0 == ltnm1 on all processors except the diagonal processors, i.e. those where mycol == myrow invariants: note that permutations are performed on the matrix, so that the factors returned are different from those returne note that permutations are performed on the matrix, so that the factors returned are different from those returne the tailored codes place no restrictions on ia, ja, mb or nb. at present, ia, ja, mb and nb are restricted to those values allowe documented below. (search for "restrictions".) note: ltnm0 == ltnm1 on all processors except the diagonal processors, i.e. those where mycol == myrow invariants: or 'c' and pivroc='r' or 'r', the last piece of this array of size mb_a (resp. nb_a) is used as workspace. in those cases note that permutations are performed on the matrix, so that the factors returned are different from those returne eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from pdstebz is expected here). |
| though though note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i pjlaenv is patterned after ilaenv and keeps the same interface in anticipation of future needs, even though pjlaenv is only sparsel data layout blocking factor as the algorithmic blocking factor - note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: banded codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i note: tridiagonal codes can use either the old two dimensional or new one-dimensional descriptors, though the processor grid i |
| three three h43h34 (global input) complex these three values are for the double shift qr iteration buf (local output) complex array of size lwork. each of these three parts are further subdivided into a.) work at the start of a border when h43h34 (global input) complex these three values are for the double shift qr iteration h43h34 (global input) double precision these three values are for the double shift qr iteration buf (local output) double precision array of size lwork. the eigenvectors of the original matrix are stored in q, and the eigenvalues are in d. the algorithm consists of three stages the first stage consists of deflating the size of the problem the permutation used to arrange the columns of the deflated q matrix into three groups: the first group contains non-zer non-zero elements only below n1, and the third is dense. each of these three parts are further subdivided into a.) work at the start of a border when h43h34 (global input) double precision these three values are for the double shift qr iteration h43h34 (global input) real these three values are for the double shift qr iteration buf (local output) real array of size lwork. the eigenvectors of the original matrix are stored in q, and the eigenvalues are in d. the algorithm consists of three stages the first stage consists of deflating the size of the problem the permutation used to arrange the columns of the deflated q matrix into three groups: the first group contains non-zer non-zero elements only below n1, and the third is dense. each of these three parts are further subdivided into a.) work at the start of a border when h43h34 (global input) real these three values are for the double shift qr iteration h43h34 (global input) complex*16 these three values are for the double shift qr iteration buf (local output) complex*16 array of size lwork. each of these three parts are further subdivided into a.) work at the start of a border when h43h34 (global input) complex*16 these three values are for the double shift qr iteration |
| THRESH THRESH THRESH is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if THRESH is a threshold value used to decide if scaling should be don scaling is done. THRESH is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if THRESH is a threshold value used to decide if scaling should be don scaling is done. THRESH is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if THRESH is a threshold value used to decide if scaling should be don scaling is done. THRESH is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if THRESH is a threshold value used to decide if scaling should be don scaling is done. |
| threshold threshold eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
thresh is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if thresh is a threshold value used to decide if scaling should be don scaling is done. eigenvalues are computed to highest accuracy ( this can be done by setting abstol to the underflow threshold to psstebz ) small (local input/local output) double precision on entry, the underflow threshold as computed by pdlamch root of small, otherwise unchanged. emin = minimum exponent before (gradual) underflow rmin = underflow threshold - base**(emin-1 rmax = overflow threshold - (base**emax)*(1-eps) thresh is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if thresh is a threshold value used to decide if scaling should be don scaling is done. eigenvalues will be computed most accurately when abstol is
set to the underflow threshold dlamch('u'), not zero
( pdstein ), abstol should be set to 2*pdlamch('s').
eigenvalues are computed to highest accuracy ( this can be done by setting abstol to the underflow threshold to pdstebz ) eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
small (local input/local output) real on entry, the underflow threshold as computed by pslamch root of small, otherwise unchanged. emin = minimum exponent before (gradual) underflow rmin = underflow threshold - base**(emin-1 rmax = overflow threshold - (base**emax)*(1-eps) thresh is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if thresh is a threshold value used to decide if scaling should be don scaling is done. eigenvalues will be computed most accurately when abstol is
set to the underflow threshold slamch('u'), not zero
( psstein ), abstol should be set to 2*pslamch('s').
eigenvalues are computed to highest accuracy ( this can be done by setting abstol to the underflow threshold to psstebz ) eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
thresh is a threshold value used to decide if row or column scalin factors. if rowcnd < thresh, row scaling is done, and if thresh is a threshold value used to decide if scaling should be don scaling is done. eigenvalues are computed to highest accuracy ( this can be done by setting abstol to the underflow threshold to pdstebz ) |
| thresholds thresholds determine the unit roundoff and over/underflow thresholds determine the unit roundoff and over/underflow thresholds |
| through through clamsh sends multiple shifts through a small (single node) matrix t subsequent shifts in an effort to maximize the number of bulges dlamsh sends multiple shifts through a small (single node) matrix t subsequent shifts in an effort to maximize the number of bulges loop through eigenvalues of block nblk info = -i. > 0: if info = 1 through n, the i(th) eigenvalue did no if info = n+1, then pcheev has detected heterogeneity info = -i. > 0: if info = 1 through n, the i(th) eigenvalue did no = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 subdiagonal elements, we need to see how many bulges we can send through without breaking the consecutive smal the routine makes only one pass through the vector sub( x ) notes the first submatrix consists of rows/columns 1 to isplit(1), the second of rows/columns isplit(1)+1 through isplit(2) isplit(nsplit-1)+1 through isplit(nsplit)=n (the output array all rotn row transforms are all complete through some column tmp. (loops within 190 are then applied in a block fashion. the routine makes only one pass through the vector sub( x ) notes parallel. the user may ask for all eigenvalues, all eigenvalues in the interval [vl, vu], or the eigenvalues indexed il through iu. results in all processes finding an (almost) equal number of the first submatrix consists of rows/columns 1 to isplit(1), the second of rows/columns isplit(1)+1 through isplit(2) isplit(nsplit-1)+1 through isplit(nsplit)=n (the output array info = -i. > 0: if info = 1 through n, the i(th) eigenvalue did no if info = n+1, then pdsyev has detected heterogeneity = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 all rotn row transforms are all complete through some column tmp. (loops within 190 are then applied in a block fashion. the routine makes only one pass through the vector sub( x ) notes parallel. the user may ask for all eigenvalues, all eigenvalues in the interval [vl, vu], or the eigenvalues indexed il through iu. results in all processes finding an (almost) equal number of the first submatrix consists of rows/columns 1 to isplit(1), the second of rows/columns isplit(1)+1 through isplit(2) isplit(nsplit-1)+1 through isplit(nsplit)=n (the output array info = -i. > 0: if info = 1 through n, the i(th) eigenvalue did no if info = n+1, then pssyev has detected heterogeneity = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 info = -i. > 0: if info = 1 through n, the i(th) eigenvalue did no if info = n+1, then pzheev has detected heterogeneity info = -i. > 0: if info = 1 through n, the i(th) eigenvalue did no = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 = 'v': all eigenvalues in the interval [vl,vu] will be found. = 'i': the il-th through iu-th eigenvalues will be found uplo (global input) character*1 subdiagonal elements, we need to see how many bulges we can send through without breaking the consecutive smal the routine makes only one pass through the vector sub( x ) notes the first submatrix consists of rows/columns 1 to isplit(1), the second of rows/columns isplit(1)+1 through isplit(2) isplit(nsplit-1)+1 through isplit(nsplit)=n (the output array slamsh sends multiple shifts through a small (single node) matrix t subsequent shifts in an effort to maximize the number of bulges loop through eigenvalues of block nblk zlamsh sends multiple shifts through a small (single node) matrix t subsequent shifts in an effort to maximize the number of bulges |
| throughout throughout ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size ******************************** values reused throughout routin user-input value of partition size |
| thru thru the eigenvectors computed by each process. process i computes eigenvectors indexed iwork(i+2)+1 thru' iwork(i+3) liwork (local input) integer on input, intvl contains the kl-kf input intervals. on output, intvl contains the converged intervals, 1 thru the eigenvectors computed by each process. process i computes eigenvectors indexed iwork(i+2)+1 thru' iwork(i+3) liwork (local input) integer on input, intvl contains the kl-kf input intervals. on output, intvl contains the converged intervals, 1 thru the eigenvectors computed by each process. process i computes eigenvectors indexed iwork(i+2)+1 thru' iwork(i+3) liwork (local input) integer the eigenvectors computed by each process. process i computes eigenvectors indexed iwork(i+2)+1 thru' iwork(i+3) liwork (local input) integer |
| thus thus from the vector v and applies it from left and right to h, thus creating a nonzero bulge below the subdiagonal each subsequent iteration determines a reflection g to the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. convergence of a double shift if their product is small relatively even if each is not very small. thus it i the lapack algorithm zlahqr, a loop of m goes from i-2 down to ipiv must always be a distributed vector (not a matrix). thus jp must be 1 the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is th the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. convergence of a double shift if their product is small relatively even if each is not very small. thus it i the lapack algorithm dlahqr, a loop of m goes from i-2 down to ipiv must always be a distributed vector (not a matrix). thus jp must be 1 let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is th the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. convergence of a double shift if their product is small relatively even if each is not very small. thus it i the lapack algorithm dlahqr, a loop of m goes from i-2 down to ipiv must always be a distributed vector (not a matrix). thus jp must be 1 let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is th the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. convergence of a double shift if their product is small relatively even if each is not very small. thus it i the lapack algorithm zlahqr, a loop of m goes from i-2 down to ipiv must always be a distributed vector (not a matrix). thus jp must be 1 the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. the 1-by-p descriptor are allowed and are equivalent for tridiagonal matrices. thus, for tridiagonal matrices without any other change. let nq = m if side = 'l' and nq = n if side = 'r'. thus nq is th from the vector v and applies it from left and right to h, thus creating a nonzero bulge below the subdiagonal each subsequent iteration determines a reflection g to |
| tied tied the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local output) real array, dimension locc(n_a) details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) complex array, details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) complex array, locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex array, on exit, if ipiv(i) = k, the local i-th column of sub( a )*p was the global k-th column of sub( a ). ipiv is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th by pcgetrf. ipiv(i) -> the global row local row i was swapped with. this array is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) complex pointer into the ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (local output) integer ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (global output) integer global row index the local row i was swapped with. this array is tied to the distributed matrix a work (local workspace/local output) complex array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) complex pointer into the taua of the elementary reflectors which represent the unitary matrix q. taua is tied to the distributed matrix a. (se reflectors which represent the unitary matrix q. taua is tied to the distributed matrix a (see further details) b (local input/local output) complex pointer into the the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dim locq(ja+n-1) the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(ia+i-1,ja+i-1). d is tied to the distribute the scalar factors of the elementary reflectors (see further details). tau is tied to the distributed matrix a t (local output) complex array, dimension (nb_a,nb_a) size mb_a (resp. nb_a) is used as workspace. in those cases, this array is tied to the distributed matrix a ip (global input) integer array of size mb_a (resp. nb_a) is used as workspace. ipiv is tied to the distributed matrix a ip (global input) integer distributed matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local input) real array, dimension locc(n_a) with the distributed matrix a, and replicated across every process column. sr is tied to the distributed matrix a sc (local input) real array, dimension locc(n_a) householder scalars related to the householder vectors. tau is tied to the distributed matrix x ===================================================================== contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) complex array, dimension (nb_v,nb_v) contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) complex array, dimension (mb_v,mb_v) row pivoting and locc(n_a)+nb_a for column pivoting. this array is tied to the matrix a, ipiv(k) = l implies row the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace) complex array, dimension (lwork) for sub( a ). sr is aligned with the distributed matrix a, and replicated across every process column. sr is tied to th is almost always a slight overestimate of the true error. this array is tied to the distributed matrix x berr (local output) real array of local dimension overestimate of the true error. this array is tied to the distributed matrix x berr (local output) real array of local dimension this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(j) as returned by pcgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(j) as returned by pcgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(i) as returned by pcgelqf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(i) as returned by pcgelqf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(j) as returned by pcgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(j) as returned by pcgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(i) as returned by pcgerqf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(i) as returned by pcgerqf. tau is tied to the distributed matrix a work (local workspace/local output) complex array, elementary reflectors h(j) as returned by pcgeqlf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(j) as returned by pcgeqrf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the as returned by pdgebrd in its array argument tauq or taup. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the contains the scalar factors tau(j) of the elementary reflectors h(j) as returned by pcgehrd. tau is tied t elementary reflectors h(i) as returned by pcgelqf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(i) as returned by pcgelqf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(j) as returned by pcgeqlf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(j) as returned by pcgeqrf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(i) as returned by pcgerqf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(i) as returned by pctzrzf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(i) as returned by pcgerqf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the elementary reflectors h(i) as returned by pctzrzf. tau is tied to the distributed matrix a c (local input/local output) complex pointer into the tau(i) must contain the scalar factor of the elementary reflector h(i), as returned by pchetrd. tau is tied to th the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local output) double precision array, dimension locc(n_a) details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, on exit, if ipiv(i) = k, the local i-th column of sub( a )*p was the global k-th column of sub( a ). ipiv is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th by pdgetrf. ipiv(i) -> the global row local row i was swapped with. this array is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) double precision pointer into the ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (local output) integer ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (global output) integer global row index the local row i was swapped with. this array is tied to the distributed matrix a work (local workspace/local output) double precision array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) double precision pointer into the taua of the elementary reflectors which represent the orthogonal matrix q. taua is tied to the distributed matri reflectors which represent the orthogonal unitary matrix q. taua is tied to the distributed matrix a (see furthe the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(ia+i-1,ja+i-1). d is tied to the distribute the scalar factors of the elementary reflectors (see further details). tau is tied to the distributed matrix a t (local output) double precision array, dimension (nb_a,nb_a) size mb_a (resp. nb_a) is used as workspace. in those cases, this array is tied to the distributed matrix a ip (global input) integer array of size mb_a (resp. nb_a) is used as workspace. ipiv is tied to the distributed matrix a ip (global input) integer distributed matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local input) double precision array, dimension locc(n_a) with the distributed matrix a, and replicated across every process column. sr is tied to the distributed matrix a sc (local input) double precision array, dimension locc(n_a) householder scalars related to the householder vectors. tau is tied to the distributed matrix x ===================================================================== contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) double precision array, dimension (nb_v,nb_v) contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) double precision array, dimension (mb_v,mb_v) row pivoting and locc(n_a)+nb_a for column pivoting. this array is tied to the matrix a, ipiv(k) = l implies row the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace) double precision array, dimension (lwork) elementary reflectors h(j) as returned by pdgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(j) as returned by pdgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(i) as returned by pdgelqf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(i) as returned by pdgelqf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(j) as returned by pdgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(j) as returned by pdgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(i) as returned by pdgerqf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(i) as returned by pdgerqf. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, elementary reflectors h(j) as returned by pdgeqlf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(j) as returned by pdgeqrf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the as returned by pdgebrd in its array argument tauq or taup. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the contains the scalar factors tau(j) of the elementary reflectors h(j) as returned by pdgehrd. tau is tied t elementary reflectors h(i) as returned by pdgelqf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(i) as returned by pdgelqf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(j) as returned by pdgeqlf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(j) as returned by pdgeqrf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(i) as returned by pdgerqf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(i) as returned by pdtzrzf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(i) as returned by pdgerqf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the elementary reflectors h(i) as returned by pdtzrzf. tau is tied to the distributed matrix a c (local input/local output) double precision pointer into the tau(i) must contain the scalar factor of the elementary reflector h(i), as returned by pdsytrd. tau is tied to th for sub( a ). sr is aligned with the distributed matrix a, and replicated across every process column. sr is tied to th is almost always a slight overestimate of the true error. this array is tied to the distributed matrix x berr (local output) double precision array of local dimension the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dim locq(ja+n-1) overestimate of the true error. this array is tied to the distributed matrix x berr (local output) double precision array of local dimension this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) double precision array, the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local output) real array, dimension locc(n_a) details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) real array, details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) real array, locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) real array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) real array, on exit, if ipiv(i) = k, the local i-th column of sub( a )*p was the global k-th column of sub( a ). ipiv is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th by psgetrf. ipiv(i) -> the global row local row i was swapped with. this array is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) real array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) real array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) real pointer into the ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (local output) integer ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (global output) integer global row index the local row i was swapped with. this array is tied to the distributed matrix a work (local workspace/local output) real array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) real pointer into the taua of the elementary reflectors which represent the orthogonal matrix q. taua is tied to the distributed matri reflectors which represent the orthogonal unitary matrix q. taua is tied to the distributed matrix a (see furthe the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(ia+i-1,ja+i-1). d is tied to the distribute the scalar factors of the elementary reflectors (see further details). tau is tied to the distributed matrix a t (local output) real array, dimension (nb_a,nb_a) size mb_a (resp. nb_a) is used as workspace. in those cases, this array is tied to the distributed matrix a ip (global input) integer array of size mb_a (resp. nb_a) is used as workspace. ipiv is tied to the distributed matrix a ip (global input) integer distributed matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local input) real array, dimension locc(n_a) with the distributed matrix a, and replicated across every process column. sr is tied to the distributed matrix a sc (local input) real array, dimension locc(n_a) householder scalars related to the householder vectors. tau is tied to the distributed matrix x ===================================================================== contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) real array, dimension (nb_v,nb_v) contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) real array, dimension (mb_v,mb_v) row pivoting and locc(n_a)+nb_a for column pivoting. this array is tied to the matrix a, ipiv(k) = l implies row the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace) real array, dimension (lwork) elementary reflectors h(j) as returned by psgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(j) as returned by psgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(i) as returned by psgelqf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(i) as returned by psgelqf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(j) as returned by psgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(j) as returned by psgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(i) as returned by psgerqf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(i) as returned by psgerqf. tau is tied to the distributed matrix a work (local workspace/local output) real array, elementary reflectors h(j) as returned by psgeqlf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(j) as returned by psgeqrf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the as returned by pdgebrd in its array argument tauq or taup. tau is tied to the distributed matrix a c (local input/local output) real pointer into the contains the scalar factors tau(j) of the elementary reflectors h(j) as returned by psgehrd. tau is tied t elementary reflectors h(i) as returned by psgelqf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(i) as returned by psgelqf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(j) as returned by psgeqlf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(j) as returned by psgeqrf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(i) as returned by psgerqf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(i) as returned by pstzrzf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(i) as returned by psgerqf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the elementary reflectors h(i) as returned by pstzrzf. tau is tied to the distributed matrix a c (local input/local output) real pointer into the tau(i) must contain the scalar factor of the elementary reflector h(i), as returned by pssytrd. tau is tied to th for sub( a ). sr is aligned with the distributed matrix a, and replicated across every process column. sr is tied to th is almost always a slight overestimate of the true error. this array is tied to the distributed matrix x berr (local output) real array of local dimension the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) real array, dim locq(ja+n-1) overestimate of the true error. this array is tied to the distributed matrix x berr (local output) real array of local dimension this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) real array, the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local output) double precision array, dimension locc(n_a) details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, details). elements ja:ja+ilo-2 and ja+ihi:ja+n-2 of tau are set to zero. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute locr(ia+min(m,n)-1). this array contains the scalar factors of the elementary reflectors. tau is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, on exit, if ipiv(i) = k, the local i-th column of sub( a )*p was the global k-th column of sub( a ). ipiv is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th locc(ja+min(m,n)-1). this array contains the scalar factors tau of the elementary reflectors. tau is tied to th by pzgetrf. ipiv(i) -> the global row local row i was swapped with. this array is tied to the distribute this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) complex*16 pointer into the ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (local output) integer ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a info (global output) integer global row index the local row i was swapped with. this array is tied to the distributed matrix a work (local workspace/local output) complex*16 array, ipiv(i) -> the global row local row i was swapped with. this array is tied to the distributed matrix a b (local input/local output) complex*16 pointer into the taua of the elementary reflectors which represent the unitary matrix q. taua is tied to the distributed matrix a. (se reflectors which represent the unitary matrix q. taua is tied to the distributed matrix a (see further details) b (local input/local output) complex*16 pointer into the the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dim locq(ja+n-1) the distributed diagonal elements of the bidiagonal matrix b: d(i) = a(ia+i-1,ja+i-1). d is tied to the distribute the scalar factors of the elementary reflectors (see further details). tau is tied to the distributed matrix a t (local output) complex*16 array, dimension (nb_a,nb_a) size mb_a (resp. nb_a) is used as workspace. in those cases, this array is tied to the distributed matrix a ip (global input) integer array of size mb_a (resp. nb_a) is used as workspace. ipiv is tied to the distributed matrix a ip (global input) integer distributed matrix a, and replicated across every process column. r is tied to the distributed matrix a c (local input) double precision array, dimension locc(n_a) with the distributed matrix a, and replicated across every process column. sr is tied to the distributed matrix a sc (local input) double precision array, dimension locc(n_a) householder scalars related to the householder vectors. tau is tied to the distributed matrix x ===================================================================== contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) complex*16 array, dimension (nb_v,nb_v) contains the householder scalars related to the householder vectors. tau is tied to the distributed matrix v t (local output) complex*16 array, dimension (mb_v,mb_v) row pivoting and locc(n_a)+nb_a for column pivoting. this array is tied to the matrix a, ipiv(k) = l implies row the diagonal elements of the tridiagonal matrix t: d(i) = a(i,i). d is tied to the distributed matrix a e (local output) double precision array, dimension locc(ja+n-1) this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace) complex*16 array, dimension (lwork) for sub( a ). sr is aligned with the distributed matrix a, and replicated across every process column. sr is tied to th is almost always a slight overestimate of the true error. this array is tied to the distributed matrix x berr (local output) double precision array of local dimension overestimate of the true error. this array is tied to the distributed matrix x berr (local output) double precision array of local dimension this array contains the scalar factors of the elementary reflectors. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(j) as returned by pzgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(j) as returned by pzgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(i) as returned by pzgelqf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(i) as returned by pzgelqf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(j) as returned by pzgeqlf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(j) as returned by pzgeqrf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(i) as returned by pzgerqf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(i) as returned by pzgerqf. tau is tied to the distributed matrix a work (local workspace/local output) complex*16 array, elementary reflectors h(j) as returned by pzgeqlf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(j) as returned by pzgeqrf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the as returned by pdgebrd in its array argument tauq or taup. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the contains the scalar factors tau(j) of the elementary reflectors h(j) as returned by pzgehrd. tau is tied t elementary reflectors h(i) as returned by pzgelqf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(i) as returned by pzgelqf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(j) as returned by pzgeqlf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(j) as returned by pzgeqrf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(i) as returned by pzgerqf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(i) as returned by pztzrzf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(i) as returned by pzgerqf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the elementary reflectors h(i) as returned by pztzrzf. tau is tied to the distributed matrix a c (local input/local output) complex*16 pointer into the tau(i) must contain the scalar factor of the elementary reflector h(i), as returned by pzhetrd. tau is tied to th |
| ties ties locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). an upper bound for these quantities may be computed by locc( n ) <= ceil( ceil(n/nb_a)/npcol )*nb_a |
| tighly tighly pcheevx does not promise orthogonality for eigenvectors associated with tighly clustered eigenvalues that are on different processes. the extent of reorthogonalization pdsyevx does not promise orthogonality for eigenvectors associated with tighly clustered eigenvalues that are on different processes. the extent of reorthogonalization pssyevx does not promise orthogonality for eigenvectors associated with tighly clustered eigenvalues that are on different processes. the extent of reorthogonalization pzheevx does not promise orthogonality for eigenvectors associated with tighly clustered eigenvalues that are on different processes. the extent of reorthogonalization |
| time time for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will at the time of the call to mvr2 where h = h( maxindex:n, 1:bindex ) and note : it is assumed that the user is on an ieee machine. if the user is not on an ieee mchine, set the compile time flag no_iee are needed for the "fast" sturm count are : (a) infinity for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will at the time of the call to mvr2 where h = h( maxindex:n, 1:bindex ) and note : it is assumed that the user is on an ieee machine. if the user is not on an ieee mchine, set the compile time flag no_iee are needed for the "fast" sturm count are : (a) infinity for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will at the time of the call to mvr2 where h = h( maxindex:n, 1:bindex ) and for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will for clustersize = n/sqrt(nprow*npcol) reorthogonalizing all eigenvectors will increase the total execution time for clustersize > n/sqrt(nprow*npcol) execution time will at the time of the call to mvr2 where h = h( maxindex:n, 1:bindex ) and |
| times times scale by 1/cnorm(j) to avoid overflow when multiplying x(j) times column j x( j ) = cladiv( x( j ), tjjs ) the minimum (absolute) width of an interval. when an interval is narrower than abstol, or than reltol times the larger (i small, i.e., converged. = 0 : when an interval is narrower than abstol, or than reltol times the larger (in magnitude) endpoint, the = 1 : when an interval is narrower than abstol, or than the minimum (absolute) width of an interval. when an interval is narrower than abstol, or than reltol times the larger (i small, i.e., converged. = 0 : when an interval is narrower than abstol, or than reltol times the larger (in magnitude) endpoint, the = 1 : when an interval is narrower than abstol, or than scale by 1/cnorm(j) to avoid overflow when multiplying x(j) times column j x( j ) = zladiv( x( j ), tjjs ) |
| tiny tiny there are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in th equation problem is reduced by one. there are two ways in which deflation can occur: when two or more eigenvalues are close together or if there is a tiny entry in th equation problem is reduced by one. |
| tion tion pcgetf2 computes an lu factorization of a general m-by- partial pivoting with row interchanges. to upper hessenberg form h by an orthogonal similarity transforma- tion: q' * sub( a ) * q = h, wher to upper hessenberg form h by an orthogonal similarity transforma- tion: q' * sub( a ) * q = h, wher pdgetf2 computes an lu factorization of a general m-by- partial pivoting with row interchanges. to upper hessenberg form h by an orthogonal similarity transforma- tion: q' * sub( a ) * q = h, wher to upper hessenberg form h by an orthogonal similarity transforma- tion: q' * sub( a ) * q = h, wher psgetf2 computes an lu factorization of a general m-by- partial pivoting with row interchanges. pzgetf2 computes an lu factorization of a general m-by- partial pivoting with row interchanges. |
| Tisseur Tisseur contributed by francoise Tisseur, university of manchester reference: f. tisseur and j. dongarra, "a parallel divide and contributed by francoise Tisseur, university of manchester reference: f. tisseur and j. dongarra, "a parallel divide and contributed by francoise Tisseur, university of manchester reference: f. tisseur and j. dongarra, "a parallel divide and contributed by francoise Tisseur, university of manchester reference: f. tisseur and j. dongarra, "a parallel divide and contributed by francoise Tisseur, university of manchester reference: f. tisseur and j. dongarra, "a parallel divide and contributed by francoise Tisseur, university of manchester reference: f. tisseur and j. dongarra, "a parallel divide and |
| TJJS TJJS TJJS = a( j, j TJJS = a( j, j |
| TMP TMP all rotn row transforms are all complete through some column TMP. (loops 250-260 are then applied in a block fashion. all rotn row transforms are all complete through some column TMP. (loops within 190 are then applied in a block fashion. all rotn row transforms are all complete through some column TMP. (loops within 190 are then applied in a block fashion. all rotn row transforms are all complete through some column TMP. (loops 250-260 are then applied in a block fashion. |
| together together dlasorte sorts eigenpairs so that real eigenpairs are together an since every 2nd subdiagonal is guaranteed to be zero. the elements of the vectors v and u together form the m-by-nb matri the transformation to the unreduced part of the matrix, using a block the elements of the vectors v together form the (n-k+1)-by-nb matri unreduced part of the matrix, using an update of the form: the elements of the vectors v together form the n-by-nb matrix part of the matrix, using a hermitian rank-2k update of the form: the elements of the vectors v and u together form the m-by-nb matri the transformation to the unreduced part of the matrix, using a block pdlaed2 sorts the two sets of eigenvalues together into a singl there are two ways in which deflation can occur: when two or more the elements of the vectors v together form the (n-k+1)-by-nb matri unreduced part of the matrix, using an update of the form: the elements of the vectors v together form the n-by-nb matrix part of the matrix, using a symmetric rank-2k update of the form: the elements of the vectors v and u together form the m-by-nb matri the transformation to the unreduced part of the matrix, using a block pslaed2 sorts the two sets of eigenvalues together into a singl there are two ways in which deflation can occur: when two or more the elements of the vectors v together form the (n-k+1)-by-nb matri unreduced part of the matrix, using an update of the form: the elements of the vectors v together form the n-by-nb matrix part of the matrix, using a symmetric rank-2k update of the form: the elements of the vectors v and u together form the m-by-nb matri the transformation to the unreduced part of the matrix, using a block the elements of the vectors v together form the (n-k+1)-by-nb matri unreduced part of the matrix, using an update of the form: the elements of the vectors v together form the n-by-nb matrix part of the matrix, using a hermitian rank-2k update of the form: slasorte sorts eigenpairs so that real eigenpairs are together an since every 2nd subdiagonal is guaranteed to be zero. |
| tol tol abstol (global input) rea the most orthogonal eigenvectors. abstol (global input) rea the most orthogonal eigenvectors. abstol (global input) double precisio the most orthogonal eigenvectors. abstol (global input) double precisio the most orthogonal eigenvectors. abstol (global input) rea the most orthogonal eigenvectors. abstol (global input) rea the most orthogonal eigenvectors. abstol (global input) double precisio the most orthogonal eigenvectors. abstol (global input) double precisio the most orthogonal eigenvectors. |
| tolerance tolerance the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] however, if the workspace is insufficient (see lwork), this tolerance may be decreased until all eigenvectors to b no orthogonalization will be done if orfac equals zero. abstol (global input) double precision the absolute tolerance for the eigenvalues. an eigenvalu determined to lie in an interval whose width is abstol or however, if the workspace is insufficient (see lwork), this tolerance may be decreased until all eigenvectors to b no orthogonalization will be done if orfac equals zero. the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] abstol (global input) real the absolute tolerance for the eigenvalues. an eigenvalu determined to lie in an interval whose width is abstol or however, if the workspace is insufficient (see lwork), this tolerance may be decreased until all eigenvectors to b no orthogonalization will be done if orfac equals zero. the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] the absolute error tolerance for the eigenvalues when it is determined to lie in an interval [a,b] however, if the workspace is insufficient (see lwork), this tolerance may be decreased until all eigenvectors to b no orthogonalization will be done if orfac equals zero. |
| tolerances tolerances be as accurate as the absolute and relative tolerances. this is generally caused by arithmeti = 2 : there is a mismatch between the number of be as accurate as the absolute and relative tolerances. this is generally caused by arithmeti = 2 : there is a mismatch between the number of |
| too too this is the lookahead loop, going until we have convergence or too many steps have been taken if eigenvalues j and j-1 are too close, add a relativel size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nb*(bwl+bwu)+6*max(bwl,bwu)*max(bwl,bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (max(bwl,bwu)*nrhs) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol+3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b 10*npcol+4*nrhs size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nrhs*(nb+2*bwl+4*bwu) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). exit the loop if the growth factor is too small size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+2*bw)*bw size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (bw*nrhs) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol + 3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (10+2*min(100,nrhs))*npcol+4*nrhs size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nb*(bwl+bwu)+6*max(bwl,bwu)*max(bwl,bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (max(bwl,bwu)*nrhs) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol+3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b 10*npcol+4*nrhs size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nrhs*(nb+2*bwl+4*bwu) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+2*bw)*bw size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (bw*nrhs) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol + 3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (10+2*min(100,nrhs))*npcol+4*nrhs the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nb*(bwl+bwu)+6*max(bwl,bwu)*max(bwl,bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (max(bwl,bwu)*nrhs) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol+3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b 10*npcol+4*nrhs size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nrhs*(nb+2*bwl+4*bwu) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+2*bw)*bw size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (bw*nrhs) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol + 3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (10+2*min(100,nrhs))*npcol+4*nrhs the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nb*(bwl+bwu)+6*max(bwl,bwu)*max(bwl,bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (max(bwl,bwu)*nrhs) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol+3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b 10*npcol+4*nrhs size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+bwu)*(bwl+bwu)+6*(bwl+bwu)*(bwl+2*bwu) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b nrhs*(nb+2*bwl+4*bwu) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). exit the loop if the growth factor is too small size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (nb+2*bw)*bw size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (bw*nrhs) the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (12*npcol + 3*nb) size of user-input workspace work. if lwork is too small, the minimal acceptable size will b (10+2*min(100,nrhs))*npcol+4*nrhs if eigenvalues j and j-1 are too close, add a relativel this is the lookahead loop, going until we have convergence or too many steps have been taken |
| tool tool the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). row. the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locp() and locq() may be determined via a call to the scalapack tool function, numroc locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). row. the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locp() and locq() may be determined via a call to the scalapack tool function, numroc locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). row. the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locp() and locq() may be determined via a call to the scalapack tool function, numroc locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). row. the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locp() and locq() may be determined via a call to the scalapack tool function, numroc locq( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). the values of locr() and locc() may be determined via a call to the scalapack tool function, numroc locc( n ) = numroc( n, nb_a, mycol, csrc_a, npcol ). |
| top top determine where the matrix splits and choose ql or qr iteration for each block, according to whether top or bottom diagona at the top of the loop, bindex gets incremented, hence where h = h( maxindex:n, 1:bindex-1 ) and l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from psstebz is expected here). l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from pdstebz is expected here). at the top of the loop, bindex gets incremented, hence where h = h( maxindex:n, 1:bindex-1 ) and l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from psstebz is expected here). at the top of the loop, bindex gets incremented, hence where h = h( maxindex:n, 1:bindex-1 ) and at the top of the loop, bindex gets incremented, hence where h = h( maxindex:n, 1:bindex-1 ) and l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of specifies in which order the permutation is applied: = 'f' (forward) applies pivots forward from top of matrix = 'b' (backward) applies pivots backward from bottom of l (global input) integer the global location of the top of the unreduced submatri unchanged on exit. eigenvalues in w -- 1 for eigenvalues belonging to the first submatrix from the top, 2 for those belonging t from pdstebz is expected here). determine where the matrix splits and choose ql or qr iteration for each block, according to whether top or bottom diagona |
| torization torization pcgesvx uses the lu factorization to compute the solution to pdgesvx uses the lu factorization to compute the solution to a rea psgesvx uses the lu factorization to compute the solution to a rea pzgesvx uses the lu factorization to compute the solution to |
| Total Total itn is the Total number of qr iterations allowed > 0: if info = 1 through n, the i(th) eigenvalue did not converge in csteqr2 after a Total of 30*n iterations by finding that eigenvalues were not identical across m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer nvs(nprocs+1) = number of eigen vectors held by [0,nprocs) == Total number of eigenvector key (global input) integer array, dimension( n ) itn is the Total number of qr iterations allowed p = nprow * npcol is the Total number of processe n (global input) integer npcol (global input) integer the Total number of columns over which the distribute npcol (global input) integer the Total number of columns over which the distribute nvs(nprocs+1) = number of eigen vectors held by [0,nprocs) == Total number of eigenvector key (global input) integer array, dimension( n ) itn is the Total number of qr iterations allowed p = nprow * npcol is the Total number of processe n (global input) integer > 0: if info = 1 through n, the i(th) eigenvalue did not converge in dsteqr2 after a Total of 30*n iterations by finding that eigenvalues were not identical across m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer npcol (global input) integer the Total number of columns over which the distribute npcol (global input) integer the Total number of columns over which the distribute nvs(nprocs+1) = number of eigen vectors held by [0,nprocs) == Total number of eigenvector key (global input) integer array, dimension( n ) itn is the Total number of qr iterations allowed p = nprow * npcol is the Total number of processe n (global input) integer > 0: if info = 1 through n, the i(th) eigenvalue did not converge in ssteqr2 after a Total of 30*n iterations by finding that eigenvalues were not identical across m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer > 0: if info = 1 through n, the i(th) eigenvalue did not converge in zsteqr2 after a Total of 30*n iterations by finding that eigenvalues were not identical across m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer m (global output) integer Total number of eigenvalues found. 0 <= m <= n nz (global output) integer nvs(nprocs+1) = number of eigen vectors held by [0,nprocs) == Total number of eigenvector key (global input) integer array, dimension( n ) itn is the Total number of qr iterations allowed p = nprow * npcol is the Total number of processe n (global input) integer itn is the Total number of qr iterations allowed |
| toward toward restore the hessenberg form in the (k-1)th column, and thus chases the bulge one step toward the bottom of the activ restore the hessenberg form in the (k-1)th column, and thus chases the bulge one step toward the bottom of the activ |
| trace trace pclatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pdlatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pslatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. pzlatra computes the trace of an n-by-n distributed matrix sub( a process of the grid. |
| track track ipiv (local input) integer array, dimension locr(m_a)+mb_a keeps track of the pivoting information. ipiv(i) is th array is tied to the distributed matrix a. ipiv (local input) integer array, dimension locr(m_a)+mb_a keeps track of the pivoting information. ipiv(i) is th array is tied to the distributed matrix a. ipiv (local input) integer array, dimension locr(m_a)+mb_a keeps track of the pivoting information. ipiv(i) is th array is tied to the distributed matrix a. ipiv (local input) integer array, dimension locr(m_a)+mb_a keeps track of the pivoting information. ipiv(i) is th array is tied to the distributed matrix a. |
| traditional traditional the traditional zlatrd.f) is: the traditional zlatrd.f) is: the traditional zlatrd.f) is: the traditional zlatrd.f) is: |
| traffic traffic in the following overview of the steps performed, m in the margin indicates message traffic and c indicates o(n^2 nb/sqrt(p) in the following overview of the steps performed, m in the margin indicates message traffic and c indicates o(n^2 nb/sqrt(p) in the following overview of the steps performed, m in the margin indicates message traffic and c indicates o(n^2 nb/sqrt(p) in the following overview of the steps performed, m in the margin indicates message traffic and c indicates o(n^2 nb/sqrt(p) |
| trailing trailing maxindex: the global row and column for the first row and column in the trailing block of a be combined. on exit, d contains the trailing (n-k) updated eigenvalue be combined. on exit, d contains the trailing (n-k) updated eigenvalue maxindex: the global row and column for the first row and column in the trailing block of a be combined. on exit, d contains the trailing (n-k) updated eigenvalue be combined. on exit, d contains the trailing (n-k) updated eigenvalue maxindex: the global row and column for the first row and column in the trailing block of a maxindex: the global row and column for the first row and column in the trailing block of a |
| tranposed tranposed where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. |
| TRANS TRANS TRANS (input) characte = 'n': a * x = b (no transpose) TRANS (input) characte = 'n': l * x = b (no transpose) TRANS (input) characte = 'n': a * x = b (no transpose) TRANS (input) characte = 'n': l * x = b (no transpose) TRANS (global input) characte = 'c': solve with conjugate_transpose( a(1:n, ja:ja+n-1) ); TRANS (global input) characte = 'c': solve with conjugate_transpose( a(1:n, ja:ja+n-1) ); end of "if( lsame( TRANS, 'n' ) )".. TRANS (global input) characte = 'c': solve with conjugate_transpose( a(1:n, ja:ja+n-1) ); systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its conjugate-TRANSpose, using a qr or lq factorization o TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) a = u * sigma * TRANSpose(v where sigma is an m-by-n matrix which is zero except for its the system: TRANS = 'n': diag(r)*a*diag(c) *inv(diag(c))*x = diag(r)* trans = 'c': (diag(r)*a*diag(c))**h *inv(diag(r))*x = diag(c)*b TRANS (global input) characte = 'n': sub( a ) * x = sub( b ) (no transpose) a' * x, if kase=2, where a' is the conjugate TRANSpose of a, and pclacon mus pclarfb applies a complex block reflector q or its conjugate TRANSpose q**h to a complex m-by-n distributed matrix sub( c pclarzb applies a complex block reflector q or its conjugate TRANSpose q**h to a complex m-by-n distributed matrix sub( c on entry, the n-by-nrhs right-hand side matrix b. on exit, if equed = 'n', b is not modified; if TRANS = 'n trans = 't' or 'c' and equed = 'c' or 'b', b is overwritten end of "if( lsame( TRANS, 'n' ) )".. TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) TRANS (global input) characte = 'n': solve sub( a ) * x = sub( b ) (no transpose) side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * TRANS (global input) characte = 't' or 'c': solve with a(1:n, ja:ja+n-1)^t; TRANS (global input) characte = 't' or 'c': solve with a(1:n, ja:ja+n-1)^t; end of "if( lsame( TRANS, 'n' ) )".. TRANS (global input) characte = 't' or 'c': solve with a(1:n, ja:ja+n-1)^t; systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its TRANSpose, using a qr or lq factorization of sub( a ). it i TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) a = u * sigma * TRANSpose(v where sigma is an m-by-n matrix which is zero except for its the system: TRANS = 'n': diag(r)*a*diag(c) *inv(diag(c))*x = diag(r)* trans = 'c': (diag(r)*a*diag(c))**h *inv(diag(r))*x = diag(c)*b TRANS (global input) characte = 'n': sub( a ) * x = sub( b ) (no transpose) a real or complex matrix, with applications to condition estimation", acm TRANS. math. soft., vol. 14, no. 4, pp. 381-396, december 1988 ===================================================================== pdlarfb applies a real block reflector q or its TRANSpose q**t to from the left or the right. pdlarzb applies a real block reflector q or its TRANSpose q**t t from the left or the right. side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * on entry, the n-by-nrhs right-hand side matrix b. on exit, if equed = 'n', b is not modified; if TRANS = 'n trans = 't' or 'c' and equed = 'c' or 'b', b is overwritten TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) TRANS (global input) characte = 'n': solve sub( a ) * x = sub( b ) (no transpose) into a single character string. for example, uplo = 'u', TRANS = 't', and diag = 'n' for a triangular routine woul TRANS (global input) characte = 't' or 'c': solve with a(1:n, ja:ja+n-1)^t; TRANS (global input) characte = 't' or 'c': solve with a(1:n, ja:ja+n-1)^t; end of "if( lsame( TRANS, 'n' ) )".. TRANS (global input) characte = 't' or 'c': solve with a(1:n, ja:ja+n-1)^t; systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its TRANSpose, using a qr or lq factorization of sub( a ). it i TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) a = u * sigma * TRANSpose(v where sigma is an m-by-n matrix which is zero except for its the system: TRANS = 'n': diag(r)*a*diag(c) *inv(diag(c))*x = diag(r)* trans = 'c': (diag(r)*a*diag(c))**h *inv(diag(r))*x = diag(c)*b TRANS (global input) characte = 'n': sub( a ) * x = sub( b ) (no transpose) a real or complex matrix, with applications to condition estimation", acm TRANS. math. soft., vol. 14, no. 4, pp. 381-396, december 1988 ===================================================================== pslarfb applies a real block reflector q or its TRANSpose q**t to from the left or the right. pslarzb applies a real block reflector q or its TRANSpose q**t t from the left or the right. side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * on entry, the n-by-nrhs right-hand side matrix b. on exit, if equed = 'n', b is not modified; if TRANS = 'n trans = 't' or 'c' and equed = 'c' or 'b', b is overwritten TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) TRANS (global input) characte = 'n': solve sub( a ) * x = sub( b ) (no transpose) TRANS (global input) characte = 'c': solve with conjugate_transpose( a(1:n, ja:ja+n-1) ); TRANS (global input) characte = 'c': solve with conjugate_transpose( a(1:n, ja:ja+n-1) ); end of "if( lsame( TRANS, 'n' ) )".. TRANS (global input) characte = 'c': solve with conjugate_transpose( a(1:n, ja:ja+n-1) ); systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its conjugate-TRANSpose, using a qr or lq factorization o TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) a = u * sigma * TRANSpose(v where sigma is an m-by-n matrix which is zero except for its the system: TRANS = 'n': diag(r)*a*diag(c) *inv(diag(c))*x = diag(r)* trans = 'c': (diag(r)*a*diag(c))**h *inv(diag(r))*x = diag(c)*b TRANS (global input) characte = 'n': sub( a ) * x = sub( b ) (no transpose) a' * x, if kase=2, where a' is the conjugate TRANSpose of a, and pzlacon mus pzlarfb applies a complex block reflector q or its conjugate TRANSpose q**h to a complex m-by-n distributed matrix sub( c pzlarzb applies a complex block reflector q or its conjugate TRANSpose q**h to a complex m-by-n distributed matrix sub( c on entry, the n-by-nrhs right-hand side matrix b. on exit, if equed = 'n', b is not modified; if TRANS = 'n trans = 't' or 'c' and equed = 'c' or 'b', b is overwritten end of "if( lsame( TRANS, 'n' ) )".. TRANS (global input) character* = 'n': sub( a ) * sub( x ) = sub( b ) (no transpose) TRANS (global input) characte = 'n': solve sub( a ) * x = sub( b ) (no transpose) side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * side = 'l' side = 'r' TRANS = 'n': q * sub( c ) sub( c ) * TRANS (input) characte = 'n': a * x = b (no transpose) TRANS (input) characte = 'n': l * x = b (no transpose) TRANS (input) characte = 'n': a * x = b (no transpose) TRANS (input) characte = 'n': l * x = b (no transpose) |
| Transfer Transfer Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer triangle b_i of local matrix to next processo Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer triangle b_i of local matrix to next processo Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer triangle b_i of local matrix to next processo Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer triangle b_i of local matrix to next processo Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. Transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. |
| transfor transfor m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form by an unitary transformation q' * a * p, an mation to the unreduced part of sub( a ). m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form by an unitary transformation q' * a * p, an mation to the unreduced part of sub( a ). |
| transform transform i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar pclawil gets the transform given by h44,h33, & h43h34 into i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar pdlawil gets the transform given by h44,h33, & h43h34 into i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar pslawil gets the transform given by h44,h33, & h43h34 into i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar pzlawil gets the transform given by h44,h33, & h43h34 into |
| transforma transforma pdgehd2 reduces a real general distributed matrix sub( a ) to upper hessenberg form h by an orthogonal similarity transforma sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). pdgehrd reduces a real general distributed matrix sub( a ) to upper hessenberg form h by an orthogonal similarity transforma sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). psgehd2 reduces a real general distributed matrix sub( a ) to upper hessenberg form h by an orthogonal similarity transforma sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). psgehrd reduces a real general distributed matrix sub( a ) to upper hessenberg form h by an orthogonal similarity transforma sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). |
| transformation transformation sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an unitary transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an unitary transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. pcgehd2 reduces a complex general distributed matrix sub( a ) to upper hessenberg form h by an unitary similarity transformation sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). pcgehrd reduces a complex general distributed matrix sub( a ) to upper hessenberg form h by an unitary similarity transformation sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). pchentrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pchetd2 reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pchetrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pchettrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form by an unitary transformation q' * a * p, an mation to the unreduced part of sub( a ). i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar elements below the k-th subdiagonal are zero. the reduction is performed by an unitary similarity transformation q' * a * q. th reflector i - v*t*v', and also the matrix y = a * v * t. side = 'r'. it contains the local pieces of the distributed vectors v representing the householder transformation if storev = 'c' and side = 'l', lld_v >= max(1,locr(iv+m-1)); pieces of the distributed vectors v representing the householder transformation as returned by pctzrzf distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to complex tridiagonal form by an unitary similarity transformation needed to apply the transformation to the unreduced part of sub( a ). matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an orthogonal transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an orthogonal transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form by an orthogonal transformation q' * a * p transformation to the unreduced part of sub( a ). i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar k-th subdiagonal are zero. the reduction is performed by an orthogo- nal similarity transformation q' * a * q. the routine returns th and also the matrix y = a * v * t. side = 'r'. it contains the local pieces of the distributed vectors v representing the householder transformation if storev = 'c' and side = 'l', lld_v >= max(1,locr(iv+m-1)); pieces of the distributed vectors v representing the householder transformation as returned by pdtzrzf matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to symmetric tridiagonal form by an orthogonal similarity transformation q' * sub( a ) * q transformation to the unreduced part of sub( a ). sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as pdsyntrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pdsytd2 reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pdsytrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pdsyttrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as call pjlaenv in this release. pxyytevx.f and pxyytgvx.f redistribute the data to the best data layout for each transformation. pxyyttrd. sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an orthogonal transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an orthogonal transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form by an orthogonal transformation q' * a * p transformation to the unreduced part of sub( a ). i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar k-th subdiagonal are zero. the reduction is performed by an orthogo- nal similarity transformation q' * a * q. the routine returns th and also the matrix y = a * v * t. side = 'r'. it contains the local pieces of the distributed vectors v representing the householder transformation if storev = 'c' and side = 'l', lld_v >= max(1,locr(iv+m-1)); pieces of the distributed vectors v representing the householder transformation as returned by pstzrzf matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to symmetric tridiagonal form by an orthogonal similarity transformation q' * sub( a ) * q transformation to the unreduced part of sub( a ). sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as pssyntrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pssytd2 reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pssytrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pssyttrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an unitary transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form b by an unitary transformation: q' * sub( a ) * p = b if m >= n, b is upper bidiagonal; if m < n, b is lower bidiagonal. pzgehd2 reduces a complex general distributed matrix sub( a ) to upper hessenberg form h by an unitary similarity transformation sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). pzgehrd reduces a complex general distributed matrix sub( a ) to upper hessenberg form h by an unitary similarity transformation sub( a ) = a(ia+n-1:ia+n-1,ja+n-1:ja+n-1). pzhentrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pzhetd2 reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pzhetrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pzhettrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation m-by-n distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper or lower bidiagonal form by an unitary transformation q' * a * p, an mation to the unreduced part of sub( a ). i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar elements below the k-th subdiagonal are zero. the reduction is performed by an unitary similarity transformation q' * a * q. th reflector i - v*t*v', and also the matrix y = a * v * t. side = 'r'. it contains the local pieces of the distributed vectors v representing the householder transformation if storev = 'c' and side = 'l', lld_v >= max(1,locr(iv+m-1)); pieces of the distributed vectors v representing the householder transformation as returned by pztzrzf distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to complex tridiagonal form by an unitary similarity transformation needed to apply the transformation to the unreduced part of sub( a ). matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as |
| transformations transformations i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as i1 and i2 are the indices of the first row and last column of h to which transformations must be applied. if eigenvalues only ar |
| transformed transformed eigenvalues only are being computed, only the active submatrix need be transformed on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th eigenvalues only are being computed, only the active submatrix need be transformed eigenvalues only are being computed, only the active submatrix need be transformed on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th eigenvalues only are being computed, only the active submatrix need be transformed on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th on exit, if info = 0, the transformed matrix, stored in th eigenvalues only are being computed, only the active submatrix need be transformed eigenvalues only are being computed, only the active submatrix need be transformed |
| transforms transforms "a" row defs : main row transforms from localk to locali "a" row defs : main row transforms from localk to locali "a" row defs : main row transforms from localk to locali "a" row defs : main row transforms from localk to locali |
| transmitted transmitted receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. transpose transmitted upper triangular (trapezoidal) matri receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. transpose transmitted upper triangular (trapezoidal) matri receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. receive previously transmitted matrix section, which form the "spike" fillin. |
| Transpose Transpose specifies the form of the system of equations: = 'n': a * x = b (no Transpose = 'c': a**h * x = b (conjugate transpose) specifies the form of the system of equations: = 'n': l * x = b (no Transpose = 'c': u**h * x = b (conjugate transpose) specifies the form of the system of equations: = 'n': a * x = b (no Transpose = 'c': a**h * x = b (conjugate transpose) specifies the form of the system of equations: = 'n': l * x = b (no Transpose apply factorization to lower connection block bl_i conjugate Transpose the connection block in preparation move the connection block in preparation. note: for ease of use in solution of reduced system, store l's off-diagonal block in conjugate Transpose form systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its conjugate-Transpose, using a qr or lq factorization o specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**h * sub( x ) = sub( b ) a = u * sigma * Transpose(v where sigma is an m-by-n matrix which is zero except for its = 'n': a(ia:ia+n-1,ja:ja+n-1) * x(ix:ix+n-1,jx:jx+nrhs-1) = b(ib:ib+n-1,jb:jb+nrhs-1) (no Transpose = b(ib:ib+n-1,jb:jb+nrhs-1) (transpose) specifies the form of the system of equations: = 'n': sub( a ) * x = sub( b ) (no Transpose = 'c': sub( a )**h * x = sub( b ) (conjugate transpose) where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the conjugate Transpose of matrix z notes where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the conjugate Transpose of matrix z notes work ( inh ) dimension ( np, anb+1): array h work ( invt ) dimension ( nq, anb+1): Transpose of the array work ( invtt ) dimension ( nq, 1): transpose of the array vt a' * x, if kase=2, where a' is the conjugate Transpose of a, and pclacon mus or a column. the pivot vector should be aligned with the distributed matrix a. this routine will Transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. Transpose row vector pclarfb applies a complex block reflector q or its conjugate Transpose q**h to a complex m-by-n distributed matrix sub( c Transpose row vector Transpose row vector v (icoffv = iroffc2 pclarzb applies a complex block reflector q or its conjugate Transpose q**h to a complex m-by-n distributed matrix sub( c Transpose row vector v (icoffv = iroffc2 the factorization is obtained by householder's method. the kth transformation matrix, z( k ), whose conjugate Transpose is used t the form conjugate Transpose the connection block in preparation note: for ease of use in solution of reduced system, store l's off-diagonal block in conjugate Transpose form where y' denotes the conjugate Transpose of the vector y if all eigenvectors are requested, the routine may either return the specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**h * sub( x ) = sub( b ) specifies the form of the system of equations: = 'n': solve sub( a ) * x = sub( b ) (no Transpose = 'c': solve sub( a )**h * x = sub( b ) (conjugate transpose) the factorization is obtained by householder's method. the kth transformation matrix, z( k ), whose conjugate Transpose is used t the form trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q or p trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q apply factorization to lower connection block bl_i Transpose the connection block in preparation move the connection block in preparation. note: for ease of use in solution of reduced system, store l's off-diagonal block in Transpose form Transpose transmitted upper triangular (trapezoidal) matri systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its Transpose, using a qr or lq factorization of sub( a ). it i specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**t * sub( x ) = sub( b ) a = u * sigma * Transpose(v where sigma is an m-by-n matrix which is zero except for its = 'n': a(ia:ia+n-1,ja:ja+n-1) * x(ix:ix+n-1,jx:jx+nrhs-1) = b(ib:ib+n-1,jb:jb+nrhs-1) (no Transpose = b(ib:ib+n-1,jb:jb+nrhs-1) (transpose) specifies the form of the system of equations: = 'n': sub( a ) * x = sub( b ) (no Transpose = 'c': sub( a )**t * x = sub( b ) (transpose) where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the Transpose of matrix z notes where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the Transpose of matrix z notes or a column. the pivot vector should be aligned with the distributed matrix a. this routine will Transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. Transpose row vector pdlarfb applies a real block reflector q or its Transpose q**t to from the left or the right. Transpose row vector v (icoffv = iroffc2 pdlarzb applies a real block reflector q or its Transpose q**t t from the left or the right. trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q or p trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q Transpose the connection block in preparation note: for ease of use in solution of reduced system, store l's off-diagonal block in Transpose form work ( inh ) dimension ( np, anb+1): array h work ( invt ) dimension ( nq, anb+1): Transpose of the array work ( invtt ) dimension ( nq, 1): transpose of the array vt specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**t * sub( x ) = sub( b ) specifies the form of the system of equations: = 'n': solve sub( a ) * x = sub( b ) (no Transpose = 'c': solve sub( a )**t * x = sub( b ) (transpose) apply factorization to lower connection block bl_i Transpose the connection block in preparation move the connection block in preparation. note: for ease of use in solution of reduced system, store l's off-diagonal block in Transpose form Transpose transmitted upper triangular (trapezoidal) matri systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its Transpose, using a qr or lq factorization of sub( a ). it i specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**t * sub( x ) = sub( b ) a = u * sigma * Transpose(v where sigma is an m-by-n matrix which is zero except for its = 'n': a(ia:ia+n-1,ja:ja+n-1) * x(ix:ix+n-1,jx:jx+nrhs-1) = b(ib:ib+n-1,jb:jb+nrhs-1) (no Transpose = b(ib:ib+n-1,jb:jb+nrhs-1) (transpose) specifies the form of the system of equations: = 'n': sub( a ) * x = sub( b ) (no Transpose = 'c': sub( a )**t * x = sub( b ) (transpose) where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the Transpose of matrix z notes where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the Transpose of matrix z notes or a column. the pivot vector should be aligned with the distributed matrix a. this routine will Transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. Transpose row vector pslarfb applies a real block reflector q or its Transpose q**t to from the left or the right. Transpose row vector v (icoffv = iroffc2 pslarzb applies a real block reflector q or its Transpose q**t t from the left or the right. trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q or p trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q Transpose the connection block in preparation note: for ease of use in solution of reduced system, store l's off-diagonal block in Transpose form work ( inh ) dimension ( np, anb+1): array h work ( invt ) dimension ( nq, anb+1): Transpose of the array work ( invtt ) dimension ( nq, 1): transpose of the array vt specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**t * sub( x ) = sub( b ) specifies the form of the system of equations: = 'n': solve sub( a ) * x = sub( b ) (no Transpose = 'c': solve sub( a )**t * x = sub( b ) (transpose) apply factorization to lower connection block bl_i conjugate Transpose the connection block in preparation move the connection block in preparation. note: for ease of use in solution of reduced system, store l's off-diagonal block in conjugate Transpose form systems involving an m-by-n matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1), or its conjugate-Transpose, using a qr or lq factorization o specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**h * sub( x ) = sub( b ) a = u * sigma * Transpose(v where sigma is an m-by-n matrix which is zero except for its = 'n': a(ia:ia+n-1,ja:ja+n-1) * x(ix:ix+n-1,jx:jx+nrhs-1) = b(ib:ib+n-1,jb:jb+nrhs-1) (no Transpose = b(ib:ib+n-1,jb:jb+nrhs-1) (transpose) specifies the form of the system of equations: = 'n': sub( a ) * x = sub( b ) (no Transpose = 'c': sub( a )**h * x = sub( b ) (conjugate transpose) where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the conjugate Transpose of matrix z notes where inv( sub( b ) ) denotes the inverse of the matrix sub( b ), and z' denotes the conjugate Transpose of matrix z notes work ( inh ) dimension ( np, anb+1): array h work ( invt ) dimension ( nq, anb+1): Transpose of the array work ( invtt ) dimension ( nq, 1): transpose of the array vt a' * x, if kase=2, where a' is the conjugate Transpose of a, and pzlacon mus or a column. the pivot vector should be aligned with the distributed matrix a. this routine will Transpose the pivot vector if necessary sub( a ), pass rowcol='c' and pivroc='c'. Transpose row vector pzlarfb applies a complex block reflector q or its conjugate Transpose q**h to a complex m-by-n distributed matrix sub( c Transpose row vector Transpose row vector v (icoffv = iroffc2 pzlarzb applies a complex block reflector q or its conjugate Transpose q**h to a complex m-by-n distributed matrix sub( c Transpose row vector v (icoffv = iroffc2 the factorization is obtained by householder's method. the kth transformation matrix, z( k ), whose conjugate Transpose is used t the form conjugate Transpose the connection block in preparation note: for ease of use in solution of reduced system, store l's off-diagonal block in conjugate Transpose form where y' denotes the conjugate Transpose of the vector y if all eigenvectors are requested, the routine may either return the specifies the form of the system of equations. = 'n': sub( a ) * sub( x ) = sub( b ) (no Transpose = 'c': sub( a )**h * sub( x ) = sub( b ) specifies the form of the system of equations: = 'n': solve sub( a ) * x = sub( b ) (no Transpose = 'c': solve sub( a )**h * x = sub( b ) (conjugate transpose) the factorization is obtained by householder's method. the kth transformation matrix, z( k ), whose conjugate Transpose is used t the form trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q or p trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q trans (global input) character = 'n': no Transpose, apply q specifies the form of the system of equations: = 'n': a * x = b (no Transpose = 'c': a**h * x = b (conjugate transpose) specifies the form of the system of equations: = 'n': l * x = b (no Transpose specifies the form of the system of equations: = 'n': a * x = b (no Transpose = 'c': a**h * x = b (conjugate transpose) specifies the form of the system of equations: = 'n': l * x = b (no Transpose = 'c': u**h * x = b (conjugate transpose) |
| transposed transposed n (global input) integer the size of the matrix to be transposed a (local output) complex*16 pointer into the irsr0 : pointer to part of work used to store the rowsums after they have been transposed to be along a process ro irsr0 : pointer to part of work used to store the rowsums after they have been transposed to be along a process ro the following restrictions apply when ipiv must be transposed descip(mb_) must equal desca(nb_) n (global input) integer the size of the matrix to be transposed a (local output) complex*16 pointer into the irsr0 : pointer to part of work used to store the rowsums after they have been transposed to be along a process ro the following restrictions apply when ipiv must be transposed descip(mb_) must equal desca(nb_) n (global input) integer the size of the matrix to be transposed a (local output) complex*16 pointer into the irsr0 : pointer to part of work used to store the rowsums after they have been transposed to be along a process ro the following restrictions apply when ipiv must be transposed descip(mb_) must equal desca(nb_) n (global input) integer the size of the matrix to be transposed a (local output) complex*16 pointer into the irsr0 : pointer to part of work used to store the rowsums after they have been transposed to be along a process ro irsr0 : pointer to part of work used to store the rowsums after they have been transposed to be along a process ro the following restrictions apply when ipiv must be transposed descip(mb_) must equal desca(nb_) |
| transposing transposing the dimension of the array iwork used as workspace for physically transposing the pivots if nprow == npcol then the dimension of the array iwork used as workspace for physically transposing the pivots if nprow == npcol then the dimension of the array iwork used as workspace for physically transposing the pivots if nprow == npcol then the dimension of the array iwork used as workspace for physically transposing the pivots if nprow == npcol then |
| transposition transposition where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. where ldw is equal to the workspace necessary for transposition, and the storage of the tranposed ipiv let lcm be the least common multiple of nprow and npcol. |
| trapezoidal trapezoidal and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). permutation matrix, l is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and u is upper triangula permutation matrix, l is lower triangular with unit diagonal ele- ments (lower trapezoidal if m > n), and u is upper triangula and above the diagonal of sub( a ) contain the min(n,m) by m upper trapezoidal matrix r (r is upper triangular if n >= m) represent the unitary matrix q as a product of min(n,m) and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). pclatrz reduces the m-by-n ( m<=n ) complex upper trapezoidal to upper triangular form by means of unitary transformations. pctzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matri of unitary transformations. transpose transmitted upper triangular (trapezoidal) matri and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). permutation matrix, l is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and u is upper triangula permutation matrix, l is lower triangular with unit diagonal ele- ments (lower trapezoidal if m > n), and u is upper triangula and above the diagonal of sub( a ) contain the min(n,m) by m upper trapezoidal matrix r (r is upper triangular if n >= m) represent the orthogonal matrix q as a product of min(n,m) and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). pdlatrz reduces the m-by-n ( m<=n ) real upper trapezoidal matri upper triangular form by means of orthogonal transformations. pdtzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matri of orthogonal transformations. transpose transmitted upper triangular (trapezoidal) matri and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). permutation matrix, l is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and u is upper triangula permutation matrix, l is lower triangular with unit diagonal ele- ments (lower trapezoidal if m > n), and u is upper triangula and above the diagonal of sub( a ) contain the min(n,m) by m upper trapezoidal matrix r (r is upper triangular if n >= m) represent the orthogonal matrix q as a product of min(n,m) and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). pslatrz reduces the m-by-n ( m<=n ) real upper trapezoidal matri upper triangular form by means of orthogonal transformations. pstzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matri of orthogonal transformations. and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). the (n-m)-th superdiagonal contain the m by n lower trapezoidal matrix l; the remaining elements, with th elementary reflectors (see further details). and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). permutation matrix, l is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and u is upper triangula permutation matrix, l is lower triangular with unit diagonal ele- ments (lower trapezoidal if m > n), and u is upper triangula and above the diagonal of sub( a ) contain the min(n,m) by m upper trapezoidal matrix r (r is upper triangular if n >= m) represent the unitary matrix q as a product of min(n,m) and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix r; the remaining elements, with the arra elementary reflectors (see further details). pzlatrz reduces the m-by-n ( m<=n ) complex upper trapezoidal to upper triangular form by means of unitary transformations. pztzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matri of unitary transformations. |
| tree tree determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo determine number of steps in tree loo |
| trian trian uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular t (local input) complex array, dimension mb_v by mb_v if storev = 'r' and nb_v by nb_v if storev = 'c'. the trian matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as pctzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular t (local input) double precision array, dimension mb_v by mb_v if storev = 'r' and nb_v by nb_v if storev = 'c'. the trian sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as pdtzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular t (local input) real array, dimension mb_v by mb_v if storev = 'r' and nb_v by nb_v if storev = 'c'. the trian sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as pstzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular t (local input) complex*16 array, dimension mb_v by mb_v if storev = 'r' and nb_v by nb_v if storev = 'c'. the trian matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as pztzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean |
| triang triang transfer triangle b_i of local matrix to next processo transfer triangle b_i of local matrix to next processo transfer triangle b_i of local matrix to next processo transfer triangle b_i of local matrix to next processo |
| triangle triangle sizes of the extra triangles communicated bewtween processor transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. transfer triangle b_i of local matrix to next processo general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( b ) which is to be factored. on exit, if n <= p, the upper triangle of b(ib:ib+n-1,jb+p-n:jb+p-1) contains th and above the (n-p)-th subdiagonal contain the n by p upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper on exit, the lower triangle (if uplo='l') or the uppe destroyed. on exit, the lower triangle (if uplo='l') or the uppe destroyed. on exit, the lower triangle (if uplo='l') or the uppe destroyed. uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is if uplo = 'u', pclatrd reduces the last nb rows and columns of a matrix, of which the upper triangle is supplied matrix, of which the lower triangle is supplied. if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored sizes of the extra triangles communicated bewtween processor uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of a is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character*1 = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored uplo (global input) character = 'u': upper triangle of a(ia:*,ja:*) contains elementar = 'l': lower triangle of a(ia:*,ja:*) contains elementary sizes of the extra triangles communicated bewtween processor transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. transfer triangle b_i of local matrix to next processo general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( b ) which is to be factored. on exit, if n <= p, the upper triangle of b(ib:ib+n-1,jb+p-n:jb+p-1) contains th and above the (n-p)-th subdiagonal contain the n by p upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper if uplo = 'u', pdlatrd reduces the last nb rows and columns of a matrix, of which the upper triangle is supplied matrix, of which the lower triangle is supplied. if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, uplo (global input) character = 'u': upper triangle of a(ia:*,ja:*) contains elementar = 'l': lower triangle of a(ia:*,ja:*) contains elementary uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored sizes of the extra triangles communicated bewtween processor uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of a is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character*1 = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. on exit, the lower triangle (if uplo='l') or the uppe destroyed. symmetric matrix. on exit, the lower triangle (if uplo='l') or the uppe destroyed. on exit, the lower triangle (if uplo='l') or the uppe destroyed. uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is sizes of the extra triangles communicated bewtween processor transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. transfer triangle b_i of local matrix to next processo general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( b ) which is to be factored. on exit, if n <= p, the upper triangle of b(ib:ib+n-1,jb+p-n:jb+p-1) contains th and above the (n-p)-th subdiagonal contain the n by p upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper if uplo = 'u', pslatrd reduces the last nb rows and columns of a matrix, of which the upper triangle is supplied matrix, of which the lower triangle is supplied. if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, uplo (global input) character = 'u': upper triangle of a(ia:*,ja:*) contains elementar = 'l': lower triangle of a(ia:*,ja:*) contains elementary uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored sizes of the extra triangles communicated bewtween processor uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of a is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character*1 = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. on exit, the lower triangle (if uplo='l') or the uppe destroyed. symmetric matrix. on exit, the lower triangle (if uplo='l') or the uppe destroyed. on exit, the lower triangle (if uplo='l') or the uppe destroyed. uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is sizes of the extra triangles communicated bewtween processor transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. transfer triangle b_i of local matrix to next processo general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- general distributed matrix sub( a ) to be reduced. on exit, the upper triangle and the first subdiagonal of sub( a ) ar ments below the first subdiagonal, with the array tau, repre- sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m >= n, the lower triangle of the distributed submatri triangular matrix l; if m <= n, the elements on and below sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper sub( b ) which is to be factored. on exit, if n <= p, the upper triangle of b(ib:ib+n-1,jb+p-n:jb+p-1) contains th and above the (n-p)-th subdiagonal contain the n by p upper sub( a ) which is to be factored. on exit, if m <= n, the upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains th and above the (m-n)-th subdiagonal contain the m by n upper on exit, the lower triangle (if uplo='l') or the uppe destroyed. on exit, the lower triangle (if uplo='l') or the uppe destroyed. on exit, the lower triangle (if uplo='l') or the uppe destroyed. uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored and sub( b ) i = 'l': lower triangle of sub( a ) is stored and sub( b ) is if uplo = 'u', pzlatrd reduces the last nb rows and columns of a matrix, of which the upper triangle is supplied matrix, of which the lower triangle is supplied. if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, if uplo = 'u' or 'u' then the upper triangle of the result is stored if uplo = 'l' or 'l' then the lower triangle of the result is stored, uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored sizes of the extra triangles communicated bewtween processor uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of a is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character*1 = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of sub( a ) is stored uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored transfer last triangle d_i of local matrix to next processo its main (odd) block a_i. uplo (global input) character = 'u': upper triangle of a(1:n, ja:ja+n-1) is stored uplo (global input) character = 'u': upper triangle of a(ia:*,ja:*) contains elementar = 'l': lower triangle of a(ia:*,ja:*) contains elementary |
| triangles triangles sizes of the extra triangles communicated bewtween processor uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored sizes of the extra triangles communicated bewtween processor sizes of the extra triangles communicated bewtween processor sizes of the extra triangles communicated bewtween processor uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored sizes of the extra triangles communicated bewtween processor sizes of the extra triangles communicated bewtween processor uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored sizes of the extra triangles communicated bewtween processor uplo (global input) character*1 = 'u': upper triangles of sub( a ) and sub( b ) are stored sizes of the extra triangles communicated bewtween processor |
| triangular triangular on exit, details of the factorization: u is stored as an upper triangular band matrix with kl+ku superdiagonals i factorization are stored in rows kl+ku+2 to 2*kl+ku+1. where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonzeros in only the mai d (input) complex array, dimension (n) the n diagonal elements of the upper triangular matrix u fro cpttrsv solves one of the triangular system u * x = b, or u**h * x = b, where x is an n element vector and t is an n by n upper or lower triangular matrix arguments on exit, details of the factorization: u is stored as an upper triangular band matrix with kl+ku superdiagonals i factorization are stored in rows kl+ku+2 to 2*kl+ku+1. where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonzeros in only the mai d (input) complex array, dimension (n) the n diagonal elements of the upper triangular matrix u fro dpttrsv solves one of the triangular system where l is the cholesky factor of a hermitian positive where x is an n element vector and t is an n by n upper or lower triangular matrix arguments offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto lbwl, lbwu: lower and upper bandwidth of local solver note that for mycol > 0 one has lower triangular blocks mycol = 0 where it is bwu less and mycol=npcol-1 where it ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+jhi:ja+n-1. see further details. if n > 0, ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+ihi:ja+n-1. see further details. if n > 0, and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). a = p * l * u, where p is a permutation matrix, l is a unit lower triangular the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagona (upper trapezoidal if m < n). the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagonal ele (upper trapezoidal if m < n). l and u are stored in sub( a ). where r11 is upper triangular, an if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, where r12 or r21 is upper triangular, an if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 t12 ) p, uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular n-by-n hermitian distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n hermitian distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n hermitian distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain leading n-by-n lower triangular part of sub( a ) contains rank 2k updates, which are faster and more scalable than triangular solves (the basis of pchengst) pchengst calls pchegst when uplo='u', hence pchengst provides uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly t (local output) complex array, dimension (nb_a,nb_a) the upper triangular matrix t y (local output) complex pointer into the local memory if the matrix is hermitian, we address only a triangular portio can be obtained by adding along row i and column i of the the if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the upper triangular matri uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular pclarft forms the triangular factor t of a complex block reflector t (local input) complex array, dimension mb_v by mb_v the lower triangular matrix t in the representation of th pclarzt forms the triangular factor t of a complex block reflecto reflectors as returned by pctzrzf. cto * a(i,j) / cfrom does not over/underflow. type specifies that sub( a ) may be full, upper triangular, lower triangular or uppe set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as a is upper triangular pclauu2 computes the product u * u' or l' * l, where the triangular the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pclauum computes the product u * u' or l' * l, where the triangular the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1).
perform the triangular system solve {l_i}{{b'}_i}^c = {b_i}^
specifies whether the factor stored in a(ia:ia+n-1,ja:ja+n-1) is upper or lower triangular = 'l': lower triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular where u is an upper triangular matrix and l is a lower triangula system of equations. a = l * l**t, if uplo = 'l', where u is an upper triangular matrix and l is a lower triangula where u is an upper triangular matrix and l is lower triangular notes where u is an upper triangular matrix and l is lower triangular notes local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, the local pieces of the triangular factor u or sub( a ) = u**h*u or l*l**h, as computed by pcpotrf.
perform the triangular system solve {l_i}{{b'}_i}^c = {b_i}^
pctrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th pctrevc computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix t in parallel the right eigenvector x and the left eigenvector y of t corresponding pctrrfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular pctrti2 computes the inverse of a complex upper or lower triangular contained in one and only one process memory space (local operation). pctrtri computes the inverse of a upper or lower triangular pctrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ) or pctzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto lbwl, lbwu: lower and upper bandwidth of local solver note that for mycol > 0 one has lower triangular blocks mycol = 0 where it is bwu less and mycol=npcol-1 where it ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+jhi:ja+n-1. see further details. if n > 0, ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+ihi:ja+n-1. see further details. if n > 0, and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). a = p * l * u, where p is a permutation matrix, l is a unit lower triangular the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagona (upper trapezoidal if m < n). the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagonal ele (upper trapezoidal if m < n). l and u are stored in sub( a ). where r11 is upper triangular, an if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, where r12 or r21 is upper triangular, an if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 t12 ) p, copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly t (local output) double precision array, dimension (nb_a,nb_a) the upper triangular matrix t y (local output) double precision pointer into the local memory if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the upper triangular matri uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular pdlarft forms the triangular factor t of a real block reflector t (local input) double precision array, dimension mb_v by mb_v the lower triangular matrix t in the representation of th pdlarzt forms the triangular factor t of a real block reflecto reflectors as returned by pdtzrzf. cto * a(i,j) / cfrom does not over/underflow. type specifies that sub( a ) may be full, upper triangular, lower triangular or uppe set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as pdlauu2 computes the product u * u' or l' * l, where the triangular the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pdlauum computes the product u * u' or l' * l, where the triangular the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1).
perform the triangular system solve {l_i}{{b'}_i}^t = {b_i}^
specifies whether the factor stored in a(ia:ia+n-1,ja:ja+n-1) is upper or lower triangular = 'l': lower triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular where u is an upper triangular matrix and l is a lower triangula system of equations. a = l * l**t, if uplo = 'l', where u is an upper triangular matrix and l is a lower triangula where u is an upper triangular matrix and l is lower triangular notes where u is an upper triangular matrix and l is lower triangular notes local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, the local pieces of the triangular factor u or sub( a ) = u**t*u or l*l**t, as computed by pdpotrf.
perform the triangular system solve {l_i}{{b'}_i}^t = {b_i}^
uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular n-by-n symmetric distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n symmetric distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n symmetric distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain leading n-by-n lower triangular part of sub( a ) contains rank 2k updates, which are faster and more scalable than triangular solves (the basis of pdsyngst) pdsyngst calls pdhegst when uplo='u', hence pdhengst provides uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular pdtrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th pdtrrfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular pdtrti2 computes the inverse of a real upper or lower triangular contained in one and only one process memory space (local operation). pdtrtri computes the inverse of a upper or lower triangular pdtrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ), pdtzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean into a single character string. for example, uplo = 'u', trans = 't', and diag = 'n' for a triangular routine woul offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto lbwl, lbwu: lower and upper bandwidth of local solver note that for mycol > 0 one has lower triangular blocks mycol = 0 where it is bwu less and mycol=npcol-1 where it ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+jhi:ja+n-1. see further details. if n > 0, ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+ihi:ja+n-1. see further details. if n > 0, and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the orthogonal matrix q as a product of elementary a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the orthogonal matrix q as a product of elementary upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). a = p * l * u, where p is a permutation matrix, l is a unit lower triangular the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagona (upper trapezoidal if m < n). the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagonal ele (upper trapezoidal if m < n). l and u are stored in sub( a ). where r11 is upper triangular, an if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, where r12 or r21 is upper triangular, an if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 t12 ) p, copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly t (local output) real array, dimension (nb_a,nb_a) the upper triangular matrix t y (local output) real pointer into the local memory if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the upper triangular matri uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular pslarft forms the triangular factor t of a real block reflector t (local input) real array, dimension mb_v by mb_v the lower triangular matrix t in the representation of th pslarzt forms the triangular factor t of a real block reflecto reflectors as returned by pstzrzf. cto * a(i,j) / cfrom does not over/underflow. type specifies that sub( a ) may be full, upper triangular, lower triangular or uppe set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular sub( a ) = [ a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1) ] to upper triangular form by means of orthogonal transformations the upper trapezoidal matrix sub( a ) is factored as pslauu2 computes the product u * u' or l' * l, where the triangular the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pslauum computes the product u * u' or l' * l, where the triangular the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1).
perform the triangular system solve {l_i}{{b'}_i}^t = {b_i}^
specifies whether the factor stored in a(ia:ia+n-1,ja:ja+n-1) is upper or lower triangular = 'l': lower triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular where u is an upper triangular matrix and l is a lower triangula system of equations. a = l * l**t, if uplo = 'l', where u is an upper triangular matrix and l is a lower triangula where u is an upper triangular matrix and l is lower triangular notes where u is an upper triangular matrix and l is lower triangular notes local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, the local pieces of the triangular factor u or sub( a ) = u**t*u or l*l**t, as computed by pspotrf.
perform the triangular system solve {l_i}{{b'}_i}^t = {b_i}^
uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular n-by-n symmetric distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n symmetric distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n symmetric distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain leading n-by-n lower triangular part of sub( a ) contains rank 2k updates, which are faster and more scalable than triangular solves (the basis of pssyngst) pssyngst calls pshegst when uplo='u', hence pshengst provides uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular pstrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th pstrrfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular pstrti2 computes the inverse of a real upper or lower triangular contained in one and only one process memory space (local operation). pstrtri computes the inverse of a upper or lower triangular pstrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ), pstzrzf reduces the m-by-n ( m<=n ) real upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto offset to workspace for upper triangular facto lbwl, lbwu: lower and upper bandwidth of local solver note that for mycol > 0 one has lower triangular blocks mycol = 0 where it is bwu less and mycol=npcol-1 where it ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+jhi:ja+n-1. see further details. if n > 0, ihi (global input) integer it is assumed that sub( a ) is already upper triangular i and ja+ihi:ja+n-1. see further details. if n > 0, and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary and below the diagonal of sub( a ) contain the m by min(m,n) lower trapezoidal matrix l (l is lower triangular if m <= n) sent the unitary matrix q as a product of elementary a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the a( ia+m-n:ia+m-1, ja:ja+n-1 ) contains the n-by-n lower triangular matrix l; if m <= n, the elements on and belo trapezoidal matrix l; the remaining elements, with the and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) sent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary and above the diagonal of sub( a ) contain the min(m,n) by n upper trapezoidal matrix r (r is upper triangular if m >= n) represent the unitary matrix q as a product of elementary upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array upper triangle of a( ia:ia+m-1, ja+n-m:ja+n-1 ) contains the m by m upper triangular matrix r; if m >= n, the elements o trapezoidal matrix r; the remaining elements, with the array used to factor sub( a ) as sub( a ) = p * l * u, where p is a permu- tation matrix, l is unit lower triangular, and u is upper triangular used to solve the system of equations sub( a ) * x = sub( b ). a = p * l * u, where p is a permutation matrix, l is a unit lower triangular the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagona (upper trapezoidal if m < n). the factorization has the form sub( a ) = p * l * u, where p is a permutation matrix, l is lower triangular with unit diagonal ele (upper trapezoidal if m < n). l and u are stored in sub( a ). where r11 is upper triangular, an if n <= p, t = ( 0 t12 ) n, or if n > p, t = ( t11 ) n-p, where r12 or r21 is upper triangular, an if p >= n, t = ( t11 ) n , or if p < n, t = ( t11 t12 ) p, uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular n-by-n hermitian distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n hermitian distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain lower triangular part is not referenced. if uplo = 'l', the n-by-n hermitian distributed matrix sub( a ). if uplo = 'u', the leading n-by-n upper triangular part of sub( a ) contain leading n-by-n lower triangular part of sub( a ) contains rank 2k updates, which are faster and more scalable than triangular solves (the basis of pzhengst) pzhengst calls pzhegst when uplo='u', hence pzhengst provides uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly copied: = 'u': upper triangular part is copied; the strictl = 'l': lower triangular part is copied; the strictly t (local output) complex*16 array, dimension (nb_a,nb_a) the upper triangular matrix t y (local output) complex*16 pointer into the local memory if the matrix is hermitian, we address only a triangular portio can be obtained by adding along row i and column i of the the if the matrix is symmetric, we address only a triangular portio can be obtained by adding along row i and column i of the the upper triangular matri uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular pzlarft forms the triangular factor t of a complex block reflector t (local input) complex*16 array, dimension mb_v by mb_v the lower triangular matrix t in the representation of th pzlarzt forms the triangular factor t of a complex block reflecto reflectors as returned by pztzrzf. cto * a(i,j) / cfrom does not over/underflow. type specifies that sub( a ) may be full, upper triangular, lower triangular or uppe set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper set: = 'u': upper triangular part is set; the strictly lowe = 'l': lower triangular part is set; the strictly upper uplo (global input) character specifies whether the upper or lower triangular part of th = 'u': upper triangular matrix sub( a ) = [a(ia:ia+m-1,ja:ja+m-1) a(ia:ia+m-1,ja+n-l:ja+n-1)] to upper triangular form by means of unitary transformations the upper trapezoidal matrix sub( a ) is factored as a is upper triangular pzlauu2 computes the product u * u' or l' * l, where the triangular the matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1). pzlauum computes the product u * u' or l' * l, where the triangular the distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1).
perform the triangular system solve {l_i}{{b'}_i}^c = {b_i}^
specifies whether the factor stored in a(ia:ia+n-1,ja:ja+n-1) is upper or lower triangular = 'l': lower triangular uplo (global input) character*1 specifies whether the upper or lower triangular part of th = 'u': upper triangular where u is an upper triangular matrix and l is a lower triangula system of equations. a = l * l**t, if uplo = 'l', where u is an upper triangular matrix and l is a lower triangula where u is an upper triangular matrix and l is lower triangular notes where u is an upper triangular matrix and l is lower triangular notes local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, the local pieces of the triangular factor u or sub( a ) = u**h*u or l*l**h, as computed by pzpotrf.
perform the triangular system solve {l_i}{{b'}_i}^c = {b_i}^
pztrcon estimates the reciprocal of the condition number of a triangular distributed matrix a(ia:ia+n-1,ja:ja+n-1), in either th pztrevc computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix t in parallel the right eigenvector x and the left eigenvector y of t corresponding pztrrfs provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular pztrti2 computes the inverse of a complex upper or lower triangular contained in one and only one process memory space (local operation). pztrtri computes the inverse of a upper or lower triangular pztrtrs solves a triangular system of the for sub( a ) * x = sub( b ) or sub( a )**t * x = sub( b ) or pztzrzf reduces the m-by-n ( m<=n ) complex upper trapezoidal matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1) to upper triangular form by mean on exit, details of the factorization: u is stored as an upper triangular band matrix with kl+ku superdiagonals i factorization are stored in rows kl+ku+2 to 2*kl+ku+1. where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonzeros in only the mai d (input) complex array, dimension (n) the n diagonal elements of the upper triangular matrix u fro spttrsv solves one of the triangular system where l is the cholesky factor of a hermitian positive where x is an n element vector and t is an n by n upper or lower triangular matrix arguments on exit, details of the factorization: u is stored as an upper triangular band matrix with kl+ku superdiagonals i factorization are stored in rows kl+ku+2 to 2*kl+ku+1. where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonzeros in only the mai d (input) complex array, dimension (n) the n diagonal elements of the upper triangular matrix u fro zpttrsv solves one of the triangular system u * x = b, or u**h * x = b, where x is an n element vector and t is an n by n upper or lower triangular matrix arguments |
| tributed tributed a description vector is associated with each 2d block-cyclicly dis- tributed matrix. this vector stores the information required t process and memory location. pclaqsy equilibrates a symmetric distributed matri vectors sr and sc. pdlaqsy equilibrates a symmetric distributed matri vectors sr and sc. a description vector is associated with each 2d block-cyclicly dis- tributed matrix. this vector stores the information required t process and memory location. pslaqsy equilibrates a symmetric distributed matri vectors sr and sc. a description vector is associated with each 2d block-cyclicly dis- tributed matrix. this vector stores the information required t process and memory location. a description vector is associated with each 2d block-cyclicly dis- tributed matrix. this vector stores the information required t process and memory location. pzlaqsy equilibrates a symmetric distributed matri vectors sr and sc. |
| tridiagonal tridiagonal cdttrf computes an lu factorization of a complex tridiagonal matrix u * x = b, u**t * x = b, or u**h * x = b, with factors of the tridiagonal matrix a from the lu factorizatio where l or u is the cholesky factor of a hermitian positive definite tridiagonal matrix a such tha ddttrf computes an lu factorization of a complex tridiagonal matrix u * x = b, u**t * x = b, or u**h * x = b, with factors of the tridiagonal matrix a from the lu factorizatio where l is the cholesky factor of a hermitian positive definite tridiagonal matrix a such tha compute the eigenvalues and eigenvectors of the tridiagonal the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distribute a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distribute the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri pchentrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pchetd2 reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pchetrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pchettrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. pclamr1d has not been tested except withint the contect of pcheptrd, the prototype reduction to tridiagonal form code purpose a (global input) complex array, dimension (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to complex tridiagonal form by an unitary similarity transformatio needed to apply the transformation to the unreduced part of sub( a ). the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distribute a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distribute depending on the value of uplo, a stores either u or l in the equn pcstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pcstein does not the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distribute a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distribute the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. j = 1,...,minp. it uses and computes the function n(w), which is the count of eigenvalues of a symmetric tridiagonal matrix less tha pdlaed0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method n (global input) integer the order of the tridiagonal matrix t. n >= 0 n (input) integer the dimension of the symmetric tridiagonal matrix. n >= 0 n1 (input) integer n (input) integer the dimension of the symmetric tridiagonal matrix. n >= 0 nb (global input) integer pdlamr1d has not been tested except withint the contect of pdsyptrd, the prototype reduction to tridiagonal form code purpose n (input) integer the order of the tridiagonal matrix t. n >= 1 d (input) double precision array, dimension (2*n - 1) (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. pdlatrd reduces nb rows and columns of a real symmetric distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to symmetric tridiagonal and returns the matrices v and w which are needed to apply the the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distribute a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distribute pdstebz computes the eigenvalues of a symmetric tridiagonal matrix i the interval [vl, vu], or the eigenvalues indexed il through iu. a pdstedc computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix in parallel, using the divide an pdstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pdstein does not or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri pdsyntrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pdsytd2 reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pdsytrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pdsyttrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distribute a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal diagonally dominant-like distribute the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. j = 1,...,minp. it uses and computes the function n(w), which is the count of eigenvalues of a symmetric tridiagonal matrix less tha pslaed0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method n (global input) integer the order of the tridiagonal matrix t. n >= 0 n (input) integer the dimension of the symmetric tridiagonal matrix. n >= 0 n1 (input) integer n (input) integer the dimension of the symmetric tridiagonal matrix. n >= 0 nb (global input) integer pslamr1d has not been tested except withint the contect of pssyptrd, the prototype reduction to tridiagonal form code purpose n (input) integer the order of the tridiagonal matrix t. n >= 1 d (input) real array, dimension (2*n - 1) (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. pslatrd reduces nb rows and columns of a real symmetric distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to symmetric tridiagonal and returns the matrices v and w which are needed to apply the the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distribute a(1:n, ja:ja+n-1) is an n-by-n real tridiagonal symmetric positive definite distribute psstebz computes the eigenvalues of a symmetric tridiagonal matrix i the interval [vl, vu], or the eigenvalues indexed il through iu. a psstedc computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix in parallel, using the divide an psstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. psstein does not or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri pssyntrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pssytd2 reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pssytrd reduces a real symmetric matrix sub( a ) to symmetric tridiagonal form t by an orthogonal similarity transformation pssyttrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distribute a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal diagonally dominant-like distribute the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri or equal to zero, then eps*norm(t) will be used in its place, where norm(t) is the 1-norm of the tridiagonal matri pzhentrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pzhetd2 reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pzhetrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation pzhettrd reduces a complex hermitian matrix sub( a ) to hermitian tridiagonal form t by an unitary similarity transformation (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. pzlamr1d has not been tested except withint the contect of pzheptrd, the prototype reduction to tridiagonal form code purpose a (global input) complex*16 array, dimension (desca(lld_),*) on entry, the hessenberg matrix whose tridiagonal part i unchanged on exit. distributed matrix sub( a ) = a(ia:ia+n-1,ja:ja+n-1) to complex tridiagonal form by an unitary similarity transformatio needed to apply the transformation to the unreduced part of sub( a ). the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are the best algorithm for solving banded and tridiagonal linear system currently, only algorithms designed for the case n/p >> bw are where a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distribute a(1:n, ja:ja+n-1) is an n-by-n complex tridiagonal symmetric positive definite distribute depending on the value of uplo, a stores either u or l in the equn pzstein computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pzstein does not sdttrf computes an lu factorization of a complex tridiagonal matrix u * x = b, u**t * x = b, or u**h * x = b, with factors of the tridiagonal matrix a from the lu factorizatio where l is the cholesky factor of a hermitian positive definite tridiagonal matrix a such tha compute the eigenvalues and eigenvectors of the tridiagonal zdttrf computes an lu factorization of a complex tridiagonal matrix u * x = b, u**t * x = b, or u**h * x = b, with factors of the tridiagonal matrix a from the lu factorizatio where l or u is the cholesky factor of a hermitian positive definite tridiagonal matrix a such tha |
| tries tries pdlaed2 sorts the two sets of eigenvalues together into a single sorted set. then it tries to deflate the size of the problem eigenvalues are close together or if there is a tiny entry in the pslaed2 sorts the two sets of eigenvalues together into a single sorted set. then it tries to deflate the size of the problem eigenvalues are close together or if there is a tiny entry in the |
| tril tril triangular portion of a is updated, av is computed as: tril(a) * v + v^t * tril(a,-1). this is performed a mvr2) followed by a transpose and a sum across the columns. triangular portion of a is updated, av is computed as: tril(a) * v + v^t * tril(a,-1). this is performed a mvr2) followed by a transpose and a sum across the columns. triangular portion of a is updated, av is computed as: tril(a) * v + v^t * tril(a,-1). this is performed a mvr2) followed by a transpose and a sum across the columns. triangular portion of a is updated, av is computed as: tril(a) * v + v^t * tril(a,-1). this is performed a mvr2) followed by a transpose and a sum across the columns. |
| TRILWMIN TRILWMIN lwork (local input) integer lwork >= max( 1+6*n+2*np*nq, TRILWMIN ) + 2* np = numroc( n, nb, myrow, iarow, nprow ) lwork (local input) integer lwork >= max( 1+6*n+2*np*nq, TRILWMIN ) + 2* np = numroc( n, nb, myrow, iarow, nprow ) |
| trough trough the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). one interchange is initiated for each of rows or columns k1 trough k2 o already been broadcast along the process row or column. the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). one interchange is initiated for each of rows or columns k1 trough k2 o already been broadcast along the process row or column. the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). one interchange is initiated for each of rows or columns k1 trough k2 o already been broadcast along the process row or column. the distributed matrix sub( a ) = a(ia:ia+m-1,ja:ja+n-1). one interchange is initiated for each of rows or columns k1 trough k2 o already been broadcast along the process row or column. |
| true true wantz (global input) logical if .true., then apply any column reflections to z as well wantz (global input) logical if .true., then apply any column reflections to z as well the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') been premultiplied by diag(r). the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( mb_a.eq.mb_b .and. iroffa.eq.iroffb .and. iarow.eq.ibrow ) the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( nb_a.eq.nb_b .and. icoffa.eq.icoffb .and. iacol.eq.ibcol ) must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. some alignment properties, namely the following expression should be true iroffa.eq.0 .and.iroffa.eq.iroffz. and. iarow.eq.izrow) must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. and b( ib:ib+n-1, jb:jb+n-1 ) must verify some alignment properties, namely the following expressions should be true desca(mb_) = desca(nb_) the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') diag(sr) * a * diag(sc). to select the eigenvector corresponding to the j-th eigenvalue, select(j) must be set to .true. n (global input) integer locc(jb+nrhs-1). the estimated forward error bounds for each solution vector of sub( x ). if xtrue is the tru in (sub( x ) - xtrue) divided by the magnitude of the must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if vect = 'q', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') been premultiplied by diag(r). the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( mb_a.eq.mb_b .and. iroffa.eq.iroffb .and. iarow.eq.ibrow ) the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( nb_a.eq.nb_b .and. icoffa.eq.icoffb .and. iacol.eq.ibcol ) must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if vect = 'q', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') diag(sr) * a * diag(sc). must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. some alignment properties, namely the following expression should be true iroffa.eq.0 .and.iroffa.eq.iroffz. and. iarow.eq.izrow) must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. and b( ib:ib+n-1, jb:jb+n-1 ) must verify some alignment properties, namely the following expressions should be true desca(mb_) = desca(nb_) the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). locc(jb+nrhs-1). the estimated forward error bounds for each solution vector of sub( x ). if xtrue is the tru in (sub( x ) - xtrue) divided by the magnitude of the the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') been premultiplied by diag(r). the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( mb_a.eq.mb_b .and. iroffa.eq.iroffb .and. iarow.eq.ibrow ) the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( nb_a.eq.nb_b .and. icoffa.eq.icoffb .and. iacol.eq.ibcol ) must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if vect = 'q', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') diag(sr) * a * diag(sc). must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. some alignment properties, namely the following expression should be true iroffa.eq.0 .and.iroffa.eq.iroffz. and. iarow.eq.izrow) must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. and b( ib:ib+n-1, jb:jb+n-1 ) must verify some alignment properties, namely the following expressions should be true desca(mb_) = desca(nb_) the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). locc(jb+nrhs-1). the estimated forward error bounds for each solution vector of sub( x ). if xtrue is the tru in (sub( x ) - xtrue) divided by the magnitude of the the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expressions should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') been premultiplied by diag(r). the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( mb_a.eq.mb_b .and. iroffa.eq.iroffb .and. iarow.eq.ibrow ) the distributed submatrices sub( a ) and sub( b ) must verify some alignment properties, namely the following expression should be true ( nb_a.eq.nb_b .and. icoffa.eq.icoffb .and. iacol.eq.ibcol ) must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. some alignment properties, namely the following expression should be true iroffa.eq.0 .and.iroffa.eq.iroffz. and. iarow.eq.izrow) must verify some alignment properties, namely the following expressions should be true ( mb_a.eq.nb_a.eq.mb_z .and. iroffa.eq.iroffz .and. iroffa.eq.0 .and. and b( ib:ib+n-1, jb:jb+n-1 ) must verify some alignment properties, namely the following expressions should be true desca(mb_) = desca(nb_) the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). the distributed submatrix sub( a ) must verify some alignment proper- ties, namely the following expression should be true iroffa = mod( ia-1, mb_a ) and icoffa = mod( ja-1, nb_a ). must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' must verify some alignment properties, namely the following expressions should be true if storev = 'columnwise' the estimated forward error bound for each solution vector of sub( x ). if xtrue is the true solution correspondin magnitude of the largest element in (sub( x ) - xtrue) specifies the form of equilibration that was done. = 'n': no equilibration (always true if fact = 'n') diag(sr) * a * diag(sc). to select the eigenvector corresponding to the j-th eigenvalue, select(j) must be set to .true. n (global input) integer locc(jb+nrhs-1). the estimated forward error bounds for each solution vector of sub( x ). if xtrue is the tru in (sub( x ) - xtrue) divided by the magnitude of the must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if vect = 'q', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', must verify some alignment properties, namely the following expressions should be true if side = 'l', wantz (global input) logical if .true., then apply any column reflections to z as well wantz (global input) logical if .true., then apply any column reflections to z as well |
| trueA trueA the value of a is confusing. it is easiest to state the difference between trueA and a at the point that mvr2 is called the value of a is confusing. it is easiest to state the difference between trueA and a at the point that mvr2 is called the value of a is confusing. it is easiest to state the difference between trueA and a at the point that mvr2 is called the value of a is confusing. it is easiest to state the difference between trueA and a at the point that mvr2 is called |
| try try reduce its condition number. r returns the row scale factors and c the column scale factors, chosen to try to make the largest entry i b(i,j) = r(i) * a(i,j) * c(j) have absolute value 1. on entry, the hermitian matrix a. if uplo = 'u', only th the hermitian matrix. if uplo = 'l', only the lower local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, this array contains the local pieces of th the leading n-by-n upper triangular part of sub( a ) contains reduce its condition number. r returns the row scale factors and c the column scale factors, chosen to try to make the largest entry i b(i,j) = r(i) * a(i,j) * c(j) have absolute value 1. avoid overflow, the matrix must be scaled so that its largest entry is no greater than overflow**(1/2) * underflow**(1/4 be much smaller than that. on entry, the symmetric matrix a. if uplo = 'u', only th the symmetric matrix. if uplo = 'l', only the lower local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, this array contains the local pieces of th the leading n-by-n upper triangular part of sub( a ) contains reduce its condition number. r returns the row scale factors and c the column scale factors, chosen to try to make the largest entry i b(i,j) = r(i) * a(i,j) * c(j) have absolute value 1. avoid overflow, the matrix must be scaled so that its largest entry is no greater than overflow**(1/2) * underflow**(1/4 be much smaller than that. on entry, the symmetric matrix a. if uplo = 'u', only th the symmetric matrix. if uplo = 'l', only the lower local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, this array contains the local pieces of th the leading n-by-n upper triangular part of sub( a ) contains reduce its condition number. r returns the row scale factors and c the column scale factors, chosen to try to make the largest entry i b(i,j) = r(i) * a(i,j) * c(j) have absolute value 1. on entry, the hermitian matrix a. if uplo = 'u', only th the hermitian matrix. if uplo = 'l', only the lower local memory to an array of dimension (lld_a, locc(ja+n-1)). on entry, this array contains the local pieces of th the leading n-by-n upper triangular part of sub( a ) contains |
| TSCAL TSCAL scale the column norms by TSCAL if the maximum element in cnorm i scale the column norms by TSCAL if the maximum element in cnorm i |
| TST1 TST1 do 20 k = i, l + 1, -1 TST1 = cabs1( h( k-1, k-1 ) ) + cabs1( h( k, k ) $ tst1 = clanhs( '1', i-l+1, h( l, l ), ldh, work ) do 20 k = i, l + 1, -1 TST1 = abs( h( k-1, k-1 ) ) + abs( h( k, k ) $ tst1 = dlanhs( '1', i-l+1, h( l, l ), ldh, work ) do 20 k = i, l + 1, -1 TST1 = abs( h( k-1, k-1 ) ) + abs( h( k, k ) $ tst1 = slanhs( '1', i-l+1, h( l, l ), ldh, work ) do 20 k = i, l + 1, -1 TST1 = cabs1( h( k-1, k-1 ) ) + cabs1( h( k, k ) $ tst1 = zlanhs( '1', i-l+1, h( l, l ), ldh, work ) |
| TTRD TTRD at present, only n1 is used, and it (n1) is used only for 'TTRD (pjlaenv) (global or local output) integer |
| tuning tuning computers. users are encouraged to modify this subroutine to set the tuning parameters for their particular machine using the optio |
| twice twice eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
real roots: use wilkinson's shift twice eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
real roots: use wilkinson's shift twice eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pslamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
eigenvalues will be computed most accurately when abstol is
set to twice the underflow threshold 2*pdlamch('s') not zero
(mod(info/8,2).ne.0)), indicating that some eigenvalues or
|
| two two look for two consecutive small subdiagonal elements (nbulge > 1) and the first shift is starting in the middle of an unreduced hessenberg matrix because of two or more consecutiv rt2 (output) complex the two eigenvalues cs (output) real claref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei = 'l': e is the subdiagonal of l, and a = l*d*l'. (the two forms are equivalent if a is real. trans (input) character gp = ( ( oldgp+p )-( d( l )-p ) ) / $ ( two*( c*oldrp-b )+safmin (nbulge > 1) and the first shift is starting in the middle of an unreduced hessenberg matrix because of two or more consecutive smal dlaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. the two integers npact (nu. of active processors) and npst loop. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. tril(a) * v + v^t * tril(a,-1). this is performed as two local triangular matrix-vector multiplications (both i in the local computation, work( invt ) is used to compute incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. pclaconsb looks for two consecutive small subdiagonal elements b given by h44, h33, & h43h34 and see if this would make a look for two consecutive small subdiagonal elements incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. incx (global input) pointer to integer the global increment for the elements of x. only two value note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. the two integers npact (nu. of active processors) and npst loop. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. pdlaconsb looks for two consecutive small subdiagonal elements b given by h44, h33, & h43h34 and see if this would make a pdlaed2 sorts the two sets of eigenvalues together into a singl there are two ways in which deflation can occur: when two or more d (input/output) double precision array, dimension (n) on entry, d contains the eigenvalues of the two submatrices t on exit, d contains the trailing (n-k) updated eigenvalues look for two consecutive small subdiagonal elements incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. incx (global input) pointer to integer the global increment for the elements of x. only two value tril(a) * v + v^t * tril(a,-1). this is performed as two local triangular matrix-vector multiplications (both i in the local computation, work( invt ) is used to compute incx (global input) pointer to integer the global increment for the elements of x. only two value incx (global input) pointer to integer the global increment for the elements of x. only two value note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. the two integers npact (nu. of active processors) and npst loop. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. pslaconsb looks for two consecutive small subdiagonal elements b given by h44, h33, & h43h34 and see if this would make a pslaed2 sorts the two sets of eigenvalues together into a singl there are two ways in which deflation can occur: when two or more d (input/output) real array, dimension (n) on entry, d contains the eigenvalues of the two submatrices t on exit, d contains the trailing (n-k) updated eigenvalues look for two consecutive small subdiagonal elements incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. incx (global input) pointer to integer the global increment for the elements of x. only two value tril(a) * v + v^t * tril(a,-1). this is performed as two local triangular matrix-vector multiplications (both i in the local computation, work( invt ) is used to compute note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. incx (global input) pointer to integer the global increment for the elements of x. only two value note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. the two integers npact (nu. of active processors) and npst loop. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. tril(a) * v + v^t * tril(a,-1). this is performed as two local triangular matrix-vector multiplications (both i in the local computation, work( invt ) is used to compute incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. pzlaconsb looks for two consecutive small subdiagonal elements b given by h44, h33, & h43h34 and see if this would make a look for two consecutive small subdiagonal elements incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. incx (global input) integer the global increment for the elements of x. only two value incx must not be zero. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: banded codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. sub( a ) = a(ia:ia+n-1,ja:ja+n-1) and reduce its condition number (with respect to the two-norm). sr and sc contain the scal buted matrix b with elements b(i,j) = s(i)*a(i,j)*s(j) has ones on note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. note: tridiagonal codes can use either the old two dimensiona both cases *must be one-dimensional*. we describe both types below. (nbulge > 1) and the first shift is starting in the middle of an unreduced hessenberg matrix because of two or more consecutive smal slaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei look for two consecutive small subdiagonal elements (nbulge > 1) and the first shift is starting in the middle of an unreduced hessenberg matrix because of two or more consecutiv rt2 (output) complex*16 the two eigenvalues cs (output) double precision zlaref applies one or several householder reflectors of size 3 to one or two matrices (if column is specified) on either thei = 'l': e is the subdiagonal of l, and a = l*d*l'. (the two forms are equivalent if a is real. trans (input) character gp = ( ( oldgp+p )-( d( l )-p ) ) / $ ( two*( c*oldrp-b )+safmin |
| twos twos sort the eigenpairs so that they are in twos for doubl sort the eigenpairs so that they are in twos for doubl |
| type type type (global input) character* (apply from left) type (global input) character* (apply from left) desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_) the descriptor type the blacs process grid a is distribu- --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**h) if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**h) --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating pchengst calls pchegst when uplo='u', hence pchengst provides improved performance only when uplo='l', ibtype=1 pchengst also calls pchegst when insufficient workspace is pchentrd is a prototype version of pchetrd which uses tailore when the workspace provided by the user is adequate. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- ----------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies tha hessenberg. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ --------------- -------------- -------------------------------------- dt_a (global) desca[ dt_ ] the descriptor type. in this case ctxt_a (global) desca[ ctxt_ ] the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies tha hessenberg. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ --------------- -------------- -------------------------------------- dt_a (global) desca[ dt_ ] the descriptor type. in this case ctxt_a (global) desca[ ctxt_ ] the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_) the descriptor type the blacs process grid a is distribu- --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**t) if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**t) --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating pdsyngst calls pdhegst when uplo='u', hence pdhengst provides improved performance only when uplo='l', ibtype=1 pdsyngst also calls pdhegst when insufficient workspace is pdsyntrd is a prototype version of pdsytrd which uses tailore when the workspace provided by the user is adequate. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- ----------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies tha hessenberg. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ --------------- -------------- -------------------------------------- dt_a (global) desca[ dt_ ] the descriptor type. in this case ctxt_a (global) desca[ ctxt_ ] the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_) the descriptor type the blacs process grid a is distribu- --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**t) if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**t) --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating pssyngst calls pshegst when uplo='u', hence pshengst provides improved performance only when uplo='l', ibtype=1 pssyngst also calls pshegst when insufficient workspace is pssyntrd is a prototype version of pssytrd which uses tailore when the workspace provided by the user is adequate. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- ----------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dt_a (global) desca[ dt_ ] the descriptor type. in this case ctxt_a (global) desca[ ctxt_ ] the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_) the descriptor type the blacs process grid a is distribu- --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**h) if ibtype = 1, the problem is sub( a )*x = lambda*sub( b )*x inv(l)*sub( a )*inv(l**h) --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating pzhengst calls pzhegst when uplo='u', hence pzhengst provides improved performance only when uplo='l', ibtype=1 pzhengst also calls pzhegst when insufficient workspace is pzhentrd is a prototype version of pzhetrd which uses tailore when the workspace provided by the user is adequate. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- ----------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating is done without over/underflow as long as the final result cto * a(i,j) / cfrom does not over/underflow. type specifies tha hessenberg. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501), dlen >= 7 the array descriptor for the distributed matrix a. --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ desca (global and local input) integer array of dimension dlen. if 1d type (dtype_a=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. temporarily set the descriptor type to 1xp typ --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating --------------- -------------- -------------------------------------- dtype_a(global) desca( dtype_ )the descriptor type. in this case ctxt_a (global) desca( ctxt_ ) the blacs context handle, indicating type (global input) character* (apply from left) type (global input) character* (apply from left) |
| TYPE_A TYPE_A desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. desca (global and local input) integer array of dimension dlen. if 1d type (dTYPE_A=501 or 502), dlen >= 7 the array descriptor for the distributed matrix a. |
| types types descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional during execution, a label which will indicate which of the following types a column in the q2 matrix is 2 : dense; descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional during execution, a label which will indicate which of the following types a column in the q2 matrix is 2 : dense; descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: banded codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional descriptors now have *types* and differ from scalapack 1.0 note: tridiagonal codes can use either the old two dimensional |
| typically typically biggest boost in performance comes for small n, so it is wise to provide the extra workspace (typically les biggest boost in performance comes for small n, so it is wise to provide the extra workspace (typically les biggest boost in performance comes for small n, so it is wise to provide the extra workspace (typically les biggest boost in performance comes for small n, so it is wise to provide the extra workspace (typically les |