Back| Z- |
| zation zation local pieces of the factor u or l from the cholesky factori- zation sub( a ) = u**h*u or l*l**h ia (global input) integer in addition, this routine performs a global minimization and maximi local pieces of the factor u or l from the cholesky factori- zation sub( a ) = u**t*u or l*l**t ia (global input) integer in addition, this routine performs a global minimization and maximi local pieces of the factor u or l from the cholesky factori- zation sub( a ) = u**t*u or l*l**t ia (global input) integer local pieces of the factor u or l from the cholesky factori- zation sub( a ) = u**h*u or l*l**h ia (global input) integer |
| ZBDSQR ZBDSQR wbdtosvd = size*(wantu*nru + wantvt*ncvt) + max(wZBDSQR |
| ZCOMBAMAX1 ZCOMBAMAX1 ZCOMBAMAX1 finds the element having maximum real part absolut |
| Zdbtrf Zdbtrf Zdbtrf computes an lu factorization of a real m-by-n band matrix |
| ZDTTRF ZDTTRF ZDTTRF computes an lu factorization of a complex tridiagonal matrix with factors of the tridiagonal matrix a from the lu factorization computed by ZDTTRF arguments |
| ZDTTRSV ZDTTRSV ZDTTRSV solves one of the systems of equation u * x = b, u**t * x = b, or u**h * x = b, |
| Zero Zero < 0: if info = -i, the i-th argument had an illegal value > 0: if info = +i, u(i,i) is exactly Zero. the factorizatio singular, and division by zero will occur if it is used Zero the superdiagonal elements of the work array work1 where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonZeros in only the mai on entry, n specifies the order of the matrix a. n must be at least Zero < 0: if info = -i, the i-th argument had an illegal value > 0: if info = +i, u(i,i) is exactly Zero. the factorizatio singular, and division by zero will occur if it is used Zero the superdiagonal elements of the work array work1 where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonZeros in only the mai complex are together. this way one can employ 2x2 shifts easily since every 2nd subdiagonal is guaranteed to be Zero on entry, n specifies the order of the matrix a. n must be at least Zero Zero out space for filli Zero out space for filli Zero out space for filli <= m: the i-th row of the distributed matrix sub( a ) is exactly Zero matrix sub( a ) is exactly zero. 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, info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, so the solution could not be where sigma is an m-by-n matrix which is Zero except for it v is an n-by-n orthogonal matrix. the diagonal elements of sigma > 0: if info = i, and i is <= n: u(ia+i-1,ia+i-1) is exactly Zero. th factor u is exactly singular, so the solution info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ia+k-1) is exactly Zero; th computed. 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. 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. of incx are supported in this version, namely 1 and m_x. incx must not be Zero ===================================================================== set a subdiagonal to Zero now if it's possibl n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below the k-th subdiagonal are Zero. the reduction i routine returns the matrices v and t which determine q as a block of the distributed submatrix sub( a ). when m = 0, pclange is set to Zero. m >= 0 n (global input) integer if the elements of sub( x ) are all Zero and x(iax,jax) is real pclasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to Zero notes of incx are supported in this version, namely 1 and m_x. incx must not be Zero scale (local input/local output) real of incx are supported in this version, namely 1 and m_x. incx must not be Zero ===================================================================== Zero out space for filli > 0: if info = i, the (i,i) element of the factor u or l is Zero, and the inverse could not be computed ===================================================================== Zero out space for filli sub( x ). sa must be >= 0, or the subroutine will divide by Zero sx (local input/local output) complex array orthogonalized can be stored in one process. no orthogonalization will be done if orfac equals Zero orfac should be identical on all processes. info = -i. > 0: if info = k, a(ia+k-1,ja+k-1) is exactly Zero. th inverse can not be computed. > 0: if info = i, the i-th diagonal element of sub( a ) is Zero, indicating that the submatrix is singular and th Zero out space for filli Zero out space for filli Zero out space for filli <= m: the i-th row of the distributed matrix sub( a ) is exactly Zero matrix sub( a ) is exactly zero. 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, info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, so the solution could not be where sigma is an m-by-n matrix which is Zero except for it v is an n-by-n orthogonal matrix. the diagonal elements of sigma > 0: if info = i, and i is <= n: u(ia+i-1,ia+i-1) is exactly Zero. th factor u is exactly singular, so the solution info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ia+k-1) is exactly Zero; th computed. small, i.e., converged. this must be at least Zero reltol (input) double precision small, i.e., converged. note : this must be at least Zero reltol (input) double precision where z = q'u, u is a vector of length n with ones in the n1 and n1 + 1 th elements and Zeros elsewhere the eigenvectors of the original matrix are stored in q, and the the permutation used to arrange the columns of the deflated q matrix into three groups: the first group contains non-Zero non-zero elements only below n1, and the third is dense. set a subdiagonal to Zero now if it's possibl h11 = smalla(1,1,ki) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below the k-th subdiagonal are Zero. the reduction is performed by an orthogo matrices v and t which determine q as a block reflector i - v*t*v', of the distributed submatrix sub( a ). when m = 0, pdlange is set to Zero. m >= 0 n (global input) integer if the elements of sub( x ) are all Zero, then tau = 0 and h i pdlasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to Zero notes of incx are supported in this version, namely 1 and m_x. incx must not be Zero scale (local input/local output) double precision Zero out space for filli > 0: if info = i, the (i,i) element of the factor u or l is Zero, and the inverse could not be computed ===================================================================== Zero out space for filli sub( x ). sa must be >= 0, or the subroutine will divide by Zero sx (local input/local output) double precision array point number is assumed be in the 32nd bit position (c) the sign of negative Zero see w. kahan "accurate eigenvalues of a symmetric tridiagonal orthogonalized can be stored in one process. no orthogonalization will be done if orfac equals Zero orfac should be identical on all processes. 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. 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. info = -i. > 0: if info = k, a(ia+k-1,ja+k-1) is exactly Zero. th inverse can not be computed. > 0: if info = i, the i-th diagonal element of sub( a ) is Zero, indicating that the submatrix is singular and th Zero out space for filli Zero out space for filli Zero out space for filli <= m: the i-th row of the distributed matrix sub( a ) is exactly Zero matrix sub( a ) is exactly zero. 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, info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, so the solution could not be where sigma is an m-by-n matrix which is Zero except for it v is an n-by-n orthogonal matrix. the diagonal elements of sigma > 0: if info = i, and i is <= n: u(ia+i-1,ia+i-1) is exactly Zero. th factor u is exactly singular, so the solution info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ia+k-1) is exactly Zero; th computed. small, i.e., converged. this must be at least Zero reltol (input) real small, i.e., converged. note : this must be at least Zero reltol (input) real where z = q'u, u is a vector of length n with ones in the n1 and n1 + 1 th elements and Zeros elsewhere the eigenvectors of the original matrix are stored in q, and the the permutation used to arrange the columns of the deflated q matrix into three groups: the first group contains non-Zero non-zero elements only below n1, and the third is dense. set a subdiagonal to Zero now if it's possibl h11 = smalla(1,1,ki) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below the k-th subdiagonal are Zero. the reduction is performed by an orthogo matrices v and t which determine q as a block reflector i - v*t*v', of the distributed submatrix sub( a ). when m = 0, pslange is set to Zero. m >= 0 n (global input) integer if the elements of sub( x ) are all Zero, then tau = 0 and h i pslasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to Zero notes of incx are supported in this version, namely 1 and m_x. incx must not be Zero scale (local input/local output) real Zero out space for filli > 0: if info = i, the (i,i) element of the factor u or l is Zero, and the inverse could not be computed ===================================================================== Zero out space for filli sub( x ). sa must be >= 0, or the subroutine will divide by Zero sx (local input/local output) real array point number is assumed be in the 32nd or 64th bit position (c) the sign of negative Zero see w. kahan "accurate eigenvalues of a symmetric tridiagonal orthogonalized can be stored in one process. no orthogonalization will be done if orfac equals Zero orfac should be identical on all processes. 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. 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. info = -i. > 0: if info = k, a(ia+k-1,ja+k-1) is exactly Zero. th inverse can not be computed. > 0: if info = i, the i-th diagonal element of sub( a ) is Zero, indicating that the submatrix is singular and th Zero out space for filli sub( x ). sa must be >= 0, or the subroutine will divide by Zero sx (local input/local output) complex*16 array Zero out space for filli Zero out space for filli <= m: the i-th row of the distributed matrix sub( a ) is exactly Zero matrix sub( a ) is exactly zero. 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, info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, so the solution could not be where sigma is an m-by-n matrix which is Zero except for it v is an n-by-n orthogonal matrix. the diagonal elements of sigma > 0: if info = i, and i is <= n: u(ia+i-1,ia+i-1) is exactly Zero. th factor u is exactly singular, so the solution info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ja+k-1) is exactly Zero is exactly singular, and division by zero will occur if info = -i. > 0: if info = k, u(ia+k-1,ia+k-1) is exactly Zero; th computed. 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. 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. of incx are supported in this version, namely 1 and m_x. incx must not be Zero ===================================================================== set a subdiagonal to Zero now if it's possibl n-by-(n-k+1) distributed matrix a(ia:ia+n-1,ja:ja+n-k) so that elements below the k-th subdiagonal are Zero. the reduction i routine returns the matrices v and t which determine q as a block of the distributed submatrix sub( a ). when m = 0, pzlange is set to Zero. m >= 0 n (global input) integer if the elements of sub( x ) are all Zero and x(iax,jax) is real pzlasmsub looks for a small subdiagonal element from the bottom of the matrix that it can safely set to Zero notes of incx are supported in this version, namely 1 and m_x. incx must not be Zero scale (local input/local output) double precision of incx are supported in this version, namely 1 and m_x. incx must not be Zero ===================================================================== Zero out space for filli > 0: if info = i, the (i,i) element of the factor u or l is Zero, and the inverse could not be computed ===================================================================== Zero out space for filli orthogonalized can be stored in one process. no orthogonalization will be done if orfac equals Zero orfac should be identical on all processes. info = -i. > 0: if info = k, a(ia+k-1,ja+k-1) is exactly Zero. th inverse can not be computed. > 0: if info = i, the i-th diagonal element of sub( a ) is Zero, indicating that the submatrix is singular and th < 0: if info = -i, the i-th argument had an illegal value > 0: if info = +i, u(i,i) is exactly Zero. the factorizatio singular, and division by zero will occur if it is used Zero the superdiagonal elements of the work array work1 where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonZeros in only the mai complex are together. this way one can employ 2x2 shifts easily since every 2nd subdiagonal is guaranteed to be Zero on entry, n specifies the order of the matrix a. n must be at least Zero < 0: if info = -i, the i-th argument had an illegal value > 0: if info = +i, u(i,i) is exactly Zero. the factorizatio singular, and division by zero will occur if it is used Zero the superdiagonal elements of the work array work1 where l is a product of unit lower bidiagonal matrices and u is upper triangular with nonZeros in only the mai on entry, n specifies the order of the matrix a. n must be at least Zero |
| zeros zeros transformation matrix, z( k ), whose conjugate transpose is used to introduce zeros into the (m - k + 1)th row of sub( a ), is given i transformation matrix, z( k ), whose conjugate transpose is used to introduce zeros into the (m - k + 1)th row of sub( a ), is given i where z = q'u, u is a vector of length n with ones in the n1 and n1 + 1 th elements and zeros elsewhere the eigenvectors of the original matrix are stored in q, and the the factorization is obtained by householder's method. the kth transformation matrix, z( k ), which is used to introduce zeros int the factorization is obtained by householder's method. the kth transformation matrix, z( k ), which is used to introduce zeros int where z = q'u, u is a vector of length n with ones in the n1 and n1 + 1 th elements and zeros elsewhere the eigenvectors of the original matrix are stored in q, and the the factorization is obtained by householder's method. the kth transformation matrix, z( k ), which is used to introduce zeros int the factorization is obtained by householder's method. the kth transformation matrix, z( k ), which is used to introduce zeros int transformation matrix, z( k ), whose conjugate transpose is used to introduce zeros into the (m - k + 1)th row of sub( a ), is given i transformation matrix, z( k ), whose conjugate transpose is used to introduce zeros into the (m - k + 1)th row of sub( a ), is given i |
| ZGBTRS ZGBTRS update the last bw columns of a_i (code modified from ZGBTRS only the eliminations of unknowns > ln-bw have an effect on |
| ZGEBR2D ZGEBR2D the first column of a send data and only processes that own the first column of b receive data. the calls to zgebs2d/ZGEBR2D |
| ZGEBS2D ZGEBS2D the first column of a send data and only processes that own the first column of b receive data. the calls to ZGEBS2D/zgebr2 |
| ZHEEVX ZHEEVX pZHEEVX computes selected eigenvalues and, optionally, eigenvector of scalapack routines. eigenvalues/vectors can be selected by |
| ZHETRD ZHETRD support for uplo='u' is limited to calling the old, slow, pZHETRD |
| ZHSEQR ZHSEQR contain an n-by-n matrix q (usually the unitary matrix q of schur vectors returned by ZHSEQR) if howmny = 'a', the matrix y of left eigenvectors of t; |
| ZIN ZIN ZIN (local input) real array the eigenvectors on input. each eigenvector resides entirely ZIN (local input) double precision array the eigenvectors on input. each eigenvector resides entirely ZIN (local input) real array the eigenvectors on input. each eigenvector resides entirely ZIN (local input) double precision array the eigenvectors on input. each eigenvector resides entirely |
| ZLACON ZLACON the serial version of this routine was originally contributed by nick higham for use with ZLACON notes pZLACON estimates the 1-norm of a square, complex distributed matri products. x and v are aligned with the distributed matrix a, this the serial version was contributed to lapack by nick higham for use with ZLACON arguments |
| ZLADIV ZLADIV x( j ) = ZLADIV( x( j ), tjjs |
| ZLAHQR ZLAHQR necessary to scan the "tridiagonal portion of the matrix." in the lapack algorithm ZLAHQR, a loop of m goes from i-2 down t h(m,m),h(m+1,m+1),h(m+1,m),h(m,m+1),h(m-1,m-1),h(m,m-1), and necessary to scan the "tridiagonal portion of the matrix." in the lapack algorithm ZLAHQR, a loop of m goes from i-2 down t h(m,m),h(m+1,m+1),h(m+1,m),h(m,m+1),h(m-1,m-1),h(m,m-1), and ZLAHQR used to have a single row application and a singl more clever. we break each transformation down into 3 this code is basically a parallelization of the following snip of lapack code from ZLAHQR look for a single small subdiagonal element. |
| ZLAMSH ZLAMSH ZLAMSH sends multiple shifts through a small (single node) matrix t subsequent shifts in an effort to maximize the number of bulges |
| ZLANHS ZLANHS if( tst1.eq.zero ) $ tst1 = ZLANHS( '1', i-l+1, h( l, l ), ldh, work $ go to 30 |
| ZLANV2 ZLANV2 ZLANV2 computes the schur factorization of a complex 2-by- |
| ZLAREF ZLAREF ZLAREF applies one or several householder reflectors of size rows or columns. |
| zlatrd zlatrd the traditional way of computing v (and the one used in pzlatrd.f an v = tau * v the traditional way of computing v (and the one used in pzlatrd.f an v = tau * v the traditional way of computing v (and the one used in pzlatrd.f an v = tau * v the traditional way of computing v (and the one used in pzlatrd.f an v = tau * v |
| ZPTTRF ZPTTRF definite tridiagonal matrix a such that a = u**h*d*u or a = l*d*l**h (computed by ZPTTRF) arguments |
| ZPTTRSV ZPTTRSV ZPTTRSV solves one of the triangular system u * x = b, or u**h * x = b, |
| ZSTEIN ZSTEIN performance. in the limit (i.e. clustersize = n-1) pZSTEIN will perform no better than zstein on for clustersize = n/sqrt(nprow*npcol) reorthogonalizing performance. in the limit (i.e. clustersize = n-1) pZSTEIN will perform no better than zstein on 1 processor all eigenvectors will increase the total execution time pZSTEIN computes the eigenvectors of a symmetric tridiagonal matri correspond to user specified eigenvalues. pzstein does not |
| ZSTEIN2 ZSTEIN2 nvec - ceil(m/p) + 1 are guaranteed to be orthogonal ( the orthogonality is similar to that obtained from ZSTEIN2) max(5*n,np00*mq00) + ceil(m/p)*n, |
| ZSTEQR2 ZSTEQR2 > 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 |
| ZTRMM ZTRMM copy matrix hu_i (the last bwl rows of gu_i) to afl storage as per requirements of blas routine ZTRMM conjugate transpose hu_i to hu_i^c. copy matrix h_i (the last bw cols of g_i) to af storage as per requirements of blas routine ZTRMM h_i^c to h_i. |
| ZTRMVT ZTRMVT ZTRMVT performs the matrix-vector operation x := conjg( t' ) *y, and w := t *z, |
| Zurich Zurich and marbwus hegland, australian natonal university. feb., 1997. based on code written by : peter arbenz, eth Zurich, 1996 ===================================================================== and markus hegland, australian national university. feb., 1997. based on code written by : peter arbenz, eth Zurich, 1996 eth, zurich. and markus hegland, australian national university. feb., 1997. based on code written by : peter arbenz, eth Zurich, 1996 eth, zurich. and marbwus hegland, australian natonal university. feb., 1997. based on code written by : peter arbenz, eth Zurich, 1996 ===================================================================== |