| Routine : CCOMBAMAX1() | Class : | |
| Author : | Date : | Lines: 45 |
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Purpose ======= CCOMBAMAX1 finds the element having maximum real part absolute value as well as its corresponding globl index. Arguments ========= V1 (local input/local output) COMPLEX array of dimension 2. The first maximum absolute value element and its global index. V1(1) = AMAX, V1(2) = INDX. ... |
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| Routine : CDBTF2() | Class : | |
| Author : | Date : | Lines: 177 |
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.. Array Arguments .. .. Purpose ======= Cdbtrf computes an LU factorization of a real m-by-n band matrix A without using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 BLAS. Arguments ========= ... |
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| Routine : CDBTRF() | Class : | |
| Author : | Date : | Lines: 339 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : CDTTRF() | Class : | |
| Author : | Date : | Lines: 112 |
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.. Array Arguments .. .. Purpose ======= CDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. The factorization has the form A = L * U where L is a product of unit lower bidiagonal ... |
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| Routine : CDTTRSV() | Class : | |
| Author : | Date : | Lines: 206 |
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.. Array Arguments .. .. Purpose ======= CDTTRSV solves one of the systems of equations L * X = B, L**T * X = B, or L**H * X = B, U * X = B, U**T * X = B, or U**H * X = B, with factors of the tridiagonal matrix A from the LU factorization computed by CDTTRF. ... |
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| Routine : CLAHQR2() | Class : | |
| Author : | Date : | Lines: 444 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : CLAMSH() | Class : | |
| Author : | Date : | Lines: 260 |
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.. Array Arguments .. .. Purpose ======= CLAMSH sends multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. CLAMSH should only be called when there are multiple shifts/bulges ... |
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| Routine : CLANV2() | Class : | |
| Author : | Date : | Lines: 145 |
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Purpose ======= CLANV2 computes the Schur factorization of a complex 2-by-2 nonhermitian matrix in standard form: [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ] [ C D ] [ SN CS ] [ 0 DD ] [-SN CS ] Arguments ========= A (input/output) COMPLEX ... |
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| Routine : CLAREF() | Class : | |
| Author : | Date : | Lines: 331 |
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.. Array Arguments .. .. Purpose ======= CLAREF applies one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns. Arguments ========= ... |
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| Routine : CPTTRSV() | Class : | |
| Author : | Date : | Lines: 177 |
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.. Array Arguments .. .. Purpose ======= CPTTRSV solves one of the triangular systems L * X = B, or L**H * X = B, U * X = B, or U**H * X = B, where L or U is the Cholesky factor of a Hermitian positive definite tridiagonal matrix A such that ... |
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| Routine : CSTEQR2() | Class : | |
| Author : | Date : | Lines: 662 |
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Skip the current step: the subdiagonal info is just noise.
Lookahead over Inner loop If eigenvectors are desired, then save rotations. If eigenvectors are desired, then apply saved rotations. Eigenvalue found. QR Iteration Look for small superdiagonal element. If remaining matrix is 2-by-2, use SLAE2 or SLAEV2 to compute its eigensystem. ... |
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| Routine : CTRMVT() | Class : | |
| Author : | Date : | Lines: 161 |
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.. Array Arguments .. .. Purpose ======= CTRMVT performs the matrix-vector operations x := conjg( T' ) *y, and w := T *z, where x is an n element vector and T is an n by n upper or lower triangular matrix. Arguments ... |
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| Routine : DDBTF2() | Class : | |
| Author : | Date : | Lines: 174 |
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.. Array Arguments .. .. Purpose ======= Ddbtrf computes an LU factorization of a real m-by-n band matrix A without using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 BLAS. Arguments ========= ... |
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| Routine : DDBTRF() | Class : | |
| Author : | Date : | Lines: 336 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : DDTTRF() | Class : | |
| Author : | Date : | Lines: 112 |
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.. Array Arguments .. .. Purpose ======= DDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. The factorization has the form A = L * U where L is a product of unit lower bidiagonal ... |
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| Routine : DDTTRSV() | Class : | |
| Author : | Date : | Lines: 174 |
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.. Array Arguments .. .. Purpose ======= DDTTRSV solves one of the systems of equations L * X = B, L**T * X = B, or L**H * X = B, U * X = B, U**T * X = B, or U**H * X = B, with factors of the tridiagonal matrix A from the LU factorization computed by DDTTRF. ... |
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| Routine : DLAMSH() | Class : | |
| Author : | Date : | Lines: 236 |
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.. Array Arguments .. .. Purpose ======= DLAMSH sends multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. DLAMSH should only be called when there are multiple shifts/bulges ... |
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| Routine : DLAPST() | Class : | |
| Author : | Date : | Lines: 251 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. ... |
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| Routine : DLAREF() | Class : | |
| Author : | Date : | Lines: 278 |
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.. Array Arguments .. .. Purpose ======= DLAREF applies one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns. Arguments ========= ... |
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| Routine : DLASORTE() | Class : | |
| Author : | Date : | Lines: 145 |
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.. Array Arguments .. .. Purpose ======= DLASORTE sorts eigenpairs so that real eigenpairs are together and complex are together. This way one can employ 2x2 shifts easily since every 2nd subdiagonal is guaranteed to be zero. This routine does no parallel work. Arguments ... |
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| Routine : DLASRT2() | Class : | |
| Author : | Date : | Lines: 268 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. ... |
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| Routine : DPTTRSV() | Class : | |
| Author : | Date : | Lines: 132 |
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.. Array Arguments .. .. Purpose ======= DPTTRSV solves one of the triangular systems L**T* X = B, or L * X = B, where L is the Cholesky factor of a Hermitian positive definite tridiagonal matrix A such that A = L*D*L**H (computed by DPTTRF). ... |
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| Routine : DSTEIN2() | Class : | |
| Author : | Date : | Lines: 372 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : DSTEQR2() | Class : | |
| Author : | Date : | Lines: 499 |
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.. Local Scalars .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : DTRMVT() | Class : | |
| Author : | Date : | Lines: 161 |
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.. Array Arguments .. .. Purpose ======= DTRMVT performs the matrix-vector operations x := T' *y, and w := T *z, where x is an n element vector and T is an n by n upper or lower triangular matrix. Arguments ... |
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| Routine : PCDBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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.. Array Arguments .. .. Purpose ======= PCDBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PCDBTRF() | Class : | |
| Author : | Date : | Lines: 1268 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCDBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 764 |
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.. Array Arguments .. .. Purpose ======= PCDBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PCDBTRSV() | Class : | |
| Author : | Date : | Lines: 1599 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCDTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 466 |
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.. Array Arguments .. .. Purpose ======= PCDTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex tridiagonal diagonally dominant-like distributed matrix. ... |
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| Routine : PCDTTRF() | Class : | |
| Author : | Date : | Lines: 1074 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCDTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 795 |
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.. Array Arguments .. .. Purpose ======= PCDTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PCDTTRSV() | Class : | |
| Author : | Date : | Lines: 1530 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCGBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 458 |
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.. Array Arguments .. .. Purpose ======= PCGBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex banded distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PCGBTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1110 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCGBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1182 |
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.. Array Arguments .. .. Purpose ======= PCGBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PCGEBD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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.. Array Arguments .. .. Purpose ======= PCGEBD2 reduces a complex general M-by-N distributed matrix 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. Notes ... |
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| Routine : PCGEBRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 414 |
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.. Array Arguments .. .. Purpose ======= PCGEBRD reduces a complex general M-by-N distributed matrix 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. Notes ... |
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| Routine : PCGECON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 422 |
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.. Array Arguments .. .. Purpose ======= 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 the 1-norm or the infinity-norm, using the LU factorization computed by PCGETRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and ... |
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| Routine : PCGEEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 375 |
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.. Array Arguments .. .. Purpose ======= 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) and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest entry in each row and column of the distributed matrix B with elements ... |
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| Routine : PCGEHD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 294 |
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.. Array Arguments .. .. Purpose ======= PCGEHD2 reduces a complex general distributed matrix sub( A ) to upper Hessenberg form H by an unitary similarity transformation: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PCGEHRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 383 |
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.. Array Arguments .. .. Purpose ======= PCGEHRD reduces a complex general distributed matrix sub( A ) to upper Hessenberg form H by an unitary similarity transformation: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PCGELQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 274 |
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.. Array Arguments .. .. Purpose ======= PCGELQ2 computes a LQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGELQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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.. Array Arguments .. .. Purpose ======= PCGELQF computes a LQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGELS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 593 |
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.. Array Arguments .. .. Purpose ======= PCGELS solves overdetermined or underdetermined complex linear 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 of sub( A ). It is assumed that sub( A ) has full rank. The following options are provided: ... |
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| Routine : PCGEQL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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.. Array Arguments .. .. Purpose ======= PCGEQL2 computes a QL factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGEQLF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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.. Array Arguments .. .. Purpose ======= PCGEQLF computes a QL factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGEQPF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 565 |
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.. Array Arguments .. .. Purpose ======= 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. Notes ===== ... |
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| Routine : PCGEQR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 308 |
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.. Array Arguments .. .. Purpose ======= PCGEQR2 computes a QR factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGEQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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.. Array Arguments .. .. Purpose ======= PCGEQRF computes a QR factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGERFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 895 |
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.. Array Arguments .. .. Purpose ======= PCGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutions. Notes ===== ... |
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| Routine : PCGERQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 271 |
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.. Array Arguments .. .. Purpose ======= PCGERQ2 computes a RQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGERQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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.. Array Arguments .. .. Purpose ======= PCGERQF computes a RQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCGESV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 244 |
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.. Array Arguments .. .. Purpose ======= PCGESV computes the solution to a complex system of linear equations sub( A ) * X = sub( B ), where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed matrices. ... |
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| Routine : PCGESVD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 648 |
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.. Scalar Arguments ..
.. .. Array Arguments .. .. Purpose ======= PCGESVD computes the singular value decomposition (SVD) of an M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written as A = U * SIGMA * transpose(V) ... |
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| Routine : PCGESVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 830 |
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.. Array Arguments .. .. Purpose ======= PCGESVX uses the LU factorization to compute the solution to a complex system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PCGETF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 252 |
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.. Array Arguments .. .. Purpose ======= PCGETF2 computes an LU factorization of a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ... |
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| Routine : PCGETRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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.. Array Arguments .. .. Purpose ======= PCGETRF computes an LU factorization of a general M-by-N distributed matrix sub( A ) = (IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ele- ... |
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| Routine : PCGETRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 374 |
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.. Array Arguments .. .. Purpose ======= PCGETRI computes the inverse of a distributed matrix using the LU factorization computed by PCGETRF. This method inverts U and then computes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA by solving the system InvA*L = inv(U) for InvA. Notes ... |
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| Routine : PCGETRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 291 |
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.. Array Arguments .. .. Purpose ======= PCGETRS solves a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) using the LU factorization computed by PCGETRF. sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), op( A ) = A, A**T or A**H ... |
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| Routine : PCGGQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 370 |
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.. Array Arguments .. .. Purpose ======= PCGGQRF computes a generalized QR factorization of an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1): sub( A ) = Q*R, sub( B ) = Q*T*Z, where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, ... |
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| Routine : PCGGRQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 370 |
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.. Array Arguments .. .. Purpose ======= PCGGRQF computes a generalized RQ factorization of an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) and a P-by-N matrix sub( B ) = B(IB:IB+P-1,JB:JB+N-1): sub( A ) = R*Q, sub( B ) = Z*T*Q, where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, ... |
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| Routine : PCHEEV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 634 |
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.. Array Arguments .. .. Purpose ======= PCHEEV computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. In its present form, PCHEEV assumes a homogeneous system and makes only spot checks of the consistency of the eigenvalues across the ... |
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| Routine : PCHEEVD() | Class : | |
| Author : | Date : | Lines: 441 |
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.. Array Arguments .. .. Purpose ======= PCHEEVD computes all the eigenvalues and eigenvectors of a Hermitian matrix A by using a divide and conquer algorithm. Arguments ========= NP = the number of rows local to a given process. ... |
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| Routine : PCHEEVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1001 |
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.. Array Arguments .. .. Purpose ======= PCHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex hermitian matrix A by calling the recommended sequence of ScaLAPACK routines. Eigenvalues/vectors can be selected by specifying a range of values or a range of indices for the desired eigenvalues. ... |
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| Routine : PCHEGS2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 431 |
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.. Array Arguments .. .. Purpose ======= PCHEGS2 reduces a complex Hermitian-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PCHEGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 441 |
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.. Array Arguments .. .. Purpose ======= PCHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PCHEGVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 836 |
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.. Array Arguments .. .. Purpose ======= PCHEGVX computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form sub( A )*x=(lambda)*sub( B )*x, sub( A )*sub( B )x=(lambda)*x, or sub( B )*sub( A )*x=(lambda)*x. ... |
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| Routine : PCHENGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 426 |
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.. Array Arguments .. .. Purpose ======= PCHENGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. PCHENGST performs the same function as PCHEGST, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of PCHENGST). ... |
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| Routine : PCHENTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 587 |
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.. Array Arguments .. .. Bugs ==== Support for UPLO='U' is limited to calling the old, slow, PCHETRD code. Purpose ======= PCHENTRD is a prototype version of PCHETRD which uses tailored ... |
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| Routine : PCHETD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 471 |
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.. Array Arguments .. .. Purpose ======= PCHETD2 reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PCHETRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 428 |
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..
.. Array Arguments .. .. Purpose ======= PCHETRD reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PCHETTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1204 |
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..
.. Array Arguments .. .. Purpose ======= PCHETTRD reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PCLABRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 515 |
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..
.. Array Arguments .. .. Purpose ======= 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 upper or lower bidiagonal form by an unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transfor- mation to the unreduced part of sub( A ). ... |
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| Routine : PCLACGV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 188 |
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..
.. Array Arguments .. .. Purpose ======= PCLACGV conjugates a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1, and Notes ===== ... |
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| Routine : PCLACON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 384 |
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..
.. Array Arguments .. .. Purpose ======= PCLACON estimates the 1-norm of a square, complex distributed matrix A. Reverse communication is used for evaluating matrix-vector products. X and V are aligned with the distributed matrix A, this information is implicitly contained within IV, IX, DESCV, and DESCX. Notes ... |
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| Routine : PCLACONSB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 585 |
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..
.. Array Arguments .. .. Purpose ======= PCLACONSB looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift QR iteration given by H44, H33, & H43H34 and see if this would make a subdiagonal negligible. Notes ... |
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| Routine : PCLACP2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 406 |
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..
.. Array Arguments .. .. Purpose ======= PCLACP2 copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PCLACP2 performs a local copy sub( A ) := sub( B ), where sub( A ) denotes 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 is ... |
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| Routine : PCLACP3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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..
.. Array Arguments .. .. Purpose ======= PCLACP3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. Notice that the entire submatrix that is copied gets placed on one node or more. The receiving node can be specified precisely, or all nodes can receive, or just one row or column of nodes. ... |
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| Routine : PCLACPY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 231 |
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..
.. Array Arguments .. .. Purpose ======= PCLACPY copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PCLACPY performs a local copy sub( A ) := sub( B ), where sub( A ) denotes A(IA:IA+M-1,JA:JA+N-1) and sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1). Notes ... |
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| Routine : PCLAEVSWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 285 |
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.. Array Arguments .. .. Purpose ======= PCLAEVSWP moves the eigenvectors (potentially unsorted) from where they are computed, to a ScaLAPACK standard block cyclic array, sorted so that the corresponding eigenvalues are sorted. Notes ===== ... |
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| Routine : PCLAHQR() | Class : | |
| Author : | Date : | Lines: 2550 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : PCLAHRD() | Class : | |
| Author : | Date : | Lines: 290 |
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..
.. Array Arguments .. .. Purpose ======= 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 elements below the k-th subdiagonal are zero. The reduction is performed by an unitary similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block ... |
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| Routine : PCLAMR1D() | Class : | |
| Author : | Date : | Lines: 144 |
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..
.. Array Arguments .. .. Bugs ==== I am not sure that this works correctly when IB and JB are not equal to 1. Indeed, I suspect that IB should always be set to 1 or ignored with 1 used in its place. PCLAMR1D has not been tested except withint the contect of PCHEPTRD, the prototype reduction to tridiagonal form code. ... |
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| Routine : PCLANGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 324 |
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..
.. Array Arguments .. .. Purpose ======= PCLANGE returns the value of the one norm, or the Frobenius norm, 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 ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+M-1, ... |
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| Routine : PCLANHE() | Class : | |
| Author : | Date : | Lines: 948 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCLANHS() | Class : | |
| Author : | Date : | Lines: 741 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCLANSY() | Class : | |
| Author : | Date : | Lines: 835 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCLANTR() | Class : | |
| Author : | Date : | Lines: 1031 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCLAPIV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 356 |
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..
.. Array Arguments .. .. Purpose ======= PCLAPIV applies either P (permutation matrix indicated by IPIV) or inv( P ) to a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector may be distributed across a process row or a column. The pivot vector should be aligned with the distributed ... |
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| Routine : PCLAPV2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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..
.. Array Arguments .. .. Purpose ======= PCLAPV2 applies either P (permutation matrix indicated by IPIV) or inv( P ) to a M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector should be aligned with the distributed matrix A. For pivoting the rows of sub( A ), IPIV should be distributed along a ... |
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| Routine : PCLAQGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 271 |
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..
.. Array Arguments .. .. Purpose ======= PCLAQGE equilibrates a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using the row and scaling factors in the vectors R and C. Notes ===== ... |
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| Routine : PCLAQSY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 360 |
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..
.. Array Arguments .. .. Purpose ======= PCLAQSY equilibrates a symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and SC. Notes ===== ... |
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| Routine : PCLARF() | Class : | |
| Author : | Date : | Lines: 814 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PCLARFB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 889 |
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..
.. Array Arguments .. .. Purpose ======= PCLARFB applies a complex block reflector Q or its conjugate 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 ===== ... |
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| Routine : PCLARFC() | Class : | |
| Author : | Date : | Lines: 810 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PCLARFG() | Class : | |
| Author : Scalapack Team | Date : | Lines: 290 |
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..
.. Array Arguments .. .. Purpose ======= PCLARFG generates a complex elementary reflector H of order n, such that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I. ( x ) ( 0 ) where alpha is a real scalar, and sub( X ) is an (N-1)-element ... |
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| Routine : PCLARFT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 543 |
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..
.. Array Arguments .. .. Purpose ======= PCLARFT forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector ... |
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| Routine : PCLARZ() | Class : | |
| Author : | Date : | Lines: 915 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PCLARZB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 626 |
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..
.. Array Arguments .. .. Purpose ======= PCLARZB applies a complex block reflector Q or its conjugate 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. Currently, only STOREV = 'R' and DIRECT = 'B' are supported. ... |
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| Routine : PCLARZC() | Class : | |
| Author : | Date : | Lines: 917 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PCLARZT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 301 |
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..
.. Array Arguments .. .. Purpose ======= PCLARZT forms the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors as returned by PCTZRZF. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. ... |
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| Routine : PCLASCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 512 |
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..
.. Array Arguments .. .. Purpose ======= 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 is done without over/underflow as long as the final result CTO * A(I,J) / CFROM does not over/underflow. TYPE specifies that sub( A ) may be full, upper triangular, lower triangular or upper ... |
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| Routine : PCLASE2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 411 |
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..
.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. PCLASE2 requires that only dimension of the matrix operand is distributed. Notes ... |
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| Routine : PCLASET() | Class : | |
| Author : Scalapack Team | Date : | Lines: 220 |
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..
.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. Notes ===== ... |
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| Routine : PCLASMSUB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 377 |
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..
.. Array Arguments .. .. Purpose ======= PCLASMSUB looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCLASSQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 286 |
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..
.. Array Arguments .. .. Purpose ======= PCLASSQ returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, where x( i ) = sub( X ) = abs( X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ) ). The value of sumsq is assumed to be at least unity and the value of ssq will then satisfy ... |
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| Routine : PCLASWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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..
.. Array Arguments .. .. Purpose: ======== PCLASWP performs a series of row or column interchanges on 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 of sub( A ). This routine assumes that the pivoting information has already been broadcast along the process row or column. ... |
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| Routine : PCLATRA() | Class : | |
| Author : Scalapack Team | Date : | Lines: 187 |
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.. Array Arguments .. .. Purpose ======= PCLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). The result is left on every process of the grid. Notes ===== ... |
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| Routine : PCLATRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 435 |
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..
.. Array Arguments .. .. Purpose ======= PCLATRD reduces NB rows and columns of a complex Hermitian distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) to complex tridiagonal form by an unitary similarity transformation Q' * sub( A ) * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of sub( A ). ... |
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| Routine : PCLATRS() | Class : | |
| Author : | Date : | Lines: 87 |
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.. Local Scalars ..
.. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. Get grid parameters Quick return if possible |
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| Routine : PCLATRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 255 |
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.. Array Arguments .. .. Purpose ======= PCLATRZ reduces the M-by-N ( M<=N ) complex upper trapezoidal 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 ) = ( R 0 ) * Z, ... |
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| Routine : PCLATTRS() | Class : | |
| Author : | Date : | Lines: 1213 |
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..
.. Local Scalars .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. .. .. Statement Functions .. ... |
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| Routine : PCLAUU2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 214 |
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..
.. Array Arguments .. .. Purpose ======= PCLAUU2 computes the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the 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, overwriting the factor U in sub( A ). ... |
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| Routine : PCLAUUM() | Class : | |
| Author : Scalapack Team | Date : | Lines: 220 |
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..
.. Array Arguments .. .. Purpose ======= PCLAUUM computes the product U * U' or L' * L, where the triangular 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, overwriting the factor U in sub( A ). ... |
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| Routine : PCLAWIL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 273 |
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..
.. Array Arguments .. .. Purpose ======= PCLAWIL gets the transform given by H44,H33, & H43H34 into V starting at row M. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCMAX1() | Class : | |
| Author : Scalapack Team | Date : | Lines: 359 |
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..
.. Array Arguments .. .. Purpose ======= PCMAX1 computes the global index of the maximum element in absolute value of a distributed vector sub( X ). The global index is returned in INDX and the value is returned in AMAX, where sub( X ) denotes X(IX:IX+N-1,JX) if INCX = 1, X(IX,JX:JX+N-1) if INCX = M_X. ... |
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| Routine : PCPBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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..
.. Array Arguments .. .. Purpose ======= PCPBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex banded symmetric positive definite distributed matrix with bandwidth BW. ... |
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| Routine : PCPBTRF() | Class : | |
| Author : | Date : | Lines: 1510 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCPBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 753 |
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..
.. Array Arguments .. .. Purpose ======= PCPBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PCPBTRF. A(1:N, JA:JA+N-1) is an N-by-N complex ... |
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| Routine : PCPBTRSV() | Class : | |
| Author : | Date : | Lines: 1565 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCPOCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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..
.. Array Arguments .. .. Purpose ======= PCPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite distributed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by PCPOTRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and ... |
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| Routine : PCPOEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 358 |
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..
.. Array Arguments .. .. Purpose ======= PCPOEQU computes row and column scalings intended to equilibrate a distributed Hermitian positive definite matrix 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 scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled distri- ... |
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| Routine : PCPORFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 870 |
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..
.. Array Arguments .. .. Purpose ======= PCPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and provides error bounds and backward error estimates for the solutions. Notes ... |
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| Routine : PCPOSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 263 |
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..
.. Array Arguments .. .. Purpose ======= PCPOSV computes the solution to a complex system of linear equations sub( A ) * X = sub( B ), 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 ) denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed ... |
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| Routine : PCPOSVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 667 |
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..
.. Array Arguments .. .. Purpose ======= PCPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PCPOTF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 358 |
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..
.. Array Arguments .. .. Purpose ======= 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 sub( A ) = U' * U , if UPLO = 'U', or sub( A ) = L * L', if UPLO = 'L', ... |
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| Routine : PCPOTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 363 |
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..
.. Array Arguments .. .. Purpose ======= PCPOTRF computes the Cholesky factorization of an N-by-N complex hermitian positive definite distributed matrix sub( A ) denoting A(IA:IA+N-1, JA:JA+N-1). The factorization has the form sub( A ) = U' * U , if UPLO = 'U', or ... |
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| Routine : PCPOTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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..
.. Array Arguments .. .. Purpose ======= PCPOTRI computes the inverse of a complex Hermitian positive definite distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the Cholesky factorization sub( A ) = U**H*U or L*L**H computed by PCPOTRF. Notes ... |
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| Routine : PCPOTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 266 |
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..
.. Array Arguments .. .. Purpose ======= PCPOTRS solves a system of linear equations sub( A ) * X = sub( B ) A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1) 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 Cholesky ... |
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| Routine : PCPTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 461 |
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..
.. Array Arguments .. .. Purpose ======= PCPTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex tridiagonal symmetric positive definite distributed matrix. ... |
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| Routine : PCPTTRF() | Class : | |
| Author : | Date : | Lines: 1039 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCPTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 798 |
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..
.. Array Arguments .. .. Purpose ======= PCPTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PCPTTRF. A(1:N, JA:JA+N-1) is an N-by-N complex ... |
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| Routine : PCPTTRSV() | Class : | |
| Author : | Date : | Lines: 1511 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PCSRSCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 206 |
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..
.. Array Arguments .. .. Purpose ======= PCSRSCL multiplies an N-element complex distributed vector sub( X ) by the real scalar 1/a. This is done without overflow or underflow as long as the final sub( X )/a does not overflow or underflow. where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1, ... |
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| Routine : PCSTEIN() | Class : | |
| Author : Scalapack Team | Date : | Lines: 643 |
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..
.. Array Arguments .. .. Purpose ======= PCSTEIN computes the eigenvectors of a symmetric tridiagonal matrix in parallel, using inverse iteration. The eigenvectors found correspond to user specified eigenvalues. PCSTEIN does not orthogonalize vectors that are on different processes. The extent of orthogonalization is controlled by the input parameter LWORK. ... |
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| Routine : PCTRCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 431 |
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..
.. Array Arguments .. .. Purpose ======= PCTRCON estimates the reciprocal of the condition number of a triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm. 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 reciprocal ... |
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| Routine : PCTREVC() | Class : | |
| Author : Scalapack Team | Date : | Lines: 567 |
|
..
.. Array Arguments .. .. Purpose ======= 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 to an eigenvalue w are defined by: T*x = w*x, y'*T = w*y' ... |
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| Routine : PCTRRFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 806 |
|
..
.. Array Arguments .. .. Purpose ======= PCTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by PCTRTRS or some other means before entering this routine. PCTRRFS does not do iterative ... |
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| Routine : PCTRTI2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 276 |
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.. Array Arguments .. .. Purpose ======= 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 be contained in one and only one process memory space (local operation). Notes ===== ... |
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| Routine : PCTRTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 353 |
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.. Array Arguments .. .. Purpose ======= PCTRTRI computes the inverse of a upper or lower triangular distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== Each global data object is described by an associated description ... |
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| Routine : PCTRTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 335 |
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.. Array Arguments .. .. Purpose ======= PCTRTRS solves a triangular system of the form sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ) or sub( A )**H * X = sub( B ), 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 an ... |
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| Routine : PCTZRZF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 335 |
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.. Array Arguments .. .. Purpose ======= 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 means of unitary transformations. The upper trapezoidal matrix sub( A ) is factored as sub( A ) = ( R 0 ) * Z, ... |
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| Routine : PCUNG2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 279 |
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.. Array Arguments .. .. Purpose ======= PCUNG2L generates an M-by-N complex distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PCGEQLF. ... |
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| Routine : PCUNG2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 282 |
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.. Array Arguments .. .. Purpose ======= PCUNG2R generates an M-by-N complex distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PCUNGL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 290 |
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.. Array Arguments .. .. Purpose ======= PCUNGL2 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 first M rows of a product of K elementary reflectors of order N Q = H(k)' . . . H(2)' H(1)' as returned by PCGELQF. ... |
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| Routine : PCUNGLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 334 |
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.. Array Arguments .. .. Purpose ======= PCUNGLQ 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 first M rows of a product of K elementary reflectors of order N Q = H(k)' . . . H(2)' H(1)' as returned by PCGELQF. ... |
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| Routine : PCUNGQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 300 |
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.. Array Arguments .. .. Purpose ======= PCUNGQL generates an M-by-N complex distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PCGEQLF. ... |
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| Routine : PCUNGQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 336 |
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.. Array Arguments .. .. Purpose ======= PCUNGQR generates an M-by-N complex distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PCUNGR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 284 |
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.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1)' H(2)' . . . H(k)' as returned by PCGERQF. ... |
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| Routine : PCUNGRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 302 |
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.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1)' H(2)' . . . H(k)' as returned by PCGERQF. ... |
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| Routine : PCUNM2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 445 |
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.. Array Arguments .. .. Purpose ======= PCUNM2L overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNM2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 449 |
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.. Array Arguments .. .. Purpose ======= PCUNM2R overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMBR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 591 |
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.. Array Arguments .. .. Purpose ======= If VECT = 'Q', PCUNMBR overwrites the general complex distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMHR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 396 |
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.. Array Arguments .. .. Purpose ======= PCUNMHR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNML2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 402 |
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.. Array Arguments .. .. Purpose ======= PCUNML2 overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C sub( C ) * Q**H ... |
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| Routine : PCUNMLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 451 |
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.. Array Arguments .. .. Purpose ======= PCUNMLQ overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C sub( C ) * Q**H ... |
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| Routine : PCUNMQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 458 |
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.. Array Arguments .. .. Purpose ======= PCUNMQL overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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.. Array Arguments .. .. Purpose ======= PCUNMQR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 389 |
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.. Array Arguments .. .. Purpose ======= PCUNMR2 overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMR3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 395 |
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.. Array Arguments .. .. Purpose ======= PCUNMR3 overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 463 |
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.. Array Arguments .. .. Purpose ======= PCUNMRQ overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 478 |
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.. Array Arguments .. .. Purpose ======= PCUNMRZ overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PCUNMTR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 437 |
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.. Array Arguments .. .. Purpose ======= PCUNMTR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PDDBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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.. Array Arguments .. .. Purpose ======= PDDBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PDDBTRF() | Class : | |
| Author : | Date : | Lines: 1252 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDDBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 747 |
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.. Array Arguments .. .. Purpose ======= PDDBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PDDBTRSV() | Class : | |
| Author : | Date : | Lines: 1550 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDDTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 463 |
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.. Array Arguments .. .. Purpose ======= PDDTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real tridiagonal diagonally dominant-like distributed matrix. ... |
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| Routine : PDDTTRF() | Class : | |
| Author : | Date : | Lines: 1043 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDDTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 779 |
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.. Array Arguments .. .. Purpose ======= PDDTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PDDTTRSV() | Class : | |
| Author : | Date : | Lines: 1490 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDGBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 455 |
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.. Array Arguments .. .. Purpose ======= PDGBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real banded distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PDGBTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1101 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDGBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1173 |
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.. Array Arguments .. .. Purpose ======= PDGBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PDGEBD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 444 |
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.. Array Arguments .. .. Purpose ======= PDGEBD2 reduces a real general M-by-N distributed matrix 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. Notes ... |
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| Routine : PDGEBRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 412 |
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.. Array Arguments .. .. Purpose ======= PDGEBRD reduces a real general M-by-N distributed matrix 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. Notes ... |
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| Routine : PDGECON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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.. Array Arguments .. .. Purpose ======= 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-norm or the infinity-norm, using the LU factorization computed by PDGETRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and the reciprocal of the condition number is computed as ... |
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| Routine : PDGEEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 367 |
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.. Array Arguments .. .. Purpose ======= 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) and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest entry in each row and column of the distributed matrix B with elements ... |
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| Routine : PDGEHD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 294 |
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.. Array Arguments .. .. Purpose ======= PDGEHD2 reduces a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tion: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PDGEHRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 381 |
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.. Array Arguments .. .. Purpose ======= PDGEHRD reduces a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tion: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PDGELQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 271 |
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.. Array Arguments .. .. Purpose ======= PDGELQ2 computes a LQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGELQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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.. Array Arguments .. .. Purpose ======= PDGELQF computes a LQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGELS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 586 |
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.. Array Arguments .. .. Purpose ======= PDGELS solves overdetermined or underdetermined real linear 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 is assumed that sub( A ) has full rank. The following options are provided: ... |
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| Routine : PDGEQL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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.. Array Arguments .. .. Purpose ======= PDGEQL2 computes a QL factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGEQLF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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.. Array Arguments .. .. Purpose ======= PDGEQLF computes a QL factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGEQPF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 542 |
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.. Array Arguments .. .. Purpose ======= 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. Notes ===== ... |
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| Routine : PDGEQR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 308 |
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.. Array Arguments .. .. Purpose ======= PDGEQR2 computes a QR factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGEQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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.. Array Arguments .. .. Purpose ======= PDGEQRF computes a QR factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGERFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 886 |
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.. Array Arguments .. .. Purpose ======= PDGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutions. Notes ===== ... |
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| Routine : PDGERQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 269 |
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.. Array Arguments .. .. Purpose ======= PDGERQ2 computes a RQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGERQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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.. Array Arguments .. .. Purpose ======= PDGERQF computes a RQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDGESV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 244 |
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.. Array Arguments .. .. Purpose ======= PDGESV computes the solution to a real system of linear equations sub( A ) * X = sub( B ), where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed matrices. ... |
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| Routine : PDGESVD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 639 |
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.. Scalar Arguments ..
.. .. Array Arguments .. .. Purpose ======= PDGESVD computes the singular value decomposition (SVD) of an M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written as A = U * SIGMA * transpose(V) ... |
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| Routine : PDGESVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 829 |
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.. Array Arguments .. .. Purpose ======= PDGESVX uses the LU factorization to compute the solution to a real system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PDGETF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 252 |
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.. Array Arguments .. .. Purpose ======= PDGETF2 computes an LU factorization of a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ... |
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| Routine : PDGETRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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.. Array Arguments .. .. Purpose ======= PDGETRF computes an LU factorization of a general M-by-N distributed matrix sub( A ) = (IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ele- ... |
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| Routine : PDGETRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 378 |
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.. Array Arguments .. .. Purpose ======= PDGETRI computes the inverse of a distributed matrix using the LU factorization computed by PDGETRF. This method inverts U and then computes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA by solving the system InvA*L = inv(U) for InvA. Notes ... |
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| Routine : PDGETRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 291 |
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.. Array Arguments .. .. Purpose ======= PDGETRS solves a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) using the LU factorization computed by PDGETRF. sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), op( A ) = A or A**T and ... |
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| Routine : PDGGQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 370 |
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.. Array Arguments .. .. Purpose ======= PDGGQRF computes a generalized QR factorization of an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1): sub( A ) = Q*R, sub( B ) = Q*T*Z, where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal ... |
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| Routine : PDGGRQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 371 |
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..
.. Array Arguments .. .. Purpose ======= PDGGRQF computes a generalized RQ factorization of an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) and a P-by-N matrix sub( B ) = B(IB:IB+P-1,JB:JB+N-1): sub( A ) = R*Q, sub( B ) = Z*T*Q, where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal ... |
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| Routine : PDLABAD() | Class : | |
| Author : | Date : | Lines: 75 |
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..
Purpose ======= PDLABAD takes as input the values computed by PDLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large. This subroutine is intended to identify machines with a large exponent range, such as the Crays, and redefine the underflow and overflow limits to be the square roots of the values computed by PDLAMCH. This subroutine is needed because PDLAMCH does not compensate for poor arithmetic in the upper half of ... |
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| Routine : PDLABRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 494 |
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..
.. Array Arguments .. .. Purpose ======= 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 upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of sub( A ). ... |
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| Routine : PDLACON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 386 |
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..
.. Array Arguments .. .. Purpose ======= PDLACON estimates the 1-norm of a square, real distributed matrix A. Reverse communication is used for evaluating matrix-vector products. X and V are aligned with the distributed matrix A, this information is implicitly contained within IV, IX, DESCV, and DESCX. Notes ... |
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| Routine : PDLACONSB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 574 |
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..
.. Array Arguments .. .. Purpose ======= PDLACONSB looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift QR iteration given by H44, H33, & H43H34 and see if this would make a subdiagonal negligible. Notes ... |
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| Routine : PDLACP2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 406 |
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..
.. Array Arguments .. .. Purpose ======= PDLACP2 copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PDLACP2 performs a local copy sub( A ) := sub( B ), where sub( A ) denotes 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 is ... |
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| Routine : PDLACP3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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..
.. Array Arguments .. .. Purpose ======= PDLACP3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. Notice that the entire submatrix that is copied gets placed on one node or more. The receiving node can be specified precisely, or all nodes can receive, or just one row or column of nodes. ... |
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| Routine : PDLACPY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 231 |
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..
.. Array Arguments .. .. Purpose ======= PDLACPY copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PDLACPY performs a local copy sub( A ) := sub( B ), where sub( A ) denotes A(IA:IA+M-1,JA:JA+N-1) and sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1). Notes ... |
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| Routine : PDLAEBZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 332 |
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..
.. Array Arguments .. .. Purpose ======= PDLAEBZ contains the iteration loop which computes the eigenvalues contained in the input intervals [ INTVL(2*j-1), INTVL(2*j) ] where j = 1,...,MINP. It uses and computes the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix less than or equal to its argument w. ... |
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| Routine : PDLAECV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 149 |
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..
.. Array Arguments .. .. Purpose ======= PDLAECV checks if the input intervals [ INTVL(2*i-1), INTVL(2*i) ], i = KF, ... , KL-1, have "converged". PDLAECV modifies KF to be the index of the last converged interval, 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 by ... |
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| Routine : PDLAED0() | Class : | |
| Author : | Date : | Lines: 235 |
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..
.. Array Arguments .. .. Purpose ======= PDLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. Arguments ========= N (global input) INTEGER ... |
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| Routine : PDLAED1() | Class : | |
| Author : | Date : | Lines: 272 |
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..
.. Array Arguments .. .. Purpose ======= PDLAED1 computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix, in parallel. T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) where Z = Q'u, u is a vector of length N with ones in the ... |
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| Routine : PDLAED2() | Class : | |
| Author : | Date : | Lines: 455 |
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..
.. Array Arguments .. .. Purpose ======= PDLAED2 sorts the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. 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 the Z vector. For each such occurrence the order of the related secular ... |
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| Routine : PDLAED3() | Class : | |
| Author : | Date : | Lines: 360 |
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..
.. Array Arguments .. .. Purpose ======= PDLAED3 finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to SLAED4 This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in ... |
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| Routine : PDLAEDZ() | Class : | |
| Author : | Date : | Lines: 152 |
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Form z1 which consist of the last row of Q1
Proc (IQROW, IQCOL) receive the parts of z1 Form z2 which consist of the first row of Q2 Proc (IQROW, IQCOL) receive the parts of z2 proc(IQROW,IQCOL) broadcast Z=(Z1,Z2) |
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| Routine : PDLAEVSWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 284 |
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..
.. Array Arguments .. .. Purpose ======= PDLAEVSWP moves the eigenvectors (potentially unsorted) from where they are computed, to a ScaLAPACK standard block cyclic array, sorted so that the corresponding eigenvalues are sorted. Notes ===== ... |
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| Routine : PDLAHQR() | Class : | |
| Author : | Date : | Lines: 2132 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : PDLAHRD() | Class : | |
| Author : | Date : | Lines: 287 |
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..
.. Array Arguments .. .. Purpose ======= 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 the k-th subdiagonal are zero. The reduction is performed by an orthogo- nal similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V', ... |
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| Routine : PDLAMCH() | Class : | |
| Author : | Date : | Lines: 82 |
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..
Purpose ======= PDLAMCH determines double precision machine parameters. Arguments ========= ICTXT (global input) INTEGER The BLACS context handle in which the computation takes place. CMACH (global input) CHARACTER*1 ... |
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| Routine : PDLAMR1D() | Class : | |
| Author : | Date : | Lines: 144 |
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..
.. Array Arguments .. .. Bugs ==== I am not sure that this works correctly when IB and JB are not equal to 1. Indeed, I suspect that IB should always be set to 1 or ignored with 1 used in its place. PDLAMR1D has not been tested except withint the contect of PDSYPTRD, the prototype reduction to tridiagonal form code. ... |
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| Routine : PDLANGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 323 |
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..
.. Array Arguments .. .. Purpose ======= PDLANGE returns the value of the one norm, or the Frobenius norm, 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 ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+M-1, ... |
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| Routine : PDLANHS() | Class : | |
| Author : | Date : | Lines: 740 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDLANSY() | Class : | |
| Author : | Date : | Lines: 835 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDLANTR() | Class : | |
| Author : | Date : | Lines: 1030 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDLAPDCT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 95 |
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..
.. Array Arguments .. .. Purpose ======= PDLAPDCT counts the number of negative eigenvalues of (T - SIGMA I). This implementation of the Sturm Sequence loop has conditionals in the innermost loop to avoid overflow and determine the sign of a floating point number. PDLAPDCT will be referred to as the "paranoid" implementation of the Sturm Sequence loop. ... |
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| Routine : PDLAPIV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 356 |
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..
.. Array Arguments .. .. Purpose ======= PDLAPIV applies either P (permutation matrix indicated by IPIV) or inv( P ) to a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector may be distributed across a process row or a column. The pivot vector should be aligned with the distributed ... |
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| Routine : PDLAPV2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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..
.. Array Arguments .. .. Purpose ======= PDLAPV2 applies either P (permutation matrix indicated by IPIV) or inv( P ) to a M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector should be aligned with the distributed matrix A. For pivoting the rows of sub( A ), IPIV should be distributed along a ... |
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| Routine : PDLAQGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 270 |
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..
.. Array Arguments .. .. Purpose ======= PDLAQGE equilibrates a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using the row and scaling factors in the vectors R and C. Notes ===== ... |
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| Routine : PDLAQSY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 359 |
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..
.. Array Arguments .. .. Purpose ======= PDLAQSY equilibrates a symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and SC. Notes ===== ... |
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| Routine : PDLARED1D() | Class : | |
| Author : Scalapack Team | Date : | Lines: 173 |
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..
.. Array Arguments .. .. Purpose ======= PDLARED1D redistributes a 1D array It assumes that the input array, BYCOL, is distributed across rows and that all process columns contain the same copy of BYCOL. The output array, BYALL, will be identical on all processes and will contain the entire array. ... |
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| Routine : PDLARED2D() | Class : | |
| Author : Scalapack Team | Date : | Lines: 170 |
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..
.. Array Arguments .. .. Purpose ======= PDLARED2D redistributes a 1D array It assumes that the input array, BYROW, is distributed across columns and that all process rows contain the same copy of BYROW. The output array, BYALL, will be identical on all processes and will contain the entire array. ... |
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| Routine : PDLARF() | Class : | |
| Author : | Date : | Lines: 812 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PDLARFB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 886 |
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..
.. Array Arguments .. .. Purpose ======= 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) from the left or the right. Notes ===== ... |
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| Routine : PDLARFG() | Class : | |
| Author : Scalapack Team | Date : | Lines: 281 |
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..
.. Array Arguments .. .. Purpose ======= PDLARFG generates a real elementary reflector H of order n, such that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I. ( x ) ( 0 ) where alpha is a scalar, and sub( X ) is an (N-1)-element real ... |
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| Routine : PDLARFT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 538 |
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..
.. Array Arguments .. .. Purpose ======= PDLARFT forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector ... |
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| Routine : PDLARZ() | Class : | |
| Author : | Date : | Lines: 914 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PDLARZB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 612 |
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..
.. Array Arguments .. .. Purpose ======= 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) from the left or the right. Q is a product of k elementary reflectors as returned by PDTZRZF. Currently, only STOREV = 'R' and DIRECT = 'B' are supported. ... |
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| Routine : PDLARZT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 299 |
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..
.. Array Arguments .. .. Purpose ======= PDLARZT forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors as returned by PDTZRZF. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. ... |
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| Routine : PDLASCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 512 |
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..
.. Array Arguments .. .. Purpose ======= 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 is done without over/underflow as long as the final result CTO * A(I,J) / CFROM does not over/underflow. TYPE specifies that sub( A ) may be full, upper triangular, lower triangular or upper ... |
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| Routine : PDLASE2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 411 |
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..
.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. PDLASE2 requires that only dimension of the matrix operand is distributed. Notes ... |
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| Routine : PDLASET() | Class : | |
| Author : Scalapack Team | Date : | Lines: 220 |
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..
.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. Notes ===== ... |
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| Routine : PDLASMSUB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 368 |
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..
.. Array Arguments .. .. Purpose ======= PDLASMSUB looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDLASRT() | Class : | |
| Author : | Date : | Lines: 254 |
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..
.. Array Arguments .. .. Purpose ======= PDLASRT Sort the numbers in D in increasing order and the corresponding vectors in Q. Arguments ========= ID (global input) CHARACTER*1 ... |
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| Routine : PDLASSQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 263 |
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..
.. Array Arguments .. .. Purpose ======= PDLASSQ returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, where x( i ) = sub( X ) = X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ). The value of sumsq is assumed to be non-negative and scl returns the value ... |
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| Routine : PDLASWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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..
.. Array Arguments .. .. Purpose: ======== PDLASWP performs a series of row or column interchanges on 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 of sub( A ). This routine assumes that the pivoting information has already been broadcast along the process row or column. ... |
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| Routine : PDLATRA() | Class : | |
| Author : Scalapack Team | Date : | Lines: 187 |
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..
.. Array Arguments .. .. Purpose ======= PDLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). The result is left on every process of the grid. Notes ===== ... |
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| Routine : PDLATRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 415 |
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..
.. Array Arguments .. .. Purpose ======= 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 form by an orthogonal similarity transformation Q' * sub( A ) * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of sub( A ). ... |
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| Routine : PDLATRS() | Class : | |
| Author : | Date : | Lines: 87 |
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.. Local Scalars ..
.. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. Get grid parameters Quick return if possible |
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| Routine : PDLATRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 237 |
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..
.. Array Arguments .. .. Purpose ======= PDLATRZ reduces the M-by-N ( M<=N ) real upper trapezoidal 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 orthogonal transformations. The upper trapezoidal matrix sub( A ) is factored as sub( A ) = ( R 0 ) * Z, ... |
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| Routine : PDLAUU2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 205 |
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..
.. Array Arguments .. .. Purpose ======= PDLAUU2 computes the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the 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, overwriting the factor U in sub( A ). ... |
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| Routine : PDLAUUM() | Class : | |
| Author : Scalapack Team | Date : | Lines: 215 |
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..
.. Array Arguments .. .. Purpose ======= PDLAUUM computes the product U * U' or L' * L, where the triangular 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, overwriting the factor U in sub( A ). ... |
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| Routine : PDLAWIL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 262 |
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..
.. Array Arguments .. .. Purpose ======= PDLAWIL gets the transform given by H44,H33, & H43H34 into V starting at row M. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDORG2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 278 |
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..
.. Array Arguments .. .. Purpose ======= PDORG2L generates an M-by-N real distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PDGEQLF. ... |
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| Routine : PDORG2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 281 |
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..
.. Array Arguments .. .. Purpose ======= PDORG2R generates an M-by-N real distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PDORGL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 287 |
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..
.. Array Arguments .. .. Purpose ======= PDORGL2 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 first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by PDGELQF. ... |
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| Routine : PDORGLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 333 |
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..
.. Array Arguments .. .. Purpose ======= PDORGLQ 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 first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by PDGELQF. ... |
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| Routine : PDORGQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 300 |
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..
.. Array Arguments .. .. Purpose ======= PDORGQL generates an M-by-N real distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PDGEQLF. ... |
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| Routine : PDORGQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 336 |
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..
.. Array Arguments .. .. Purpose ======= PDORGQR generates an M-by-N real distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PDORGR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 281 |
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..
.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1) H(2) . . . H(k) as returned by PDGERQF. ... |
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| Routine : PDORGRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 302 |
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..
.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1) H(2) . . . H(k) as returned by PDGERQF. ... |
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| Routine : PDORM2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 432 |
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..
.. Array Arguments .. .. Purpose ======= PDORM2L overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORM2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 436 |
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..
.. Array Arguments .. .. Purpose ======= PDORM2R overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMBR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 591 |
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..
.. Array Arguments .. .. Purpose ======= If VECT = 'Q', PDORMBR overwrites the general real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMHR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 397 |
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..
.. Array Arguments .. .. Purpose ======= PDORMHR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORML2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 390 |
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..
.. Array Arguments .. .. Purpose ======= PDORML2 overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 451 |
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..
.. Array Arguments .. .. Purpose ======= PDORMLQ overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 458 |
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.. Array Arguments .. .. Purpose ======= PDORMQL overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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.. Array Arguments .. .. Purpose ======= PDORMQR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 381 |
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.. Array Arguments .. .. Purpose ======= PDORMR2 overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMR3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 390 |
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.. Array Arguments .. .. Purpose ======= PDORMR3 overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 463 |
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.. Array Arguments .. .. Purpose ======= PDORMRQ overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 478 |
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.. Array Arguments .. .. Purpose ======= PDORMRZ overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDORMTR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 437 |
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.. Array Arguments .. .. Purpose ======= PDORMTR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PDPBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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.. Array Arguments .. .. Purpose ======= PDPBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real banded symmetric positive definite distributed matrix with bandwidth BW. ... |
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| Routine : PDPBTRF() | Class : | |
| Author : | Date : | Lines: 1475 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDPBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 735 |
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.. Array Arguments .. .. Purpose ======= PDPBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PDPBTRF. A(1:N, JA:JA+N-1) is an N-by-N real ... |
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| Routine : PDPBTRSV() | Class : | |
| Author : | Date : | Lines: 1512 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDPOCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 405 |
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.. Array Arguments .. .. Purpose ======= PDPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by PDPOTRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and ... |
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| Routine : PDPOEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 357 |
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.. Array Arguments .. .. Purpose ======= PDPOEQU computes row and column scalings intended to equilibrate a distributed symmetric positive definite matrix 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 scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled distri- ... |
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| Routine : PDPORFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 861 |
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.. Array Arguments .. .. Purpose ======= PDPORFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and provides error bounds and backward error estimates for the solutions. Notes ... |
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| Routine : PDPOSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 263 |
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.. Array Arguments .. .. Purpose ======= PDPOSV computes the solution to a real system of linear equations sub( A ) * X = sub( B ), 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 ) denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed ... |
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| Routine : PDPOSVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 668 |
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.. Array Arguments .. .. Purpose ======= PDPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PDPOTF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 351 |
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.. Array Arguments .. .. Purpose ======= 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 sub( A ) = U' * U , if UPLO = 'U', or sub( A ) = L * L', if UPLO = 'L', ... |
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| Routine : PDPOTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 361 |
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.. Array Arguments .. .. Purpose ======= PDPOTRF computes the Cholesky factorization of an N-by-N real symmetric positive definite distributed matrix sub( A ) denoting A(IA:IA+N-1, JA:JA+N-1). The factorization has the form sub( A ) = U' * U , if UPLO = 'U', or ... |
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| Routine : PDPOTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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.. Array Arguments .. .. Purpose ======= PDPOTRI computes the inverse of a real symmetric positive definite distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the Cholesky factorization sub( A ) = U**T*U or L*L**T computed by PDPOTRF. Notes ... |
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| Routine : PDPOTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 264 |
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.. Array Arguments .. .. Purpose ======= PDPOTRS solves a system of linear equations sub( A ) * X = sub( B ) A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1) 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 Cholesky ... |
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| Routine : PDPTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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.. Array Arguments .. .. Purpose ======= PDPTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real tridiagonal symmetric positive definite distributed matrix. ... |
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| Routine : PDPTTRF() | Class : | |
| Author : | Date : | Lines: 1017 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDPTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 748 |
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.. Array Arguments .. .. Purpose ======= PDPTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PDPTTRF. A(1:N, JA:JA+N-1) is an N-by-N real ... |
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| Routine : PDPTTRSV() | Class : | |
| Author : | Date : | Lines: 1088 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PDRSCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 205 |
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.. Array Arguments .. .. Purpose ======= PDRSCL multiplies an N-element real distributed vector sub( X ) by the real scalar 1/a. This is done without overflow or underflow as long as the final result sub( X )/a does not overflow or underflow. where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1, X(IX:IX,JX:JX+N-1), if INCX = M_X. ... |
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| Routine : PDSTEBZ() | Class : | |
| Author : | Date : | Lines: 882 |
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.. Array Arguments .. .. Purpose ======= PDSTEBZ computes the eigenvalues of a symmetric tridiagonal matrix in parallel. The user may ask for all eigenvalues, all eigenvalues in the interval [VL, VU], or the eigenvalues indexed IL through IU. A static partitioning of work is done at the beginning of PDSTEBZ which results in all processes finding an (almost) equal number of ... |
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| Routine : PDSTEDC() | Class : | |
| Author : | Date : | Lines: 268 |
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.. Array Arguments .. .. Purpose ======= PDSTEDC computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix in parallel, using the divide and conquer algorithm. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in ... |
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| Routine : PDSTEIN() | Class : | |
| Author : Scalapack Team | Date : | Lines: 643 |
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.. Array Arguments .. .. Purpose ======= PDSTEIN computes the eigenvectors of a symmetric tridiagonal matrix in parallel, using inverse iteration. The eigenvectors found correspond to user specified eigenvalues. PDSTEIN does not orthogonalize vectors that are on different processes. The extent of orthogonalization is controlled by the input parameter LWORK. ... |
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| Routine : PDSYEV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 578 |
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.. Array Arguments .. .. Purpose ======= PDSYEV computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. In its present form, PDSYEV assumes a homogeneous system and makes no checks for consistency of the eigenvalues or eigenvectors across ... |
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| Routine : PDSYEVD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 352 |
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.. Array Arguments .. .. Purpose ======= PDSYEVD computes all the eigenvalues and eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. In its present form, PDSYEVD assumes a homogeneous system and makes no checks for consistency of the eigenvalues or eigenvectors across ... |
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| Routine : PDSYEVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 975 |
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.. Array Arguments .. .. Purpose ======= PDSYEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. Eigenvalues/vectors can be selected by specifying a range of values or a range of indices for the desired eigenvalues. ... |
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| Routine : PDSYGS2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 419 |
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.. Array Arguments .. .. Purpose ======= PDSYGS2 reduces a real symmetric-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PDSYGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 438 |
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.. Array Arguments .. .. Purpose ======= PDSYGST reduces a real symmetric-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PDSYGVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 819 |
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.. Array Arguments .. .. Purpose ======= PDSYGVX computes all the eigenvalues, and optionally, the eigenvectors of a real generalized SY-definite eigenproblem, of the form sub( A )*x=(lambda)*sub( B )*x, sub( A )*sub( B )x=(lambda)*x, or sub( B )*sub( A )*x=(lambda)*x. ... |
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| Routine : PDSYNGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 423 |
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.. Array Arguments .. .. Purpose ======= PDSYNGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. PDSYNGST performs the same function as PDHEGST, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of PDSYNGST). ... |
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| Routine : PDSYNTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 552 |
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.. Array Arguments .. .. Bugs ==== Support for UPLO='U' is limited to calling the old, slow, PDSYTRD code. Purpose ======= PDSYNTRD is a prototype version of PDSYTRD which uses tailored ... |
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| Routine : PDSYTD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 464 |
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.. Array Arguments .. .. Purpose ======= PDSYTD2 reduces a real symmetric matrix sub( A ) to symmetric tridiagonal form T by an orthogonal similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PDSYTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 425 |
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.. Array Arguments .. .. Purpose ======= PDSYTRD reduces a real symmetric matrix sub( A ) to symmetric tridiagonal form T by an orthogonal similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PDSYTTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1199 |
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.. Array Arguments .. .. Purpose ======= PDSYTTRD reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PDTRCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 426 |
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.. Array Arguments .. .. Purpose ======= PDTRCON estimates the reciprocal of the condition number of a triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm. 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 reciprocal ... |
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| Routine : PDTRRFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 796 |
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.. Array Arguments .. .. Purpose ======= PDTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by PDTRTRS or some other means before entering this routine. PDTRRFS does not do iterative ... |
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| Routine : PDTRTI2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 276 |
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.. Array Arguments .. .. Purpose ======= 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 be contained in one and only one process memory space (local operation). Notes ===== ... |
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| Routine : PDTRTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 353 |
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.. Array Arguments .. .. Purpose ======= PDTRTRI computes the inverse of a upper or lower triangular distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== Each global data object is described by an associated description ... |
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| Routine : PDTRTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 333 |
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.. Array Arguments .. .. Purpose ======= PDTRTRS solves a triangular system of the form sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ), 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 an N-by-NRHS distributed matrix denoted by sub( B ). A check is made ... |
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| Routine : PDTZRZF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 334 |
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.. Array Arguments .. .. Purpose ======= 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 means of orthogonal transformations. The upper trapezoidal matrix sub( A ) is factored as sub( A ) = ( R 0 ) * Z, ... |
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| Routine : PDZSUM1() | Class : | |
| Author : Scalapack Team | Date : | Lines: 224 |
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.. Array Arguments .. .. Purpose ======= 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, X(IX:IX,JX:JX+N-1), if INCX = M_X. Based on PDZASUM from the Level 1 PBLAS. The change is ... |
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| Routine : PJLAENV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 364 |
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Purpose ======= PJLAENV is called from the ScaLAPACK symmetric and Hermitian tailored eigen-routines to choose problem-dependent parameters for the local environment. See ISPEC for a description of the parameters. This version provides a set of parameters which should give good, but not optimal, performance on many of the currently available computers. Users are encouraged to modify this subroutine to set ... |
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| Routine : PSCSUM1() | Class : | |
| Author : Scalapack Team | Date : | Lines: 224 |
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.. Array Arguments .. .. Purpose ======= 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, X(IX:IX,JX:JX+N-1), if INCX = M_X. Based on PSCASUM from the Level 1 PBLAS. The change is ... |
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| Routine : PSDBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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.. Array Arguments .. .. Purpose ======= PSDBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PSDBTRF() | Class : | |
| Author : | Date : | Lines: 1252 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSDBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 747 |
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.. Array Arguments .. .. Purpose ======= PSDBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PSDBTRSV() | Class : | |
| Author : | Date : | Lines: 1550 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSDTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 463 |
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.. Array Arguments .. .. Purpose ======= PSDTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real tridiagonal diagonally dominant-like distributed matrix. ... |
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| Routine : PSDTTRF() | Class : | |
| Author : | Date : | Lines: 1043 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSDTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 779 |
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.. Array Arguments .. .. Purpose ======= PSDTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PSDTTRSV() | Class : | |
| Author : | Date : | Lines: 1490 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSGBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 455 |
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.. Array Arguments .. .. Purpose ======= PSGBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real banded distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PSGBTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1101 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSGBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1173 |
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.. Array Arguments .. .. Purpose ======= PSGBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PSGEBD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 444 |
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.. Array Arguments .. .. Purpose ======= PSGEBD2 reduces a real general M-by-N distributed matrix 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. Notes ... |
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| Routine : PSGEBRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 412 |
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.. Array Arguments .. .. Purpose ======= PSGEBRD reduces a real general M-by-N distributed matrix 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. Notes ... |
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| Routine : PSGECON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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.. Array Arguments .. .. Purpose ======= 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-norm or the infinity-norm, using the LU factorization computed by PSGETRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and the reciprocal of the condition number is computed as ... |
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| Routine : PSGEEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 367 |
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.. Array Arguments .. .. Purpose ======= 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) and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest entry in each row and column of the distributed matrix B with elements ... |
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| Routine : PSGEHD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 294 |
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..
.. Array Arguments .. .. Purpose ======= PSGEHD2 reduces a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tion: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PSGEHRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 381 |
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..
.. Array Arguments .. .. Purpose ======= PSGEHRD reduces a real general distributed matrix sub( A ) to upper Hessenberg form H by an orthogonal similarity transforma- tion: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PSGELQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 271 |
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..
.. Array Arguments .. .. Purpose ======= PSGELQ2 computes a LQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGELQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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..
.. Array Arguments .. .. Purpose ======= PSGELQF computes a LQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGELS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 586 |
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..
.. Array Arguments .. .. Purpose ======= PSGELS solves overdetermined or underdetermined real linear 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 is assumed that sub( A ) has full rank. The following options are provided: ... |
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| Routine : PSGEQL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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..
.. Array Arguments .. .. Purpose ======= PSGEQL2 computes a QL factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGEQLF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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..
.. Array Arguments .. .. Purpose ======= PSGEQLF computes a QL factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGEQPF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 541 |
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..
.. Array Arguments .. .. Purpose ======= 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. Notes ===== ... |
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| Routine : PSGEQR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 308 |
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..
.. Array Arguments .. .. Purpose ======= PSGEQR2 computes a QR factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGEQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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..
.. Array Arguments .. .. Purpose ======= PSGEQRF computes a QR factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGERFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 886 |
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..
.. Array Arguments .. .. Purpose ======= PSGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutions. Notes ===== ... |
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| Routine : PSGERQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 269 |
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..
.. Array Arguments .. .. Purpose ======= PSGERQ2 computes a RQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGERQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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..
.. Array Arguments .. .. Purpose ======= PSGERQF computes a RQ factorization of a real distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSGESV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 244 |
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..
.. Array Arguments .. .. Purpose ======= PSGESV computes the solution to a real system of linear equations sub( A ) * X = sub( B ), where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed matrices. ... |
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| Routine : PSGESVD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 639 |
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.. Scalar Arguments ..
.. .. Array Arguments .. .. Purpose ======= PSGESVD computes the singular value decomposition (SVD) of an M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written as A = U * SIGMA * transpose(V) ... |
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| Routine : PSGESVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 829 |
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..
.. Array Arguments .. .. Purpose ======= PSGESVX uses the LU factorization to compute the solution to a real system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PSGETF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 252 |
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..
.. Array Arguments .. .. Purpose ======= PSGETF2 computes an LU factorization of a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ... |
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| Routine : PSGETRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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..
.. Array Arguments .. .. Purpose ======= PSGETRF computes an LU factorization of a general M-by-N distributed matrix sub( A ) = (IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ele- ... |
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| Routine : PSGETRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 374 |
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..
.. Array Arguments .. .. Purpose ======= PSGETRI computes the inverse of a distributed matrix using the LU factorization computed by PSGETRF. This method inverts U and then computes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA by solving the system InvA*L = inv(U) for InvA. Notes ... |
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| Routine : PSGETRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 291 |
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..
.. Array Arguments .. .. Purpose ======= PSGETRS solves a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) using the LU factorization computed by PSGETRF. sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), op( A ) = A or A**T and ... |
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| Routine : PSGGQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 370 |
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..
.. Array Arguments .. .. Purpose ======= PSGGQRF computes a generalized QR factorization of an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1): sub( A ) = Q*R, sub( B ) = Q*T*Z, where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal ... |
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| Routine : PSGGRQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 371 |
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..
.. Array Arguments .. .. Purpose ======= PSGGRQF computes a generalized RQ factorization of an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) and a P-by-N matrix sub( B ) = B(IB:IB+P-1,JB:JB+N-1): sub( A ) = R*Q, sub( B ) = Z*T*Q, where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal ... |
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| Routine : PSLABAD() | Class : | |
| Author : | Date : | Lines: 75 |
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..
Purpose ======= PSLABAD takes as input the values computed by PSLAMCH for underflow and overflow, and returns the square root of each of these values if the log of LARGE is sufficiently large. This subroutine is intended to identify machines with a large exponent range, such as the Crays, and redefine the underflow and overflow limits to be the square roots of the values computed by PSLAMCH. This subroutine is needed because PSLAMCH does not compensate for poor arithmetic in the upper half of ... |
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| Routine : PSLABRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 494 |
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..
.. Array Arguments .. .. Purpose ======= 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 upper or lower bidiagonal form by an orthogonal transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transformation to the unreduced part of sub( A ). ... |
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| Routine : PSLACON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 386 |
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..
.. Array Arguments .. .. Purpose ======= PSLACON estimates the 1-norm of a square, real distributed matrix A. Reverse communication is used for evaluating matrix-vector products. X and V are aligned with the distributed matrix A, this information is implicitly contained within IV, IX, DESCV, and DESCX. Notes ... |
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| Routine : PSLACONSB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 574 |
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..
.. Array Arguments .. .. Purpose ======= PSLACONSB looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift QR iteration given by H44, H33, & H43H34 and see if this would make a subdiagonal negligible. Notes ... |
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| Routine : PSLACP2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 406 |
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..
.. Array Arguments .. .. Purpose ======= PSLACP2 copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PSLACP2 performs a local copy sub( A ) := sub( B ), where sub( A ) denotes 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 is ... |
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| Routine : PSLACP3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 307 |
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..
.. Array Arguments .. .. Purpose ======= PSLACP3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. Notice that the entire submatrix that is copied gets placed on one node or more. The receiving node can be specified precisely, or all nodes can receive, or just one row or column of nodes. ... |
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| Routine : PSLACPY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 231 |
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..
.. Array Arguments .. .. Purpose ======= PSLACPY copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PSLACPY performs a local copy sub( A ) := sub( B ), where sub( A ) denotes A(IA:IA+M-1,JA:JA+N-1) and sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1). Notes ... |
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| Routine : PSLAEBZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 326 |
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..
.. Array Arguments .. .. Purpose ======= PSLAEBZ contains the iteration loop which computes the eigenvalues contained in the input intervals [ INTVL(2*j-1), INTVL(2*j) ] where j = 1,...,MINP. It uses and computes the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix less than or equal to its argument w. ... |
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| Routine : PSLAECV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 149 |
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..
.. Array Arguments .. .. Purpose ======= PSLAECV checks if the input intervals [ INTVL(2*i-1), INTVL(2*i) ], i = KF, ... , KL-1, have "converged". PSLAECV modifies KF to be the index of the last converged interval, 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 by ... |
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| Routine : PSLAED0() | Class : | |
| Author : | Date : | Lines: 231 |
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..
.. Array Arguments .. .. Purpose ======= PSLAED0 computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. Arguments ========= N (global input) INTEGER ... |
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| Routine : PSLAED1() | Class : | |
| Author : | Date : | Lines: 271 |
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..
.. Array Arguments .. .. Purpose ======= PSLAED1 computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix, in parallel. T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) where Z = Q'u, u is a vector of length N with ones in the ... |
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| Routine : PSLAED2() | Class : | |
| Author : | Date : | Lines: 453 |
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..
.. Array Arguments .. .. Purpose ======= PSLAED2 sorts the two sets of eigenvalues together into a single sorted set. Then it tries to deflate the size of the problem. 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 the Z vector. For each such occurrence the order of the related secular ... |
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| Routine : PSLAED3() | Class : | |
| Author : | Date : | Lines: 356 |
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..
.. Array Arguments .. .. Purpose ======= PSLAED3 finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K. It makes the appropriate calls to SLAED4 This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in ... |
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| Routine : PSLAEDZ() | Class : | |
| Author : | Date : | Lines: 153 |
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Form z1 which consist of the last row of Q1
Proc (IQROW, IQCOL) receive the parts of z1 Form z2 which consist of the first row of Q2 Proc (IQROW, IQCOL) receive the parts of z2 proc(IQROW,IQCOL) broadcast Z=(Z1,Z2) |
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| Routine : PSLAEVSWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 284 |
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..
.. Array Arguments .. .. Purpose ======= PSLAEVSWP moves the eigenvectors (potentially unsorted) from where they are computed, to a ScaLAPACK standard block cyclic array, sorted so that the corresponding eigenvalues are sorted. Notes ===== ... |
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| Routine : PSLAHQR() | Class : | |
| Author : | Date : | Lines: 2132 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : PSLAHRD() | Class : | |
| Author : | Date : | Lines: 287 |
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..
.. Array Arguments .. .. Purpose ======= 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 the k-th subdiagonal are zero. The reduction is performed by an orthogo- nal similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block reflector I - V*T*V', ... |
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| Routine : PSLAMCH() | Class : | |
| Author : | Date : | Lines: 82 |
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..
Purpose ======= PSLAMCH determines single precision machine parameters. Arguments ========= ICTXT (global input) INTEGER The BLACS context handle in which the computation takes place. CMACH (global input) CHARACTER*1 ... |
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| Routine : PSLAMR1D() | Class : | |
| Author : | Date : | Lines: 144 |
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..
.. Array Arguments .. .. Bugs ==== I am not sure that this works correctly when IB and JB are not equal to 1. Indeed, I suspect that IB should always be set to 1 or ignored with 1 used in its place. PSLAMR1D has not been tested except withint the contect of PSSYPTRD, the prototype reduction to tridiagonal form code. ... |
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| Routine : PSLANGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 323 |
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..
.. Array Arguments .. .. Purpose ======= PSLANGE returns the value of the one norm, or the Frobenius norm, 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 ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+M-1, ... |
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| Routine : PSLANHS() | Class : | |
| Author : | Date : | Lines: 740 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSLANSY() | Class : | |
| Author : | Date : | Lines: 834 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSLANTR() | Class : | |
| Author : | Date : | Lines: 1030 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSLAPDCT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 95 |
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..
.. Array Arguments .. .. Purpose ======= PSLAPDCT counts the number of negative eigenvalues of (T - SIGMA I). This implementation of the Sturm Sequence loop has conditionals in the innermost loop to avoid overflow and determine the sign of a floating point number. PSLAPDCT will be referred to as the "paranoid" implementation of the Sturm Sequence loop. ... |
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| Routine : PSLAPIV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 356 |
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..
.. Array Arguments .. .. Purpose ======= PSLAPIV applies either P (permutation matrix indicated by IPIV) or inv( P ) to a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector may be distributed across a process row or a column. The pivot vector should be aligned with the distributed ... |
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| Routine : PSLAPV2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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..
.. Array Arguments .. .. Purpose ======= PSLAPV2 applies either P (permutation matrix indicated by IPIV) or inv( P ) to a M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector should be aligned with the distributed matrix A. For pivoting the rows of sub( A ), IPIV should be distributed along a ... |
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| Routine : PSLAQGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 270 |
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..
.. Array Arguments .. .. Purpose ======= PSLAQGE equilibrates a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using the row and scaling factors in the vectors R and C. Notes ===== ... |
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| Routine : PSLAQSY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 359 |
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..
.. Array Arguments .. .. Purpose ======= PSLAQSY equilibrates a symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and SC. Notes ===== ... |
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| Routine : PSLARED1D() | Class : | |
| Author : Scalapack Team | Date : | Lines: 172 |
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..
.. Array Arguments .. .. Purpose ======= PSLARED1D redistributes a 1D array It assumes that the input array, BYCOL, is distributed across rows and that all process columns contain the same copy of BYCOL. The output array, BYALL, will be identical on all processes and will contain the entire array. ... |
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| Routine : PSLARED2D() | Class : | |
| Author : Scalapack Team | Date : | Lines: 170 |
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..
.. Array Arguments .. .. Purpose ======= PSLARED2D redistributes a 1D array It assumes that the input array, BYROW, is distributed across columns and that all process rows contain the same copy of BYROW. The output array, BYALL, will be identical on all processes and will contain the entire array. ... |
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| Routine : PSLARF() | Class : | |
| Author : | Date : | Lines: 812 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PSLARFB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 886 |
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..
.. Array Arguments .. .. Purpose ======= 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) from the left or the right. Notes ===== ... |
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| Routine : PSLARFG() | Class : | |
| Author : Scalapack Team | Date : | Lines: 281 |
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..
.. Array Arguments .. .. Purpose ======= PSLARFG generates a real elementary reflector H of order n, such that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I. ( x ) ( 0 ) where alpha is a scalar, and sub( X ) is an (N-1)-element real ... |
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| Routine : PSLARFT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 538 |
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..
.. Array Arguments .. .. Purpose ======= PSLARFT forms the triangular factor T of a real block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector ... |
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| Routine : PSLARZ() | Class : | |
| Author : | Date : | Lines: 914 |
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..
.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PSLARZB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 613 |
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..
.. Array Arguments .. .. Purpose ======= 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) from the left or the right. Q is a product of k elementary reflectors as returned by PSTZRZF. Currently, only STOREV = 'R' and DIRECT = 'B' are supported. ... |
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| Routine : PSLARZT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 299 |
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..
.. Array Arguments .. .. Purpose ======= PSLARZT forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors as returned by PSTZRZF. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. ... |
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| Routine : PSLASCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 512 |
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..
.. Array Arguments .. .. Purpose ======= 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 is done without over/underflow as long as the final result CTO * A(I,J) / CFROM does not over/underflow. TYPE specifies that sub( A ) may be full, upper triangular, lower triangular or upper ... |
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| Routine : PSLASE2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 411 |
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..
.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. PSLASE2 requires that only dimension of the matrix operand is distributed. Notes ... |
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| Routine : PSLASET() | Class : | |
| Author : Scalapack Team | Date : | Lines: 220 |
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..
.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. Notes ===== ... |
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| Routine : PSLASMSUB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 368 |
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..
.. Array Arguments .. .. Purpose ======= PSLASMSUB looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSLASRT() | Class : | |
| Author : | Date : | Lines: 254 |
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..
.. Array Arguments .. .. Purpose ======= PSLASRT Sort the numbers in D in increasing order and the corresponding vectors in Q. Arguments ========= ID (global input) CHARACTER*1 ... |
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| Routine : PSLASSQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 263 |
|
..
.. Array Arguments .. .. Purpose ======= PSLASSQ returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, where x( i ) = sub( X ) = X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ). The value of sumsq is assumed to be non-negative and scl returns the value ... |
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| Routine : PSLASWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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..
.. Array Arguments .. .. Purpose: ======== PSLASWP performs a series of row or column interchanges on 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 of sub( A ). This routine assumes that the pivoting information has already been broadcast along the process row or column. ... |
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| Routine : PSLATRA() | Class : | |
| Author : Scalapack Team | Date : | Lines: 187 |
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..
.. Array Arguments .. .. Purpose ======= PSLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). The result is left on every process of the grid. Notes ===== ... |
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| Routine : PSLATRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 415 |
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..
.. Array Arguments .. .. Purpose ======= 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 form by an orthogonal similarity transformation Q' * sub( A ) * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of sub( A ). ... |
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| Routine : PSLATRS() | Class : | |
| Author : | Date : | Lines: 87 |
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.. Local Scalars ..
.. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. Get grid parameters Quick return if possible |
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| Routine : PSLATRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 237 |
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..
.. Array Arguments .. .. Purpose ======= PSLATRZ reduces the M-by-N ( M<=N ) real upper trapezoidal 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 orthogonal transformations. The upper trapezoidal matrix sub( A ) is factored as sub( A ) = ( R 0 ) * Z, ... |
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| Routine : PSLAUU2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 205 |
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..
.. Array Arguments .. .. Purpose ======= PSLAUU2 computes the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the 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, overwriting the factor U in sub( A ). ... |
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| Routine : PSLAUUM() | Class : | |
| Author : Scalapack Team | Date : | Lines: 215 |
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..
.. Array Arguments .. .. Purpose ======= PSLAUUM computes the product U * U' or L' * L, where the triangular 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, overwriting the factor U in sub( A ). ... |
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| Routine : PSLAWIL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 262 |
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..
.. Array Arguments .. .. Purpose ======= PSLAWIL gets the transform given by H44,H33, & H43H34 into V starting at row M. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSORG2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 278 |
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..
.. Array Arguments .. .. Purpose ======= PSORG2L generates an M-by-N real distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PSGEQLF. ... |
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| Routine : PSORG2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 281 |
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..
.. Array Arguments .. .. Purpose ======= PSORG2R generates an M-by-N real distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PSORGL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 287 |
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..
.. Array Arguments .. .. Purpose ======= PSORGL2 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 first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by PSGELQF. ... |
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| Routine : PSORGLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 333 |
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..
.. Array Arguments .. .. Purpose ======= PSORGLQ 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 first M rows of a product of K elementary reflectors of order N Q = H(k) . . . H(2) H(1) as returned by PSGELQF. ... |
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| Routine : PSORGQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 300 |
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..
.. Array Arguments .. .. Purpose ======= PSORGQL generates an M-by-N real distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PSGEQLF. ... |
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| Routine : PSORGQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 336 |
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..
.. Array Arguments .. .. Purpose ======= PSORGQR generates an M-by-N real distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PSORGR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 281 |
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..
.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1) H(2) . . . H(k) as returned by PSGERQF. ... |
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| Routine : PSORGRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 302 |
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..
.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1) H(2) . . . H(k) as returned by PSGERQF. ... |
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| Routine : PSORM2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 432 |
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..
.. Array Arguments .. .. Purpose ======= PSORM2L overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORM2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 436 |
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..
.. Array Arguments .. .. Purpose ======= PSORM2R overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMBR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 591 |
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..
.. Array Arguments .. .. Purpose ======= If VECT = 'Q', PSORMBR overwrites the general real distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMHR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 397 |
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..
.. Array Arguments .. .. Purpose ======= PSORMHR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORML2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 390 |
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..
.. Array Arguments .. .. Purpose ======= PSORML2 overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 451 |
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..
.. Array Arguments .. .. Purpose ======= PSORMLQ overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 458 |
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..
.. Array Arguments .. .. Purpose ======= PSORMQL overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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..
.. Array Arguments .. .. Purpose ======= PSORMQR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 381 |
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..
.. Array Arguments .. .. Purpose ======= PSORMR2 overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMR3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 390 |
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..
.. Array Arguments .. .. Purpose ======= PSORMR3 overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 463 |
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..
.. Array Arguments .. .. Purpose ======= PSORMRQ overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 478 |
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..
.. Array Arguments .. .. Purpose ======= PSORMRZ overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSORMTR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 437 |
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..
.. Array Arguments .. .. Purpose ======= PSORMTR overwrites the general real M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'T': Q**T * sub( C ) sub( C ) * Q**T ... |
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| Routine : PSPBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 450 |
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..
.. Array Arguments .. .. Purpose ======= PSPBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real banded symmetric positive definite distributed matrix with bandwidth BW. ... |
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| Routine : PSPBTRF() | Class : | |
| Author : | Date : | Lines: 1475 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSPBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 735 |
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..
.. Array Arguments .. .. Purpose ======= PSPBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PSPBTRF. A(1:N, JA:JA+N-1) is an N-by-N real ... |
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| Routine : PSPBTRSV() | Class : | |
| Author : | Date : | Lines: 1511 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSPOCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 405 |
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..
.. Array Arguments .. .. Purpose ======= PSPOCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite distributed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by PSPOTRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and ... |
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| Routine : PSPOEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 357 |
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..
.. Array Arguments .. .. Purpose ======= PSPOEQU computes row and column scalings intended to equilibrate a distributed symmetric positive definite matrix 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 scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled distri- ... |
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| Routine : PSPORFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 861 |
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..
.. Array Arguments .. .. Purpose ======= PSPORFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and provides error bounds and backward error estimates for the solutions. Notes ... |
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| Routine : PSPOSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 263 |
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..
.. Array Arguments .. .. Purpose ======= PSPOSV computes the solution to a real system of linear equations sub( A ) * X = sub( B ), 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 ) denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed ... |
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| Routine : PSPOSVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 668 |
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..
.. Array Arguments .. .. Purpose ======= PSPOSVX uses the Cholesky factorization A = U**T*U or A = L*L**T to compute the solution to a real system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PSPOTF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 351 |
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..
.. Array Arguments .. .. Purpose ======= 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 sub( A ) = U' * U , if UPLO = 'U', or sub( A ) = L * L', if UPLO = 'L', ... |
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| Routine : PSPOTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 361 |
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..
.. Array Arguments .. .. Purpose ======= PSPOTRF computes the Cholesky factorization of an N-by-N real symmetric positive definite distributed matrix sub( A ) denoting A(IA:IA+N-1, JA:JA+N-1). The factorization has the form sub( A ) = U' * U , if UPLO = 'U', or ... |
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| Routine : PSPOTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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..
.. Array Arguments .. .. Purpose ======= PSPOTRI computes the inverse of a real symmetric positive definite distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the Cholesky factorization sub( A ) = U**T*U or L*L**T computed by PSPOTRF. Notes ... |
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| Routine : PSPOTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 264 |
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..
.. Array Arguments .. .. Purpose ======= PSPOTRS solves a system of linear equations sub( A ) * X = sub( B ) A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1) 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 Cholesky ... |
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| Routine : PSPTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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..
.. Array Arguments .. .. Purpose ======= PSPTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N real tridiagonal symmetric positive definite distributed matrix. ... |
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| Routine : PSPTTRF() | Class : | |
| Author : | Date : | Lines: 1017 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSPTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 748 |
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..
.. Array Arguments .. .. Purpose ======= PSPTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PSPTTRF. A(1:N, JA:JA+N-1) is an N-by-N real ... |
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| Routine : PSPTTRSV() | Class : | |
| Author : | Date : | Lines: 1088 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PSRSCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 205 |
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..
.. Array Arguments .. .. Purpose ======= PSRSCL multiplies an N-element real distributed vector sub( X ) by the real scalar 1/a. This is done without overflow or underflow as long as the final result sub( X )/a does not overflow or underflow. where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1, X(IX:IX,JX:JX+N-1), if INCX = M_X. ... |
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| Routine : PSSTEBZ() | Class : | |
| Author : | Date : | Lines: 872 |
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..
.. Array Arguments .. .. Purpose ======= PSSTEBZ computes the eigenvalues of a symmetric tridiagonal matrix in parallel. The user may ask for all eigenvalues, all eigenvalues in the interval [VL, VU], or the eigenvalues indexed IL through IU. A static partitioning of work is done at the beginning of PSSTEBZ which results in all processes finding an (almost) equal number of ... |
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| Routine : PSSTEDC() | Class : | |
| Author : | Date : | Lines: 267 |
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..
.. Array Arguments .. .. Purpose ======= PSSTEDC computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix in parallel, using the divide and conquer algorithm. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in ... |
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| Routine : PSSTEIN() | Class : | |
| Author : Scalapack Team | Date : | Lines: 643 |
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..
.. Array Arguments .. .. Purpose ======= PSSTEIN computes the eigenvectors of a symmetric tridiagonal matrix in parallel, using inverse iteration. The eigenvectors found correspond to user specified eigenvalues. PSSTEIN does not orthogonalize vectors that are on different processes. The extent of orthogonalization is controlled by the input parameter LWORK. ... |
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| Routine : PSSYEV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 578 |
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..
.. Array Arguments .. .. Purpose ======= PSSYEV computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. In its present form, PSSYEV assumes a homogeneous system and makes no checks for consistency of the eigenvalues or eigenvectors across ... |
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| Routine : PSSYEVD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 351 |
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..
.. Array Arguments .. .. Purpose ======= PSSYEVD computes all the eigenvalues and eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. In its present form, PSSYEVD assumes a homogeneous system and makes no checks for consistency of the eigenvalues or eigenvectors across ... |
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| Routine : PSSYEVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 976 |
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..
.. Array Arguments .. .. Purpose ======= PSSYEVX computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. Eigenvalues/vectors can be selected by specifying a range of values or a range of indices for the desired eigenvalues. ... |
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| Routine : PSSYGS2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 419 |
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..
.. Array Arguments .. .. Purpose ======= PSSYGS2 reduces a real symmetric-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PSSYGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 438 |
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..
.. Array Arguments .. .. Purpose ======= PSSYGST reduces a real symmetric-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PSSYGVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 820 |
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..
.. Array Arguments .. .. Purpose ======= PSSYGVX computes all the eigenvalues, and optionally, the eigenvectors of a real generalized SY-definite eigenproblem, of the form sub( A )*x=(lambda)*sub( B )*x, sub( A )*sub( B )x=(lambda)*x, or sub( B )*sub( A )*x=(lambda)*x. ... |
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| Routine : PSSYNGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 423 |
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..
.. Array Arguments .. .. Purpose ======= PSSYNGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. PSSYNGST performs the same function as PSHEGST, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of PSSYNGST). ... |
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| Routine : PSSYNTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 551 |
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..
.. Array Arguments .. .. Bugs ==== Support for UPLO='U' is limited to calling the old, slow, PSSYTRD code. Purpose ======= PSSYNTRD is a prototype version of PSSYTRD which uses tailored ... |
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| Routine : PSSYTD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 464 |
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..
.. Array Arguments .. .. Purpose ======= PSSYTD2 reduces a real symmetric matrix sub( A ) to symmetric tridiagonal form T by an orthogonal similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PSSYTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 425 |
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..
.. Array Arguments .. .. Purpose ======= PSSYTRD reduces a real symmetric matrix sub( A ) to symmetric tridiagonal form T by an orthogonal similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PSSYTTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1198 |
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..
.. Array Arguments .. .. Purpose ======= PSSYTTRD reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PSTRCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 426 |
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..
.. Array Arguments .. .. Purpose ======= PSTRCON estimates the reciprocal of the condition number of a triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm. 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 reciprocal ... |
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| Routine : PSTRRFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 796 |
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..
.. Array Arguments .. .. Purpose ======= PSTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by PSTRTRS or some other means before entering this routine. PSTRRFS does not do iterative ... |
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| Routine : PSTRTI2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 276 |
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..
.. Array Arguments .. .. Purpose ======= 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 be contained in one and only one process memory space (local operation). Notes ===== ... |
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| Routine : PSTRTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 353 |
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.. Array Arguments .. .. Purpose ======= PSTRTRI computes the inverse of a upper or lower triangular distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== Each global data object is described by an associated description ... |
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| Routine : PSTRTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 333 |
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.. Array Arguments .. .. Purpose ======= PSTRTRS solves a triangular system of the form sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ), 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 an N-by-NRHS distributed matrix denoted by sub( B ). A check is made ... |
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| Routine : PSTZRZF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 334 |
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.. Array Arguments .. .. Purpose ======= 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 means of orthogonal transformations. The upper trapezoidal matrix sub( A ) is factored as sub( A ) = ( R 0 ) * Z, ... |
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| Routine : PZDBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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.. Array Arguments .. .. Purpose ======= PZDBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex banded diagonally dominant-like distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PZDBTRF() | Class : | |
| Author : | Date : | Lines: 1268 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZDBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 764 |
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.. Array Arguments .. .. Purpose ======= PZDBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PZDBTRSV() | Class : | |
| Author : | Date : | Lines: 1599 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZDRSCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 206 |
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.. Array Arguments .. .. Purpose ======= PZDRSCL multiplies an N-element complex distributed vector sub( X ) by the real scalar 1/a. This is done without overflow or underflow as long as the final sub( X )/a does not overflow or underflow. where sub( X ) denotes X(IX:IX+N-1,JX:JX), if INCX = 1, ... |
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| Routine : PZDTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 466 |
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.. Array Arguments .. .. Purpose ======= PZDTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex tridiagonal diagonally dominant-like distributed matrix. ... |
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| Routine : PZDTTRF() | Class : | |
| Author : | Date : | Lines: 1074 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZDTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 795 |
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.. Array Arguments .. .. Purpose ======= PZDTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PZDTTRSV() | Class : | |
| Author : | Date : | Lines: 1530 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZGBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 458 |
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.. Array Arguments .. .. Purpose ======= PZGBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex banded distributed matrix with bandwidth BWL, BWU. ... |
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| Routine : PZGBTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1110 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZGBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1182 |
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.. Array Arguments .. .. Purpose ======= PZGBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) or A(1:N, JA:JA+N-1)' * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors ... |
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| Routine : PZGEBD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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.. Array Arguments .. .. Purpose ======= PZGEBD2 reduces a complex general M-by-N distributed matrix 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. Notes ... |
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| Routine : PZGEBRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 414 |
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.. Array Arguments .. .. Purpose ======= PZGEBRD reduces a complex general M-by-N distributed matrix 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. Notes ... |
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| Routine : PZGECON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 422 |
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.. Array Arguments .. .. Purpose ======= 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 the 1-norm or the infinity-norm, using the LU factorization computed by PZGETRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and ... |
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| Routine : PZGEEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 375 |
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.. Array Arguments .. .. Purpose ======= 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) and reduce its condition number. R returns the row scale factors and C the column scale factors, chosen to try to make the largest entry in each row and column of the distributed matrix B with elements ... |
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| Routine : PZGEHD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 294 |
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.. Array Arguments .. .. Purpose ======= PZGEHD2 reduces a complex general distributed matrix sub( A ) to upper Hessenberg form H by an unitary similarity transformation: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PZGEHRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 383 |
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.. Array Arguments .. .. Purpose ======= PZGEHRD reduces a complex general distributed matrix sub( A ) to upper Hessenberg form H by an unitary similarity transformation: Q' * sub( A ) * Q = H, where sub( A ) = A(IA+N-1:IA+N-1,JA+N-1:JA+N-1). Notes ... |
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| Routine : PZGELQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 274 |
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.. Array Arguments .. .. Purpose ======= PZGELQ2 computes a LQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGELQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 313 |
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.. Array Arguments .. .. Purpose ======= PZGELQF computes a LQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = L * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGELS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 593 |
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.. Array Arguments .. .. Purpose ======= PZGELS solves overdetermined or underdetermined complex linear 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 of sub( A ). It is assumed that sub( A ) has full rank. The following options are provided: ... |
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| Routine : PZGEQL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 309 |
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.. Array Arguments .. .. Purpose ======= PZGEQL2 computes a QL factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGEQLF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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.. Array Arguments .. .. Purpose ======= PZGEQLF computes a QL factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * L. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGEQPF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 566 |
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.. Array Arguments .. .. Purpose ======= 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. Notes ===== ... |
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| Routine : PZGEQR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 308 |
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.. Array Arguments .. .. Purpose ======= PZGEQR2 computes a QR factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGEQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 313 |
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.. Array Arguments .. .. Purpose ======= PZGEQRF computes a QR factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = Q * R. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGERFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 895 |
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.. Array Arguments .. .. Purpose ======= PZGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solutions. Notes ===== ... |
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| Routine : PZGERQ2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 271 |
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.. Array Arguments .. .. Purpose ======= PZGERQ2 computes a RQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGERQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 310 |
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.. Array Arguments .. .. Purpose ======= PZGERQF computes a RQ factorization of a complex distributed M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) = R * Q. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZGESV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 244 |
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.. Array Arguments .. .. Purpose ======= PZGESV computes the solution to a complex system of linear equations sub( A ) * X = sub( B ), where sub( A ) = A(IA:IA+N-1,JA:JA+N-1) is an N-by-N distributed matrix and X and sub( B ) = B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed matrices. ... |
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| Routine : PZGESVD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 648 |
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.. Scalar Arguments ..
.. .. Array Arguments .. .. Purpose ======= PZGESVD computes the singular value decomposition (SVD) of an M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written as A = U * SIGMA * transpose(V) ... |
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| Routine : PZGESVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 830 |
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.. Array Arguments .. .. Purpose ======= PZGESVX uses the LU factorization to compute the solution to a complex system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PZGETF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 252 |
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.. Array Arguments .. .. Purpose ======= PZGETF2 computes an LU factorization of a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ... |
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| Routine : PZGETRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 311 |
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.. Array Arguments .. .. Purpose ======= PZGETRF computes an LU factorization of a general M-by-N distributed matrix sub( A ) = (IA:IA+M-1,JA:JA+N-1) using partial pivoting with row interchanges. The factorization has the form sub( A ) = P * L * U, where P is a permutation matrix, L is lower triangular with unit diagonal ele- ... |
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| Routine : PZGETRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 374 |
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.. Array Arguments .. .. Purpose ======= PZGETRI computes the inverse of a distributed matrix using the LU factorization computed by PZGETRF. This method inverts U and then computes the inverse of sub( A ) = A(IA:IA+N-1,JA:JA+N-1) denoted InvA by solving the system InvA*L = inv(U) for InvA. Notes ... |
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| Routine : PZGETRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 291 |
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.. Array Arguments .. .. Purpose ======= PZGETRS solves a system of distributed linear equations op( sub( A ) ) * X = sub( B ) with a general N-by-N distributed matrix sub( A ) using the LU factorization computed by PZGETRF. sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1), op( A ) = A, A**T or A**H ... |
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| Routine : PZGGQRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 370 |
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.. Array Arguments .. .. Purpose ======= PZGGQRF computes a generalized QR factorization of an N-by-M matrix sub( A ) = A(IA:IA+N-1,JA:JA+M-1) and an N-by-P matrix sub( B ) = B(IB:IB+N-1,JB:JB+P-1): sub( A ) = Q*R, sub( B ) = Q*T*Z, where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, ... |
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| Routine : PZGGRQF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 370 |
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.. Array Arguments .. .. Purpose ======= PZGGRQF computes a generalized RQ factorization of an M-by-N matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) and a P-by-N matrix sub( B ) = B(IB:IB+P-1,JB:JB+N-1): sub( A ) = R*Q, sub( B ) = Z*T*Q, where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix, ... |
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| Routine : PZHEEV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 634 |
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.. Array Arguments .. .. Purpose ======= PZHEEV computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix A by calling the recommended sequence of ScaLAPACK routines. In its present form, PZHEEV assumes a homogeneous system and makes only spot checks of the consistency of the eigenvalues across the ... |
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| Routine : PZHEEVD() | Class : | |
| Author : | Date : | Lines: 441 |
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.. Array Arguments .. Purpose ======= PZHEEVD computes all the eigenvalues and eigenvectors of a Hermitian matrix A by using a divide and conquer algorithm. Arguments ========= NP = the number of rows local to a given process. NQ = the number of columns local to a given process. ... |
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| Routine : PZHEEVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1001 |
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.. Array Arguments .. .. Purpose ======= PZHEEVX computes selected eigenvalues and, optionally, eigenvectors of a complex hermitian matrix A by calling the recommended sequence of ScaLAPACK routines. Eigenvalues/vectors can be selected by specifying a range of values or a range of indices for the desired eigenvalues. ... |
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| Routine : PZHEGS2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 431 |
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.. Array Arguments .. .. Purpose ======= PZHEGS2 reduces a complex Hermitian-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PZHEGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 441 |
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.. Array Arguments .. .. Purpose ======= PZHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. In the following sub( A ) denotes A( IA:IA+N-1, JA:JA+N-1 ) and sub( B ) denotes B( IB:IB+N-1, JB:JB+N-1 ). If IBTYPE = 1, the problem is sub( A )*x = lambda*sub( B )*x, ... |
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| Routine : PZHEGVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 836 |
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.. Array Arguments .. .. Purpose ======= PZHEGVX computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form sub( A )*x=(lambda)*sub( B )*x, sub( A )*sub( B )x=(lambda)*x, or sub( B )*sub( A )*x=(lambda)*x. ... |
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| Routine : PZHENGST() | Class : | |
| Author : Scalapack Team | Date : | Lines: 427 |
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.. Array Arguments .. .. Purpose ======= PZHENGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. PZHENGST performs the same function as PZHEGST, but is based on rank 2K updates, which are faster and more scalable than triangular solves (the basis of PZHENGST). ... |
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| Routine : PZHENTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 587 |
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.. Array Arguments .. .. Bugs ==== Support for UPLO='U' is limited to calling the old, slow, PZHETRD code. Purpose ======= PZHENTRD is a prototype version of PZHETRD which uses tailored ... |
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| Routine : PZHETD2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 471 |
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.. Array Arguments .. .. Purpose ======= PZHETD2 reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PZHETRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 428 |
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.. Array Arguments .. .. Purpose ======= PZHETRD reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PZHETTRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 1205 |
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.. Array Arguments .. .. Purpose ======= PZHETTRD reduces a complex Hermitian matrix sub( A ) to Hermitian tridiagonal form T by an unitary similarity transformation: Q' * sub( A ) * Q = T, where sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== ... |
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| Routine : PZLABRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 515 |
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.. Array Arguments .. .. Purpose ======= 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 upper or lower bidiagonal form by an unitary transformation Q' * A * P, and returns the matrices X and Y which are needed to apply the transfor- mation to the unreduced part of sub( A ). ... |
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| Routine : PZLACGV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 188 |
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.. Array Arguments .. .. Purpose ======= PZLACGV conjugates a complex vector of length N, sub( X ), where sub( X ) denotes X(IX,JX:JX+N-1) if INCX = DESCX( M_ ) and X(IX:IX+N-1,JX) if INCX = 1, and Notes ===== ... |
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| Routine : PZLACON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 384 |
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.. Array Arguments .. .. Purpose ======= PZLACON estimates the 1-norm of a square, complex distributed matrix A. Reverse communication is used for evaluating matrix-vector products. X and V are aligned with the distributed matrix A, this information is implicitly contained within IV, IX, DESCV, and DESCX. Notes ... |
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| Routine : PZLACONSB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 585 |
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.. Array Arguments .. .. Purpose ======= PZLACONSB looks for two consecutive small subdiagonal elements by seeing the effect of starting a double shift QR iteration given by H44, H33, & H43H34 and see if this would make a subdiagonal negligible. Notes ... |
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| Routine : PZLACP2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 406 |
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.. Array Arguments .. .. Purpose ======= PZLACP2 copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PZLACP2 performs a local copy sub( A ) := sub( B ), where sub( A ) denotes 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 is ... |
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| Routine : PZLACP3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 312 |
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.. Array Arguments .. .. Purpose ======= PZLACP3 is an auxiliary routine that copies from a global parallel array into a local replicated array or vise versa. Notice that the entire submatrix that is copied gets placed on one node or more. The receiving node can be specified precisely, or all nodes can receive, or just one row or column of nodes. ... |
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| Routine : PZLACPY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 231 |
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.. Array Arguments .. .. Purpose ======= PZLACPY copies all or part of a distributed matrix A to another distributed matrix B. No communication is performed, PZLACPY performs a local copy sub( A ) := sub( B ), where sub( A ) denotes A(IA:IA+M-1,JA:JA+N-1) and sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1). Notes ... |
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| Routine : PZLAEVSWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 285 |
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.. Array Arguments .. .. Purpose ======= PZLAEVSWP moves the eigenvectors (potentially unsorted) from where they are computed, to a ScaLAPACK standard block cyclic array, sorted so that the corresponding eigenvalues are sorted. Notes ===== ... |
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| Routine : PZLAHQR() | Class : | |
| Author : | Date : | Lines: 2550 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : PZLAHRD() | Class : | |
| Author : | Date : | Lines: 290 |
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.. Array Arguments .. .. Purpose ======= 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 elements below the k-th subdiagonal are zero. The reduction is performed by an unitary similarity transformation Q' * A * Q. The routine returns the matrices V and T which determine Q as a block ... |
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| Routine : PZLAMR1D() | Class : | |
| Author : | Date : | Lines: 144 |
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..
.. Array Arguments .. .. Bugs ==== I am not sure that this works correctly when IB and JB are not equal to 1. Indeed, I suspect that IB should always be set to 1 or ignored with 1 used in its place. PZLAMR1D has not been tested except withint the contect of PZHEPTRD, the prototype reduction to tridiagonal form code. ... |
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| Routine : PZLANGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 324 |
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..
.. Array Arguments .. .. Purpose ======= PZLANGE returns the value of the one norm, or the Frobenius norm, 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 ( max(abs(A(i,j))), NORM = 'M' or 'm' with IA <= i <= IA+M-1, ... |
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| Routine : PZLANHE() | Class : | |
| Author : | Date : | Lines: 949 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZLANHS() | Class : | |
| Author : | Date : | Lines: 741 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZLANSY() | Class : | |
| Author : | Date : | Lines: 836 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZLANTR() | Class : | |
| Author : | Date : | Lines: 1031 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZLAPIV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 356 |
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.. Array Arguments .. .. Purpose ======= PZLAPIV applies either P (permutation matrix indicated by IPIV) or inv( P ) to a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector may be distributed across a process row or a column. The pivot vector should be aligned with the distributed ... |
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| Routine : PZLAPV2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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.. Array Arguments .. .. Purpose ======= PZLAPV2 applies either P (permutation matrix indicated by IPIV) or inv( P ) to a M-by-N distributed matrix sub( A ) denoting A(IA:IA+M-1,JA:JA+N-1), resulting in row or column pivoting. The pivot vector should be aligned with the distributed matrix A. For pivoting the rows of sub( A ), IPIV should be distributed along a ... |
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| Routine : PZLAQGE() | Class : | |
| Author : Scalapack Team | Date : | Lines: 271 |
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.. Array Arguments .. .. Purpose ======= PZLAQGE equilibrates a general M-by-N distributed matrix sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using the row and scaling factors in the vectors R and C. Notes ===== ... |
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| Routine : PZLAQSY() | Class : | |
| Author : Scalapack Team | Date : | Lines: 360 |
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.. Array Arguments .. .. Purpose ======= PZLAQSY equilibrates a symmetric distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the vectors SR and SC. Notes ===== ... |
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| Routine : PZLARF() | Class : | |
| Author : | Date : | Lines: 814 |
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.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PZLARFB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 889 |
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.. Array Arguments .. .. Purpose ======= PZLARFB applies a complex block reflector Q or its conjugate 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 ===== ... |
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| Routine : PZLARFC() | Class : | |
| Author : | Date : | Lines: 810 |
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.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PZLARFG() | Class : | |
| Author : Scalapack Team | Date : | Lines: 291 |
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.. Array Arguments .. .. Purpose ======= PZLARFG generates a complex elementary reflector H of order n, such that H * sub( X ) = H * ( x(iax,jax) ) = ( alpha ), H' * H = I. ( x ) ( 0 ) where alpha is a real scalar, and sub( X ) is an (N-1)-element ... |
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| Routine : PZLARFT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 543 |
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.. Array Arguments .. .. Purpose ======= PZLARFT forms the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = 'C', the vector which defines the elementary reflector ... |
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| Routine : PZLARZ() | Class : | |
| Author : | Date : | Lines: 915 |
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.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PZLARZB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 626 |
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.. Array Arguments .. .. Purpose ======= PZLARZB applies a complex block reflector Q or its conjugate 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. Currently, only STOREV = 'R' and DIRECT = 'B' are supported. ... |
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| Routine : PZLARZC() | Class : | |
| Author : | Date : | Lines: 917 |
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.. Local Scalars .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : PZLARZT() | Class : | |
| Author : Scalapack Team | Date : | Lines: 301 |
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.. Array Arguments .. .. Purpose ======= PZLARZT forms the triangular factor T of a complex block reflector H of order > n, which is defined as a product of k elementary reflectors as returned by PZTZRZF. If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. ... |
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| Routine : PZLASCL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 512 |
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.. Array Arguments .. .. Purpose ======= 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 is done without over/underflow as long as the final result CTO * A(I,J) / CFROM does not over/underflow. TYPE specifies that sub( A ) may be full, upper triangular, lower triangular or upper ... |
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| Routine : PZLASE2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 411 |
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.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. PZLASE2 requires that only dimension of the matrix operand is distributed. Notes ... |
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| Routine : PZLASET() | Class : | |
| Author : Scalapack Team | Date : | Lines: 220 |
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.. Array Arguments .. .. Purpose ======= 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 the offdiagonals. Notes ===== ... |
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| Routine : PZLASMSUB() | Class : | |
| Author : Scalapack Team | Date : | Lines: 377 |
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.. Array Arguments .. .. Purpose ======= PZLASMSUB looks for a small subdiagonal element from the bottom of the matrix that it can safely set to zero. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZLASSQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 286 |
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.. Array Arguments .. .. Purpose ======= PZLASSQ returns the values scl and smsq such that ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, where x( i ) = sub( X ) = abs( X( IX+(JX-1)*DESCX(M_)+(i-1)*INCX ) ). The value of sumsq is assumed to be at least unity and the value of ssq will then satisfy ... |
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| Routine : PZLASWP() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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.. Array Arguments .. .. Purpose: ======== PZLASWP performs a series of row or column interchanges on 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 of sub( A ). This routine assumes that the pivoting information has already been broadcast along the process row or column. ... |
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| Routine : PZLATRA() | Class : | |
| Author : Scalapack Team | Date : | Lines: 187 |
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.. Array Arguments .. .. Purpose ======= PZLATRA computes the trace of an N-by-N distributed matrix sub( A ) denoting A( IA:IA+N-1, JA:JA+N-1 ). The result is left on every process of the grid. Notes ===== ... |
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| Routine : PZLATRD() | Class : | |
| Author : Scalapack Team | Date : | Lines: 435 |
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.. Array Arguments .. .. Purpose ======= PZLATRD reduces NB rows and columns of a complex Hermitian distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) to complex tridiagonal form by an unitary similarity transformation Q' * sub( A ) * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of sub( A ). ... |
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| Routine : PZLATRS() | Class : | |
| Author : | Date : | Lines: 87 |
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.. Local Scalars ..
.. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. Get grid parameters Quick return if possible |
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| Routine : PZLATRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 255 |
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.. Array Arguments .. .. Purpose ======= PZLATRZ reduces the M-by-N ( M<=N ) complex upper trapezoidal 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 ) = ( R 0 ) * Z, ... |
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| Routine : PZLATTRS() | Class : | |
| Author : | Date : | Lines: 1213 |
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.. Local Scalars .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. .. .. Statement Functions .. ... |
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| Routine : PZLAUU2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 214 |
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.. Array Arguments .. .. Purpose ======= PZLAUU2 computes the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the 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, overwriting the factor U in sub( A ). ... |
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| Routine : PZLAUUM() | Class : | |
| Author : Scalapack Team | Date : | Lines: 220 |
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.. Array Arguments .. .. Purpose ======= PZLAUUM computes the product U * U' or L' * L, where the triangular 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, overwriting the factor U in sub( A ). ... |
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| Routine : PZLAWIL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 273 |
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.. Array Arguments .. .. Purpose ======= PZLAWIL gets the transform given by H44,H33, & H43H34 into V starting at row M. Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZMAX1() | Class : | |
| Author : Scalapack Team | Date : | Lines: 358 |
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.. Array Arguments .. .. Purpose ======= PZMAX1 computes the global index of the maximum element in absolute value of a distributed vector sub( X ). The global index is returned in INDX and the value is returned in AMAX, where sub( X ) denotes X(IX:IX+N-1,JX) if INCX = 1, X(IX,JX:JX+N-1) if INCX = M_X. ... |
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| Routine : PZPBSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 453 |
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.. Array Arguments .. .. Purpose ======= PZPBSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex banded symmetric positive definite distributed matrix with bandwidth BW. ... |
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| Routine : PZPBTRF() | Class : | |
| Author : | Date : | Lines: 1510 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZPBTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 753 |
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.. Array Arguments .. .. Purpose ======= PZPBTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PZPBTRF. A(1:N, JA:JA+N-1) is an N-by-N complex ... |
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| Routine : PZPBTRSV() | Class : | |
| Author : | Date : | Lines: 1565 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZPOCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 413 |
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.. Array Arguments .. .. Purpose ======= PZPOCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite distributed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by PZPOTRF. An estimate is obtained for norm(inv(A(IA:IA+N-1,JA:JA+N-1))), and ... |
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| Routine : PZPOEQU() | Class : | |
| Author : Scalapack Team | Date : | Lines: 358 |
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.. Array Arguments .. .. Purpose ======= PZPOEQU computes row and column scalings intended to equilibrate a distributed Hermitian positive definite matrix 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 scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled distri- ... |
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| Routine : PZPORFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 870 |
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.. Array Arguments .. .. Purpose ======= PZPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and provides error bounds and backward error estimates for the solutions. Notes ... |
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| Routine : PZPOSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 263 |
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.. Array Arguments .. .. Purpose ======= PZPOSV computes the solution to a complex system of linear equations sub( A ) * X = sub( B ), 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 ) denoting B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS distributed ... |
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| Routine : PZPOSVX() | Class : | |
| Author : Scalapack Team | Date : | Lines: 667 |
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.. Array Arguments .. .. Purpose ======= PZPOSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A(IA:IA+N-1,JA:JA+N-1) * X = B(IB:IB+N-1,JB:JB+NRHS-1), where A(IA:IA+N-1,JA:JA+N-1) is an N-by-N matrix and X and B(IB:IB+N-1,JB:JB+NRHS-1) are N-by-NRHS matrices. ... |
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| Routine : PZPOTF2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 358 |
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.. Array Arguments .. .. Purpose ======= 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 sub( A ) = U' * U , if UPLO = 'U', or sub( A ) = L * L', if UPLO = 'L', ... |
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| Routine : PZPOTRF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 363 |
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.. Array Arguments .. .. Purpose ======= PZPOTRF computes the Cholesky factorization of an N-by-N complex hermitian positive definite distributed matrix sub( A ) denoting A(IA:IA+N-1, JA:JA+N-1). The factorization has the form sub( A ) = U' * U , if UPLO = 'U', or ... |
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| Routine : PZPOTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 208 |
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.. Array Arguments .. .. Purpose ======= PZPOTRI computes the inverse of a complex Hermitian positive definite distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the Cholesky factorization sub( A ) = U**H*U or L*L**H computed by PZPOTRF. Notes ... |
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| Routine : PZPOTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 266 |
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.. Array Arguments .. .. Purpose ======= PZPOTRS solves a system of linear equations sub( A ) * X = sub( B ) A(IA:IA+N-1,JA:JA+N-1)*X = B(IB:IB+N-1,JB:JB+NRHS-1) 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 Cholesky ... |
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| Routine : PZPTSV() | Class : | |
| Author : Scalapack Team | Date : | Lines: 461 |
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.. Array Arguments .. .. Purpose ======= PZPTSV solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is an N-by-N complex tridiagonal symmetric positive definite distributed matrix. ... |
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| Routine : PZPTTRF() | Class : | |
| Author : | Date : | Lines: 1039 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZPTTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 798 |
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.. Array Arguments .. .. Purpose ======= PZPTTRS solves a system of linear equations A(1:N, JA:JA+N-1) * X = B(IB:IB+N-1, 1:NRHS) where A(1:N, JA:JA+N-1) is the matrix used to produce the factors stored in A(1:N,JA:JA+N-1) and AF by PZPTTRF. A(1:N, JA:JA+N-1) is an N-by-N complex ... |
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| Routine : PZPTTRSV() | Class : | |
| Author : | Date : | Lines: 1511 |
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..
.. Local Scalars .. .. .. Local Arrays .. .. .. External Subroutines .. .. .. External Functions .. .. .. Intrinsic Functions .. ... |
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| Routine : PZSTEIN() | Class : | |
| Author : Scalapack Team | Date : | Lines: 643 |
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.. Array Arguments .. .. Purpose ======= PZSTEIN computes the eigenvectors of a symmetric tridiagonal matrix in parallel, using inverse iteration. The eigenvectors found correspond to user specified eigenvalues. PZSTEIN does not orthogonalize vectors that are on different processes. The extent of orthogonalization is controlled by the input parameter LWORK. ... |
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| Routine : PZTRCON() | Class : | |
| Author : Scalapack Team | Date : | Lines: 431 |
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.. Array Arguments .. .. Purpose ======= PZTRCON estimates the reciprocal of the condition number of a triangular distributed matrix A(IA:IA+N-1,JA:JA+N-1), in either the 1-norm or the infinity-norm. 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 reciprocal ... |
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| Routine : PZTREVC() | Class : | |
| Author : Scalapack Team | Date : | Lines: 567 |
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.. Array Arguments .. .. Purpose ======= 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 to an eigenvalue w are defined by: T*x = w*x, y'*T = w*y' ... |
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| Routine : PZTRRFS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 806 |
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.. Array Arguments .. .. Purpose ======= PZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by PZTRTRS or some other means before entering this routine. PZTRRFS does not do iterative ... |
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| Routine : PZTRTI2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 276 |
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.. Array Arguments .. .. Purpose ======= 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 be contained in one and only one process memory space (local operation). Notes ===== ... |
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| Routine : PZTRTRI() | Class : | |
| Author : Scalapack Team | Date : | Lines: 353 |
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.. Array Arguments .. .. Purpose ======= PZTRTRI computes the inverse of a upper or lower triangular distributed matrix sub( A ) = A(IA:IA+N-1,JA:JA+N-1). Notes ===== Each global data object is described by an associated description ... |
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| Routine : PZTRTRS() | Class : | |
| Author : Scalapack Team | Date : | Lines: 335 |
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..
.. Array Arguments .. .. Purpose ======= PZTRTRS solves a triangular system of the form sub( A ) * X = sub( B ) or sub( A )**T * X = sub( B ) or sub( A )**H * X = sub( B ), 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 an ... |
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| Routine : PZTZRZF() | Class : | |
| Author : Scalapack Team | Date : | Lines: 335 |
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..
.. Array Arguments .. .. Purpose ======= 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 means of unitary transformations. The upper trapezoidal matrix sub( A ) is factored as sub( A ) = ( R 0 ) * Z, ... |
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| Routine : PZUNG2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 279 |
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.. Array Arguments .. .. Purpose ======= PZUNG2L generates an M-by-N complex distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PZGEQLF. ... |
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| Routine : PZUNG2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 282 |
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..
.. Array Arguments .. .. Purpose ======= PZUNG2R generates an M-by-N complex distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PZUNGL2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 290 |
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..
.. Array Arguments .. .. Purpose ======= PZUNGL2 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 first M rows of a product of K elementary reflectors of order N Q = H(k)' . . . H(2)' H(1)' as returned by PZGELQF. ... |
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| Routine : PZUNGLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 334 |
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..
.. Array Arguments .. .. Purpose ======= PZUNGLQ 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 first M rows of a product of K elementary reflectors of order N Q = H(k)' . . . H(2)' H(1)' as returned by PZGELQF. ... |
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| Routine : PZUNGQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 300 |
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..
.. Array Arguments .. .. Purpose ======= PZUNGQL generates an M-by-N complex distributed matrix Q denoting 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 M Q = H(k) . . . H(2) H(1) as returned by PZGEQLF. ... |
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| Routine : PZUNGQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 336 |
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..
.. Array Arguments .. .. Purpose ======= PZUNGQR generates an M-by-N complex distributed matrix Q denoting 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 order M Q = H(1) H(2) . . . H(k) ... |
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| Routine : PZUNGR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 284 |
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..
.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1)' H(2)' . . . H(k)' as returned by PZGERQF. ... |
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| Routine : PZUNGRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 302 |
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..
.. Array Arguments .. .. Purpose ======= 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 last M rows of a product of K elementary reflectors of order N Q = H(1)' H(2)' . . . H(k)' as returned by PZGERQF. ... |
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| Routine : PZUNM2L() | Class : | |
| Author : Scalapack Team | Date : | Lines: 445 |
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.. Array Arguments .. .. Purpose ======= PZUNM2L overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNM2R() | Class : | |
| Author : Scalapack Team | Date : | Lines: 449 |
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.. Array Arguments .. .. Purpose ======= PZUNM2R overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMBR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 591 |
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.. Array Arguments .. .. Purpose ======= If VECT = 'Q', PZUNMBR overwrites the general complex distributed M-by-N matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMHR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 396 |
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.. Array Arguments .. .. Purpose ======= PZUNMHR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNML2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 402 |
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.. Array Arguments .. .. Purpose ======= PZUNML2 overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C sub( C ) * Q**H ... |
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| Routine : PZUNMLQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 452 |
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.. Array Arguments .. .. Purpose ======= PZUNMLQ overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C sub( C ) * Q**H ... |
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| Routine : PZUNMQL() | Class : | |
| Author : Scalapack Team | Date : | Lines: 459 |
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.. Array Arguments .. .. Purpose ======= PZUNMQL overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMQR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 451 |
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.. Array Arguments .. .. Purpose ======= PZUNMQR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMR2() | Class : | |
| Author : Scalapack Team | Date : | Lines: 389 |
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.. Array Arguments .. .. Purpose ======= PZUNMR2 overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMR3() | Class : | |
| Author : Scalapack Team | Date : | Lines: 395 |
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.. Array Arguments .. .. Purpose ======= PZUNMR3 overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMRQ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 464 |
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.. Array Arguments .. .. Purpose ======= PZUNMRQ overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMRZ() | Class : | |
| Author : Scalapack Team | Date : | Lines: 479 |
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.. Array Arguments .. .. Purpose ======= PZUNMRZ overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : PZUNMTR() | Class : | |
| Author : Scalapack Team | Date : | Lines: 437 |
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.. Array Arguments .. .. Purpose ======= PZUNMTR overwrites the general complex M-by-N distributed matrix sub( C ) = C(IC:IC+M-1,JC:JC+N-1) with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * sub( C ) sub( C ) * Q TRANS = 'C': Q**H * sub( C ) sub( C ) * Q**H ... |
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| Routine : SDBTF2() | Class : | |
| Author : | Date : | Lines: 174 |
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.. Array Arguments .. .. Purpose ======= Sdbtrf computes an LU factorization of a real m-by-n band matrix A without using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 BLAS. Arguments ========= ... |
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| Routine : SDBTRF() | Class : | |
| Author : | Date : | Lines: 336 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : SDTTRF() | Class : | |
| Author : | Date : | Lines: 112 |
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.. Array Arguments .. .. Purpose ======= SDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. The factorization has the form A = L * U where L is a product of unit lower bidiagonal ... |
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| Routine : SDTTRSV() | Class : | |
| Author : | Date : | Lines: 174 |
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.. Array Arguments .. .. Purpose ======= SDTTRSV solves one of the systems of equations L * X = B, L**T * X = B, or L**H * X = B, U * X = B, U**T * X = B, or U**H * X = B, with factors of the tridiagonal matrix A from the LU factorization computed by SDTTRF. ... |
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| Routine : SLAMSH() | Class : | |
| Author : | Date : | Lines: 236 |
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.. Array Arguments .. .. Purpose ======= SLAMSH sends multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. SLAMSH should only be called when there are multiple shifts/bulges ... |
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| Routine : SLAPST() | Class : | |
| Author : | Date : | Lines: 251 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. ... |
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| Routine : SLAREF() | Class : | |
| Author : | Date : | Lines: 277 |
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.. Array Arguments .. .. Purpose ======= SLAREF applies one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns. Arguments ========= ... |
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| Routine : SLASORTE() | Class : | |
| Author : | Date : | Lines: 145 |
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.. Array Arguments .. .. Purpose ======= SLASORTE sorts eigenpairs so that real eigenpairs are together and complex are together. This way one can employ 2x2 shifts easily since every 2nd subdiagonal is guaranteed to be zero. This routine does no parallel work. Arguments ... |
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| Routine : SLASRT2() | Class : | |
| Author : | Date : | Lines: 268 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Executable Statements .. ... |
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| Routine : SPTTRSV() | Class : | |
| Author : | Date : | Lines: 132 |
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.. Array Arguments .. .. Purpose ======= SPTTRSV solves one of the triangular systems L**T* X = B, or L * X = B, where L is the Cholesky factor of a Hermitian positive definite tridiagonal matrix A such that A = L*D*L**H (computed by SPTTRF). ... |
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| Routine : SSTEIN2() | Class : | |
| Author : | Date : | Lines: 372 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : SSTEQR2() | Class : | |
| Author : | Date : | Lines: 498 |
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.. Local Scalars .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. .. .. Executable Statements .. ... |
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| Routine : STRMVT() | Class : | |
| Author : | Date : | Lines: 161 |
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.. Array Arguments .. .. Purpose ======= STRMVT performs the matrix-vector operations x := T' *y, and w := T *z, where x is an n element vector and T is an n by n upper or lower triangular matrix. Arguments ... |
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| Routine : ZCOMBAMAX1() | Class : | |
| Author : | Date : | Lines: 45 |
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Purpose ======= ZCOMBAMAX1 finds the element having maximum real part absolute value as well as its corresponding globl index. Arguments ========= V1 (local input/local output) COMPLEX*16 array of dimension 2. The first maximum absolute value element and its global index. V1(1) = AMAX, V1(2) = INDX. ... |
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| Routine : ZDBTF2() | Class : | |
| Author : | Date : | Lines: 177 |
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.. Array Arguments .. .. Purpose ======= Zdbtrf computes an LU factorization of a real m-by-n band matrix A without using partial pivoting with row interchanges. This is the unblocked version of the algorithm, calling Level 2 BLAS. Arguments ========= ... |
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| Routine : ZDBTRF() | Class : | |
| Author : | Date : | Lines: 339 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : ZDTTRF() | Class : | |
| Author : | Date : | Lines: 112 |
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.. Array Arguments .. .. Purpose ======= ZDTTRF computes an LU factorization of a complex tridiagonal matrix A using elimination without partial pivoting. The factorization has the form A = L * U where L is a product of unit lower bidiagonal ... |
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| Routine : ZDTTRSV() | Class : | |
| Author : | Date : | Lines: 206 |
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.. Array Arguments .. .. Purpose ======= ZDTTRSV solves one of the systems of equations L * X = B, L**T * X = B, or L**H * X = B, U * X = B, U**T * X = B, or U**H * X = B, with factors of the tridiagonal matrix A from the LU factorization computed by ZDTTRF. ... |
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| Routine : ZLAHQR2() | Class : | |
| Author : | Date : | Lines: 444 |
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.. Local Scalars .. .. .. Local Arrays .. .. .. External Functions .. .. .. External Subroutines .. .. .. Intrinsic Functions .. ... |
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| Routine : ZLAMSH() | Class : | |
| Author : | Date : | Lines: 260 |
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.. Array Arguments .. .. Purpose ======= ZLAMSH sends multiple shifts through a small (single node) matrix to see how consecutive small subdiagonal elements are modified by subsequent shifts in an effort to maximize the number of bulges that can be sent through. ZLAMSH should only be called when there are multiple shifts/bulges ... |
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| Routine : ZLANV2() | Class : | |
| Author : | Date : | Lines: 145 |
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Purpose ======= ZLANV2 computes the Schur factorization of a complex 2-by-2 nonhermitian matrix in standard form: [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ] [ C D ] [ SN CS ] [ 0 DD ] [-SN CS ] Arguments ========= A (input/output) COMPLEX*16 ... |
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| Routine : ZLAREF() | Class : | |
| Author : | Date : | Lines: 331 |
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.. Array Arguments .. .. Purpose ======= ZLAREF applies one or several Householder reflectors of size 3 to one or two matrices (if column is specified) on either their rows or columns. Arguments ========= ... |
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| Routine : ZPTTRSV() | Class : | |
| Author : | Date : | Lines: 177 |
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.. Array Arguments .. .. Purpose ======= ZPTTRSV solves one of the triangular systems L * X = B, or L**H * X = B, U * X = B, or U**H * X = B, where L or U is the Cholesky factor of a Hermitian positive definite tridiagonal matrix A such that ... |
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| Routine : ZSTEQR2() | Class : | |
| Author : | Date : | Lines: 662 |
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Skip the current step: the subdiagonal info is just noise.
Lookahead over Inner loop If eigenvectors are desired, then save rotations. If eigenvectors are desired, then apply saved rotations. Eigenvalue found. QR Iteration Look for small superdiagonal element. If remaining matrix is 2-by-2, use DLAE2 or DLAEV2 to compute its eigensystem. ... |
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| Routine : ZTRMVT() | Class : | |
| Author : | Date : | Lines: 161 |
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.. Array Arguments .. .. Purpose ======= ZTRMVT performs the matrix-vector operations x := conjg( T' ) *y, and w := T *z, where x is an n element vector and T is an n by n upper or lower triangular matrix. Arguments ... |
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