version 1.1, 2010/01/26 15:22:46
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version 1.12, 2012/12/14 14:22:55
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*> \brief \b ZSYTRS |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZSYTRS + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytrs.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zsytrs.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsytrs.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, LDA, LDB, N, NRHS |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* COMPLEX*16 A( LDA, * ), B( LDB, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZSYTRS solves a system of linear equations A*X = B with a complex |
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*> symmetric matrix A using the factorization A = U*D*U**T or |
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*> A = L*D*L**T computed by ZSYTRF. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> Specifies whether the details of the factorization are stored |
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*> as an upper or lower triangular matrix. |
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*> = 'U': Upper triangular, form is A = U*D*U**T; |
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*> = 'L': Lower triangular, form is A = L*D*L**T. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] NRHS |
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*> \verbatim |
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*> NRHS is INTEGER |
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*> The number of right hand sides, i.e., the number of columns |
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*> of the matrix B. NRHS >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,N) |
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*> The block diagonal matrix D and the multipliers used to |
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*> obtain the factor U or L as computed by ZSYTRF. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in] IPIV |
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*> \verbatim |
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*> IPIV is INTEGER array, dimension (N) |
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*> Details of the interchanges and the block structure of D |
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*> as determined by ZSYTRF. |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is COMPLEX*16 array, dimension (LDB,NRHS) |
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*> On entry, the right hand side matrix B. |
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*> On exit, the solution matrix X. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date November 2011 |
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* |
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*> \ingroup complex16SYcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
SUBROUTINE ZSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 A( LDA, * ), B( LDB, * ) |
COMPLEX*16 A( LDA, * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZSYTRS solves a system of linear equations A*X = B with a complex |
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* symmetric matrix A using the factorization A = U*D*U**T or |
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* A = L*D*L**T computed by ZSYTRF. |
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* |
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* Arguments |
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* ========= |
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* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the details of the factorization are stored |
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* as an upper or lower triangular matrix. |
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* = 'U': Upper triangular, form is A = U*D*U**T; |
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* = 'L': Lower triangular, form is A = L*D*L**T. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* NRHS (input) INTEGER |
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* The number of right hand sides, i.e., the number of columns |
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* of the matrix B. NRHS >= 0. |
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* |
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* A (input) COMPLEX*16 array, dimension (LDA,N) |
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* The block diagonal matrix D and the multipliers used to |
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* obtain the factor U or L as computed by ZSYTRF. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* IPIV (input) INTEGER array, dimension (N) |
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* Details of the interchanges and the block structure of D |
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* as determined by ZSYTRF. |
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* |
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* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) |
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* On entry, the right hand side matrix B. |
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* On exit, the solution matrix X. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Solve A*X = B, where A = U*D*U'. |
* Solve A*X = B, where A = U*D*U**T. |
* |
* |
* First solve U*D*X = B, overwriting B with X. |
* First solve U*D*X = B, overwriting B with X. |
* |
* |
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GO TO 10 |
GO TO 10 |
30 CONTINUE |
30 CONTINUE |
* |
* |
* Next solve U'*X = B, overwriting B with X. |
* Next solve U**T *X = B, overwriting B with X. |
* |
* |
* K is the main loop index, increasing from 1 to N in steps of |
* K is the main loop index, increasing from 1 to N in steps of |
* 1 or 2, depending on the size of the diagonal blocks. |
* 1 or 2, depending on the size of the diagonal blocks. |
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* |
* |
* 1 x 1 diagonal block |
* 1 x 1 diagonal block |
* |
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* Multiply by inv(U'(K)), where U(K) is the transformation |
* Multiply by inv(U**T(K)), where U(K) is the transformation |
* stored in column K of A. |
* stored in column K of A. |
* |
* |
CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), |
CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), |
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* |
* |
* 2 x 2 diagonal block |
* 2 x 2 diagonal block |
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* Multiply by inv(U'(K+1)), where U(K+1) is the transformation |
* Multiply by inv(U**T(K+1)), where U(K+1) is the transformation |
* stored in columns K and K+1 of A. |
* stored in columns K and K+1 of A. |
* |
* |
CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), |
CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ), |
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* |
* |
ELSE |
ELSE |
* |
* |
* Solve A*X = B, where A = L*D*L'. |
* Solve A*X = B, where A = L*D*L**T. |
* |
* |
* First solve L*D*X = B, overwriting B with X. |
* First solve L*D*X = B, overwriting B with X. |
* |
* |
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GO TO 60 |
GO TO 60 |
80 CONTINUE |
80 CONTINUE |
* |
* |
* Next solve L'*X = B, overwriting B with X. |
* Next solve L**T *X = B, overwriting B with X. |
* |
* |
* K is the main loop index, decreasing from N to 1 in steps of |
* K is the main loop index, decreasing from N to 1 in steps of |
* 1 or 2, depending on the size of the diagonal blocks. |
* 1 or 2, depending on the size of the diagonal blocks. |
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* |
* |
* 1 x 1 diagonal block |
* 1 x 1 diagonal block |
* |
* |
* Multiply by inv(L'(K)), where L(K) is the transformation |
* Multiply by inv(L**T(K)), where L(K) is the transformation |
* stored in column K of A. |
* stored in column K of A. |
* |
* |
IF( K.LT.N ) |
IF( K.LT.N ) |
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* |
* |
* 2 x 2 diagonal block |
* 2 x 2 diagonal block |
* |
* |
* Multiply by inv(L'(K-1)), where L(K-1) is the transformation |
* Multiply by inv(L**T(K-1)), where L(K-1) is the transformation |
* stored in columns K-1 and K of A. |
* stored in columns K-1 and K of A. |
* |
* |
IF( K.LT.N ) THEN |
IF( K.LT.N ) THEN |