version 1.1, 2018/05/29 14:55:45
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version 1.3, 2023/08/07 08:39:39
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*> \verbatim |
*> \verbatim |
*> |
*> |
*> ZSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex |
*> ZSYTRS_AA_2STAGE solves a system of linear equations A*X = B with a complex |
*> symmetric matrix A using the factorization A = U*T*U**T or |
*> symmetric matrix A using the factorization A = U**T*T*U or |
*> A = L*T*L**T computed by ZSYTRF_AA_2STAGE. |
*> A = L*T*L**T computed by ZSYTRF_AA_2STAGE. |
*> \endverbatim |
*> \endverbatim |
* |
* |
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*> UPLO is CHARACTER*1 |
*> UPLO is CHARACTER*1 |
*> Specifies whether the details of the factorization are stored |
*> Specifies whether the details of the factorization are stored |
*> as an upper or lower triangular matrix. |
*> as an upper or lower triangular matrix. |
*> = 'U': Upper triangular, form is A = U*T*U**T; |
*> = 'U': Upper triangular, form is A = U**T*T*U; |
*> = 'L': Lower triangular, form is A = L*T*L**T. |
*> = 'L': Lower triangular, form is A = L*T*L**T. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
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*> |
*> |
*> \param[in] LTB |
*> \param[in] LTB |
*> \verbatim |
*> \verbatim |
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*> LTB is INTEGER |
*> The size of the array TB. LTB >= 4*N. |
*> The size of the array TB. LTB >= 4*N. |
*> \endverbatim |
*> \endverbatim |
*> |
*> |
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*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
* |
*> \date November 2017 |
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* |
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*> \ingroup complex16SYcomputational |
*> \ingroup complex16SYcomputational |
* |
* |
* ===================================================================== |
* ===================================================================== |
SUBROUTINE ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, |
SUBROUTINE ZSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, |
$ IPIV, IPIV2, B, LDB, INFO ) |
$ IPIV, IPIV2, B, LDB, INFO ) |
* |
* |
* -- LAPACK computational routine (version 3.8.0) -- |
* -- LAPACK computational routine -- |
* -- 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 2017 |
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* |
* |
IMPLICIT NONE |
IMPLICIT NONE |
* |
* |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Solve A*X = B, where A = U*T*U**T. |
* Solve A*X = B, where A = U**T*T*U. |
* |
* |
IF( N.GT.NB ) THEN |
IF( N.GT.NB ) THEN |
* |
* |
* Pivot, P**T * B |
* Pivot, P**T * B -> B |
* |
* |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) |
* |
* |
* Compute (U**T \P**T * B) -> B [ (U**T \P**T * B) ] |
* Compute (U**T \ B) -> B [ (U**T \P**T * B) ] |
* |
* |
CALL ZTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1), |
CALL ZTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1), |
$ LDA, B(NB+1, 1), LDB) |
$ LDA, B(NB+1, 1), LDB) |
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CALL ZTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1), |
CALL ZTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1), |
$ LDA, B(NB+1, 1), LDB) |
$ LDA, B(NB+1, 1), LDB) |
* |
* |
* Pivot, P * B [ P * (U \ (T \ (U**T \P**T * B) )) ] |
* Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ] |
* |
* |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 ) |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 ) |
* |
* |
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* |
* |
IF( N.GT.NB ) THEN |
IF( N.GT.NB ) THEN |
* |
* |
* Pivot, P**T * B |
* Pivot, P**T * B -> B |
* |
* |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 ) |
* |
* |
* Compute (L \P**T * B) -> B [ (L \P**T * B) ] |
* Compute (L \ B) -> B [ (L \P**T * B) ] |
* |
* |
CALL ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1), |
CALL ZTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1), |
$ LDA, B(NB+1, 1), LDB) |
$ LDA, B(NB+1, 1), LDB) |
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CALL ZTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1), |
CALL ZTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1), |
$ LDA, B(NB+1, 1), LDB) |
$ LDA, B(NB+1, 1), LDB) |
* |
* |
* Pivot, P * B [ P * (L**T \ (T \ (L \P**T * B) )) ] |
* Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ] |
* |
* |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 ) |
CALL ZLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 ) |
* |
* |