version 1.2, 2010/12/21 13:53:40
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version 1.10, 2016/08/27 15:27:11
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*> \brief \b DSYTRS2 |
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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 DSYTRS2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs2.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/dsytrs2.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/dsytrs2.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 DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, |
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* WORK, 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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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) |
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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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*> DSYTRS2 solves a system of linear equations A*X = B with a real |
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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 DSYTRF and converted by DSYCONV. |
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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,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION 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 DSYTRF. |
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*> Note that A is input / output. This might be counter-intuitive, |
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*> and one may think that A is input only. A is input / output. This |
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*> is because, at the start of the subroutine, we permute A in a |
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*> "better" form and then we permute A back to its original form at |
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*> the end. |
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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 DSYTRF. |
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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 DOUBLE PRECISION 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] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (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 June 2016 |
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* |
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*> \ingroup doubleSYcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, |
SUBROUTINE DSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, |
$ WORK, INFO ) |
$ WORK, INFO ) |
* |
* |
* -- LAPACK PROTOTYPE routine (version 3.3.0) -- |
* -- LAPACK computational routine (version 3.6.1) -- |
* -- 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 2010 |
* June 2016 |
* |
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* -- Written by Julie Langou of the Univ. of TN -- |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSYTRS2 solves a system of linear equations A*X = B with a real |
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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 DSYTRF and converted by DSYCONV. |
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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) DOUBLE PRECISION 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 DSYTRF. |
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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 DSYTRF. |
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* |
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* B (input/output) DOUBLE PRECISION 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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* WORK (workspace) REAL array, dimension (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. |
* |
* |
* P' * B |
* P**T * B |
K=N |
K=N |
DO WHILE ( K .GE. 1 ) |
DO WHILE ( K .GE. 1 ) |
IF( IPIV( K ).GT.0 ) THEN |
IF( IPIV( K ).GT.0 ) THEN |
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END IF |
END IF |
END DO |
END DO |
* |
* |
* Compute (U \P' * B) -> B [ (U \P' * B) ] |
* Compute (U \P**T * B) -> B [ (U \P**T * B) ] |
* |
* |
CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,N,B,N) |
CALL DTRSM('L','U','N','U',N,NRHS,ONE,A,LDA,B,LDB) |
* |
* |
* Compute D \ B -> B [ D \ (U \P' * B) ] |
* Compute D \ B -> B [ D \ (U \P**T * B) ] |
* |
* |
I=N |
I=N |
DO WHILE ( I .GE. 1 ) |
DO WHILE ( I .GE. 1 ) |
IF( IPIV(I) .GT. 0 ) THEN |
IF( IPIV(I) .GT. 0 ) THEN |
CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N ) |
CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB ) |
ELSEIF ( I .GT. 1) THEN |
ELSEIF ( I .GT. 1) THEN |
IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN |
IF ( IPIV(I-1) .EQ. IPIV(I) ) THEN |
AKM1K = WORK(I) |
AKM1K = WORK(I) |
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I = I - 1 |
I = I - 1 |
END DO |
END DO |
* |
* |
* Compute (U' \ B) -> B [ U' \ (D \ (U \P' * B) ) ] |
* Compute (U**T \ B) -> B [ U**T \ (D \ (U \P**T * B) ) ] |
* |
* |
CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,N,B,N) |
CALL DTRSM('L','U','T','U',N,NRHS,ONE,A,LDA,B,LDB) |
* |
* |
* P * B [ P * (U' \ (D \ (U \P' * B) )) ] |
* P * B [ P * (U**T \ (D \ (U \P**T * B) )) ] |
* |
* |
K=1 |
K=1 |
DO WHILE ( K .LE. N ) |
DO WHILE ( K .LE. N ) |
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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. |
* |
* |
* P' * B |
* P**T * B |
K=1 |
K=1 |
DO WHILE ( K .LE. N ) |
DO WHILE ( K .LE. N ) |
IF( IPIV( K ).GT.0 ) THEN |
IF( IPIV( K ).GT.0 ) THEN |
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ENDIF |
ENDIF |
END DO |
END DO |
* |
* |
* Compute (L \P' * B) -> B [ (L \P' * B) ] |
* Compute (L \P**T * B) -> B [ (L \P**T * B) ] |
* |
* |
CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,N,B,N) |
CALL DTRSM('L','L','N','U',N,NRHS,ONE,A,LDA,B,LDB) |
* |
* |
* Compute D \ B -> B [ D \ (L \P' * B) ] |
* Compute D \ B -> B [ D \ (L \P**T * B) ] |
* |
* |
I=1 |
I=1 |
DO WHILE ( I .LE. N ) |
DO WHILE ( I .LE. N ) |
IF( IPIV(I) .GT. 0 ) THEN |
IF( IPIV(I) .GT. 0 ) THEN |
CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), N ) |
CALL DSCAL( NRHS, ONE / A( I, I ), B( I, 1 ), LDB ) |
ELSE |
ELSE |
AKM1K = WORK(I) |
AKM1K = WORK(I) |
AKM1 = A( I, I ) / AKM1K |
AKM1 = A( I, I ) / AKM1K |
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I = I + 1 |
I = I + 1 |
END DO |
END DO |
* |
* |
* Compute (L' \ B) -> B [ L' \ (D \ (L \P' * B) ) ] |
* Compute (L**T \ B) -> B [ L**T \ (D \ (L \P**T * B) ) ] |
* |
* |
CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,N,B,N) |
CALL DTRSM('L','L','T','U',N,NRHS,ONE,A,LDA,B,LDB) |
* |
* |
* P * B [ P * (L' \ (D \ (L \P' * B) )) ] |
* P * B [ P * (L**T \ (D \ (L \P**T * B) )) ] |
* |
* |
K=N |
K=N |
DO WHILE ( K .GE. 1 ) |
DO WHILE ( K .GE. 1 ) |