version 1.4, 2010/08/06 15:32:35
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version 1.19, 2023/08/07 08:39:09
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*> \brief <b> DSYSV computes the solution to system of linear equations A * X = B for SY matrices</b> |
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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 DSYSV + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsysv.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/dsysv.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/dsysv.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 DSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, |
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* LWORK, 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, LWORK, 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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*> DSYSV computes the solution to a real system of linear equations |
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*> A * X = B, |
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*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS |
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*> matrices. |
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*> |
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*> The diagonal pivoting method is used to factor A as |
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*> A = U * D * U**T, if UPLO = 'U', or |
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*> A = L * D * L**T, if UPLO = 'L', |
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*> where U (or L) is a product of permutation and unit upper (lower) |
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*> triangular matrices, and D is symmetric and block diagonal with |
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*> 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then |
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*> used to solve the system of equations A * X = B. |
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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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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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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 number of linear equations, i.e., the order of the |
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*> 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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*> On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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*> N-by-N upper triangular part of A contains the upper |
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*> triangular part of the matrix A, and the strictly lower |
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*> triangular part of A is not referenced. If UPLO = 'L', the |
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*> leading N-by-N lower triangular part of A contains the lower |
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*> triangular part of the matrix A, and the strictly upper |
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*> triangular part of A is not referenced. |
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*> |
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*> On exit, if INFO = 0, the block diagonal matrix D and the |
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*> multipliers used to obtain the factor U or L from the |
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*> factorization A = U*D*U**T or A = L*D*L**T as computed by |
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*> DSYTRF. |
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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[out] 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, as |
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*> determined by DSYTRF. If IPIV(k) > 0, then rows and columns |
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*> k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 |
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*> diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, |
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*> then rows and columns k-1 and -IPIV(k) were interchanged and |
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*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and |
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*> IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and |
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*> -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 |
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*> diagonal block. |
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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 N-by-NRHS right hand side matrix B. |
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*> On exit, if INFO = 0, the N-by-NRHS 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 (MAX(1,LWORK)) |
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> The length of WORK. LWORK >= 1, and for best performance |
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*> LWORK >= max(1,N*NB), where NB is the optimal blocksize for |
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*> DSYTRF. |
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*> for LWORK < N, TRS will be done with Level BLAS 2 |
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*> for LWORK >= N, TRS will be done with Level BLAS 3 |
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*> |
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*> If LWORK = -1, then a workspace query is assumed; the routine |
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*> only calculates the optimal size of the WORK array, returns |
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*> this value as the first entry of the WORK array, and no error |
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*> message related to LWORK is issued by XERBLA. |
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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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*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization |
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*> has been completed, but the block diagonal matrix D is |
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*> exactly singular, so the solution could not be computed. |
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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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*> \ingroup doubleSYsolve |
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* |
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* ===================================================================== |
SUBROUTINE DSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, |
SUBROUTINE DSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, |
$ LWORK, INFO ) |
$ LWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver 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 2006 |
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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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* DSYSV computes the solution to a real system of linear equations |
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* A * X = B, |
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* where A is an N-by-N symmetric matrix and X and B are N-by-NRHS |
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* matrices. |
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* |
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* The diagonal pivoting method is used to factor A as |
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* A = U * D * U**T, if UPLO = 'U', or |
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* A = L * D * L**T, if UPLO = 'L', |
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* where U (or L) is a product of permutation and unit upper (lower) |
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* triangular matrices, and D is symmetric and block diagonal with |
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* 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then |
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* used to solve the system of equations A * X = B. |
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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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* = 'U': Upper triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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* |
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* N (input) INTEGER |
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* The number of linear equations, i.e., the order of the |
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* 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/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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* N-by-N upper triangular part of A contains the upper |
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* triangular part of the matrix A, and the strictly lower |
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* triangular part of A is not referenced. If UPLO = 'L', the |
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* leading N-by-N lower triangular part of A contains the lower |
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* triangular part of the matrix A, and the strictly upper |
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* triangular part of A is not referenced. |
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* |
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* On exit, if INFO = 0, the block diagonal matrix D and the |
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* multipliers used to obtain the factor U or L from the |
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* factorization A = U*D*U**T or A = L*D*L**T as computed by |
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* 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 (output) INTEGER array, dimension (N) |
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* Details of the interchanges and the block structure of D, as |
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* determined by DSYTRF. If IPIV(k) > 0, then rows and columns |
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* k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 |
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* diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, |
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* then rows and columns k-1 and -IPIV(k) were interchanged and |
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* D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and |
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* IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and |
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* -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2 |
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* diagonal block. |
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* |
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* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) |
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* On entry, the N-by-NRHS right hand side matrix B. |
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* On exit, if INFO = 0, the N-by-NRHS 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/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The length of WORK. LWORK >= 1, and for best performance |
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* LWORK >= max(1,N*NB), where NB is the optimal blocksize for |
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* DSYTRF. |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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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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* > 0: if INFO = i, D(i,i) is exactly zero. The factorization |
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* has been completed, but the block diagonal matrix D is |
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* exactly singular, so the solution could not be computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
LOGICAL LQUERY |
LOGICAL LQUERY |
INTEGER LWKOPT, NB |
INTEGER LWKOPT |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME |
INTEGER ILAENV |
EXTERNAL LSAME |
EXTERNAL LSAME, ILAENV |
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* .. |
* .. |
* .. External Subroutines .. |
* .. External Subroutines .. |
EXTERNAL DSYTRF, DSYTRS, XERBLA |
EXTERNAL XERBLA, DSYTRF, DSYTRS, DSYTRS2 |
* .. |
* .. |
* .. Intrinsic Functions .. |
* .. Intrinsic Functions .. |
INTRINSIC MAX |
INTRINSIC MAX |
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IF( N.EQ.0 ) THEN |
IF( N.EQ.0 ) THEN |
LWKOPT = 1 |
LWKOPT = 1 |
ELSE |
ELSE |
NB = ILAENV( 1, 'DSYTRF', UPLO, N, -1, -1, -1 ) |
CALL DSYTRF( UPLO, N, A, LDA, IPIV, WORK, -1, INFO ) |
LWKOPT = N*NB |
LWKOPT = INT( WORK( 1 ) ) |
END IF |
END IF |
WORK( 1 ) = LWKOPT |
WORK( 1 ) = LWKOPT |
END IF |
END IF |
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RETURN |
RETURN |
END IF |
END IF |
* |
* |
* Compute the factorization A = U*D*U' or A = L*D*L'. |
* Compute the factorization A = U*D*U**T or A = L*D*L**T. |
* |
* |
CALL DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) |
CALL DSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO ) |
IF( INFO.EQ.0 ) THEN |
IF( INFO.EQ.0 ) THEN |
* |
* |
* Solve the system A*X = B, overwriting B with X. |
* Solve the system A*X = B, overwriting B with X. |
* |
* |
CALL DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
IF ( LWORK.LT.N ) THEN |
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* |
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* Solve with TRS ( Use Level BLAS 2) |
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* |
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CALL DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |
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* |
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ELSE |
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* |
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* Solve with TRS2 ( Use Level BLAS 3) |
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* |
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CALL DSYTRS2( UPLO,N,NRHS,A,LDA,IPIV,B,LDB,WORK,INFO ) |
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* |
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END IF |
* |
* |
END IF |
END IF |
* |
* |