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309 lines
8.3 KiB
309 lines
8.3 KiB
2 years ago
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*> \brief \b DSYTRS_AA
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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 DSYTRS_AA + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs_aa.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/dsytrs_aa.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/dsytrs_aa.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 DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
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* WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER N, NRHS, LDA, LDB, LWORK, INFO
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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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*> DSYTRS_AA solves a system of linear equations A*X = B with a real
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*> symmetric matrix A using the factorization A = U**T*T*U or
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*> A = L*T*L**T computed by DSYTRF_AA.
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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**T*T*U;
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*> = 'L': Lower triangular, form is A = L*T*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 DOUBLE PRECISION array, dimension (LDA,N)
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*> Details of factors computed by DSYTRF_AA.
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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 as computed by DSYTRF_AA.
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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 (MAX(1,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 dimension of the array WORK. LWORK >= max(1,3*N-2).
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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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*> \ingroup doubleSYcomputational
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*
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* =====================================================================
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SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
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$ WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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IMPLICIT NONE
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER N, NRHS, LDA, LDB, LWORK, INFO
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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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*
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER
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INTEGER K, KP, LWKOPT
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL DLACPY, DGTSV, DSWAP, DTRSM, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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LQUERY = ( LWORK.EQ.-1 )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( NRHS.LT.0 ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
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INFO = -8
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ELSE IF( LWORK.LT.MAX( 1, 3*N-2 ) .AND. .NOT.LQUERY ) THEN
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INFO = -10
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DSYTRS_AA', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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LWKOPT = (3*N-2)
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WORK( 1 ) = LWKOPT
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 .OR. NRHS.EQ.0 )
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$ RETURN
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*
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IF( UPPER ) THEN
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*
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* Solve A*X = B, where A = U**T*T*U.
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*
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* 1) Forward substitution with U**T
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*
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IF( N.GT.1 ) THEN
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*
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* Pivot, P**T * B -> B
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*
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DO K = 1, N
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END DO
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*
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* Compute U**T \ B -> B [ (U**T \P**T * B) ]
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*
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CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ),
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$ LDA, B( 2, 1 ), LDB)
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END IF
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*
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* 2) Solve with triangular matrix T
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*
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* Compute T \ B -> B [ T \ (U**T \P**T * B) ]
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*
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CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1)
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IF( N.GT.1 ) THEN
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CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 )
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CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1 )
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END IF
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CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB,
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$ INFO )
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*
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* 3) Backward substitution with U
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*
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IF( N.GT.1 ) THEN
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*
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* Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ]
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*
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CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ),
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$ LDA, B( 2, 1 ), LDB)
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*
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* Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
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*
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DO K = N, 1, -1
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END DO
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END IF
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*
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ELSE
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*
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* Solve A*X = B, where A = L*T*L**T.
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*
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* 1) Forward substitution with L
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*
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IF( N.GT.1 ) THEN
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*
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* Pivot, P**T * B -> B
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*
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DO K = 1, N
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END DO
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*
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* Compute L \ B -> B [ (L \P**T * B) ]
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*
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CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ),
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$ LDA, B( 2, 1 ), LDB)
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END IF
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*
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* 2) Solve with triangular matrix T
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*
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* Compute T \ B -> B [ T \ (L \P**T * B) ]
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*
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CALL DLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1)
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IF( N.GT.1 ) THEN
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CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 )
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CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1 )
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END IF
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CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB,
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$ INFO)
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*
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* 3) Backward substitution with L**T
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*
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IF( N.GT.1 ) THEN
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*
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* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
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*
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CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ),
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$ LDA, B( 2, 1 ), LDB)
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*
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* Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
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*
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DO K = N, 1, -1
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KP = IPIV( K )
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IF( KP.NE.K )
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$ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
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END DO
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END IF
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*
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END IF
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*
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RETURN
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*
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* End of DSYTRS_AA
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*
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END
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