*> \brief \b DSYTRS_AA * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYTRS_AA + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, * WORK, LWORK, INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER N, NRHS, LDA, LDB, LWORK, INFO * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYTRS_AA solves a system of linear equations A*X = B with a real *> symmetric matrix A using the factorization A = U**T*T*U or *> A = L*T*L**T computed by DSYTRF_AA. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the details of the factorization are stored *> as an upper or lower triangular matrix. *> = 'U': Upper triangular, form is A = U**T*T*U; *> = 'L': Lower triangular, form is A = L*T*L**T. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of right hand sides, i.e., the number of columns *> of the matrix B. NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> Details of factors computed by DSYTRF_AA. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges as computed by DSYTRF_AA. *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) *> On entry, the right hand side matrix B. *> On exit, the solution matrix X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. LDB >= max(1,N). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The dimension of the array WORK. LWORK >= max(1,3*N-2). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2017 * *> \ingroup doubleSYcomputational * * ===================================================================== SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, $ WORK, LWORK, INFO ) * * -- LAPACK computational routine (version 3.8.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2017 * IMPLICIT NONE * * .. Scalar Arguments .. CHARACTER UPLO INTEGER N, NRHS, LDA, LDB, LWORK, INFO * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * ===================================================================== * DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER INTEGER K, KP, LWKOPT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLACPY, DGTSV, DSWAP, DTRSM, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( NRHS.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 ELSE IF( LWORK.LT.MAX( 1, 3*N-2 ) .AND. .NOT.LQUERY ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYTRS_AA', -INFO ) RETURN ELSE IF( LQUERY ) THEN LWKOPT = (3*N-2) WORK( 1 ) = LWKOPT RETURN END IF * * Quick return if possible * IF( N.EQ.0 .OR. NRHS.EQ.0 ) $ RETURN * IF( UPPER ) THEN * * Solve A*X = B, where A = U**T*T*U. * * 1) Forward substitution with U**T * IF( N.GT.1 ) THEN * * Pivot, P**T * B -> B * DO K = 1, N KP = IPIV( K ) IF( KP.NE.K ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END DO * * Compute U**T \ B -> B [ (U**T \P**T * B) ] * CALL DTRSM('L', 'U', 'T', 'U', N-1, NRHS, ONE, A( 1, 2 ), $ LDA, B( 2, 1 ), LDB) END IF * * 2) Solve with triangular matrix T * * Compute T \ B -> B [ T \ (U**T \P**T * B) ] * CALL DLACPY( 'F', 1, N, A( 1, 1 ), LDA+1, WORK( N ), 1) IF( N.GT.1 ) THEN CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 1 ), 1 ) CALL DLACPY( 'F', 1, N-1, A( 1, 2 ), LDA+1, WORK( 2*N ), 1 ) END IF CALL DGTSV( N, NRHS, WORK( 1 ), WORK( N ), WORK( 2*N ), B, LDB, $ INFO ) * * 3) Backward substitution with U * IF( N.GT.1 ) THEN * * Compute U \ B -> B [ U \ (T \ (U**T \P**T * B) ) ] * CALL DTRSM( 'L', 'U', 'N', 'U', N-1, NRHS, ONE, A( 1, 2 ), $ LDA, B( 2, 1 ), LDB) * * Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ] * DO K = N, 1, -1 KP = IPIV( K ) IF( KP.NE.K ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END DO END IF * ELSE * * Solve A*X = B, where A = L*T*L**T. * * 1) Forward substitution with L * IF( N.GT.1 ) THEN * * Pivot, P**T * B -> B * DO K = 1, N KP = IPIV( K ) IF( KP.NE.K ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END DO * * Compute L \ B -> B [ (L \P**T * B) ] * CALL DTRSM( 'L', 'L', 'N', 'U', N-1, NRHS, ONE, A( 2, 1 ), $ LDA, B( 2, 1 ), LDB) END IF * * 2) Solve with triangular matrix T * * Compute T \ B -> B [ T \ (L \P**T * B) ] * CALL DLACPY( 'F', 1, N, A(1, 1), LDA+1, WORK(N), 1) IF( N.GT.1 ) THEN CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 1 ), 1 ) CALL DLACPY( 'F', 1, N-1, A( 2, 1 ), LDA+1, WORK( 2*N ), 1 ) END IF CALL DGTSV( N, NRHS, WORK( 1 ), WORK(N), WORK( 2*N ), B, LDB, $ INFO) * * 3) Backward substitution with L**T * IF( N.GT.1 ) THEN * * Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ] * CALL DTRSM( 'L', 'L', 'T', 'U', N-1, NRHS, ONE, A( 2, 1 ), $ LDA, B( 2, 1 ), LDB) * * Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ] * DO K = N, 1, -1 KP = IPIV( K ) IF( KP.NE.K ) $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB ) END DO END IF * END IF * RETURN * * End of DSYTRS_AA * END