*> \brief \b DSYTRS_AA
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
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*
* 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.
*
*> \ingroup doubleSYcomputational
*
* =====================================================================
SUBROUTINE DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB,
$ WORK, LWORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
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