*> \brief <b> DSYSV_AA computes the solution to system of linear equations A * X = B for SY matrices</b>
*
* =========== DOCUMENTATION ===========
*
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*
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*
* Definition:
* ===========
*
* SUBROUTINE DSYSV_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
*>
*> DSYSV computes the solution to a real system of linear equations
*> A * X = B,
*> where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
*> matrices.
*>
*> Aasen's algorithm is used to factor A as
*> A = U * T * U**T, if UPLO = 'U', or
*> A = L * T * L**T, if UPLO = 'L',
*> where U (or L) is a product of permutation and unit upper (lower)
*> triangular matrices, and T is symmetric tridiagonal. The factored
*> form of A is then used to solve the system of equations A * X = B.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., 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,out] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the symmetric matrix A. If UPLO = 'U', the leading
*> N-by-N upper triangular part of A contains the upper
*> triangular part of the matrix A, and the strictly lower
*> triangular part of A is not referenced. If UPLO = 'L', the
*> leading N-by-N lower triangular part of A contains the lower
*> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced.
*>
*> On exit, if INFO = 0, the tridiagonal matrix T and the
*> multipliers used to obtain the factor U or L from the
*> factorization A = U*T*U**T or A = L*T*L**T as computed by
*> DSYTRF.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> On exit, it contains the details of the interchanges, i.e.,
*> the row and column k of A were interchanged with the
*> row and column IPIV(k).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the N-by-NRHS right hand side matrix B.
*> On exit, if INFO = 0, the N-by-NRHS 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))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of WORK. LWORK >= MAX(1,2*N,3*N-2), and for
*> the best performance, LWORK >= MAX(1,N*NB), where NB is
*> the optimal blocksize for DSYTRF_AA.
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal size of the WORK array, returns
*> this value as the first entry of the WORK array, and no error
*> message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, D(i,i) is exactly zero. The factorization
*> has been completed, but the block diagonal matrix D is
*> exactly singular, so the solution could not be computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
* @precisions fortran d -> z c
*
*> \ingroup doubleSYsolve
*
* =====================================================================
SUBROUTINE DSYSV_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ LWORK, INFO )
*
* -- LAPACK driver routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, LDA, LDB, LWORK, N, NRHS
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER LWKOPT, LWKOPT_SYTRF, LWKOPT_SYTRS
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL ILAENV, LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, DSYTRF, DSYTRS, DSYTRS2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
IF( .NOT.LSAME( UPLO, 'U' ) .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(2*N, 3*N-2) .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
*
IF( INFO.EQ.0 ) THEN
CALL DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, -1, INFO )
LWKOPT_SYTRF = INT( WORK(1) )
CALL DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ -1, INFO )
LWKOPT_SYTRS = INT( WORK(1) )
LWKOPT = MAX( LWKOPT_SYTRF, LWKOPT_SYTRS )
WORK( 1 ) = LWKOPT
IF( LWORK.LT.LWKOPT .AND. .NOT.LQUERY ) THEN
INFO = -10
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSYSV_AA ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Compute the factorization A = U*T*U**T or A = L*T*L**T.
*
CALL DSYTRF_AA( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
IF( INFO.EQ.0 ) THEN
*
* Solve the system A*X = B, overwriting B with X.
*
CALL DSYTRS_AA( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
$ LWORK, INFO )
*
END IF
*
WORK( 1 ) = LWKOPT
*
RETURN
*
* End of DSYSV_AA
*
END