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dsytrs_aa_2stage.f
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*> \brief \b DSYTRS_AA_2STAGE
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DSYTRS_AA_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytrs_aa_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsytrs_aa_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsytrs_aa_2stage.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV,
* IPIV2, B, LDB, INFO )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER N, NRHS, LDA, LTB, LDB, INFO
* ..
* .. Array Arguments ..
* INTEGER IPIV( * ), IPIV2( * )
* DOUBLE PRECISION A( LDA, * ), TB( * ), B( LDB, * )
* ..
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSYTRS_AA_2STAGE 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_2STAGE.
*> \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_2STAGE.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[out] TB
*> \verbatim
*> TB is DOUBLE PRECISION array, dimension (LTB)
*> Details of factors computed by DSYTRF_AA_2STAGE.
*> \endverbatim
*>
*> \param[in] LTB
*> \verbatim
*> LTB is INTEGER
*> The size of the array TB. LTB >= 4*N.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> Details of the interchanges as computed by
*> DSYTRF_AA_2STAGE.
*> \endverbatim
*>
*> \param[in] IPIV2
*> \verbatim
*> IPIV2 is INTEGER array, dimension (N)
*> Details of the interchanges as computed by
*> DSYTRF_AA_2STAGE.
*> \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] 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_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB,
$ IPIV, IPIV2, B, LDB, 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, LTB, LDB, INFO
* ..
* .. Array Arguments ..
INTEGER IPIV( * ), IPIV2( * )
DOUBLE PRECISION A( LDA, * ), TB( * ), B( LDB, * )
* ..
*
* =====================================================================
*
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER LDTB, NB
LOGICAL UPPER
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DGBTRS, DLASWP, DTRSM, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
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( LTB.LT.( 4*N ) ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -11
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSYTRS_AA_2STAGE', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Read NB and compute LDTB
*
NB = INT( TB( 1 ) )
LDTB = LTB/N
*
IF( UPPER ) THEN
*
* Solve A*X = B, where A = U**T*T*U.
*
IF( N.GT.NB ) THEN
*
* Pivot, P**T * B -> B
*
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
*
* Compute (U**T \ B) -> B [ (U**T \P**T * B) ]
*
CALL DTRSM( 'L', 'U', 'T', 'U', N-NB, NRHS, ONE, A(1, NB+1),
$ LDA, B(NB+1, 1), LDB)
*
END IF
*
* Compute T \ B -> B [ T \ (U**T \P**T * B) ]
*
CALL DGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
$ INFO)
IF( N.GT.NB ) THEN
*
* Compute (U \ B) -> B [ U \ (T \ (U**T \P**T * B) ) ]
*
CALL DTRSM( 'L', 'U', 'N', 'U', N-NB, NRHS, ONE, A(1, NB+1),
$ LDA, B(NB+1, 1), LDB)
*
* Pivot, P * B -> B [ P * (U \ (T \ (U**T \P**T * B) )) ]
*
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
*
END IF
*
ELSE
*
* Solve A*X = B, where A = L*T*L**T.
*
IF( N.GT.NB ) THEN
*
* Pivot, P**T * B -> B
*
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, 1 )
*
* Compute (L \ B) -> B [ (L \P**T * B) ]
*
CALL DTRSM( 'L', 'L', 'N', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
$ LDA, B(NB+1, 1), LDB)
*
END IF
*
* Compute T \ B -> B [ T \ (L \P**T * B) ]
*
CALL DGBTRS( 'N', N, NB, NB, NRHS, TB, LDTB, IPIV2, B, LDB,
$ INFO)
IF( N.GT.NB ) THEN
*
* Compute (L**T \ B) -> B [ L**T \ (T \ (L \P**T * B) ) ]
*
CALL DTRSM( 'L', 'L', 'T', 'U', N-NB, NRHS, ONE, A(NB+1, 1),
$ LDA, B(NB+1, 1), LDB)
*
* Pivot, P * B -> B [ P * (L**T \ (T \ (L \P**T * B) )) ]
*
CALL DLASWP( NRHS, B, LDB, NB+1, N, IPIV, -1 )
*
END IF
END IF
*
RETURN
*
* End of DSYTRS_AA_2STAGE
*
END