*> \brief \b DSYTRS_AA_2STAGE * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYTRS_AA_2STAGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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. * *> \date November 2017 * *> \ingroup doubleSYcomputational * * ===================================================================== SUBROUTINE DSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, $ IPIV, IPIV2, B, LDB, 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, 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