*> \brief DSYSV_AA_2STAGE computes the solution to system of linear equations A * X = B for SY matrices * * @generated from SRC/chesv_aa_2stage.f, fortran c -> d, Tue Oct 31 11:22:31 2017 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DSYSV_AA_2STAGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, * IPIV, IPIV2, B, LDB, WORK, LWORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER N, NRHS, LDA, LTB, LDB, LWORK, INFO * .. * .. Array Arguments .. * INTEGER IPIV( * ), IPIV2( * ) * DOUBLE PRECISION A( LDA, * ), TB( * ), B( LDB, *), WORK( * ) * .. * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYSV_AA_2STAGE 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 2-stage algorithm is used to factor A as *> A = U**T * T * U, 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 and band. The matrix T is *> then LU-factored with partial pivoting. The factored form of A *> is then used to solve the system of equations A * X = B. *> *> This is the blocked version of the algorithm, calling Level 3 BLAS. *> \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 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, L is stored below (or above) the subdiaonal blocks, *> when UPLO is 'L' (or 'U'). *> \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) *> On exit, details of the LU factorization of the band matrix. *> \endverbatim *> *> \param[in] LTB *> \verbatim *> LTB is INTEGER *> The size of the array TB. LTB >= 4*N, internally *> used to select NB such that LTB >= (3*NB+1)*N. *> *> If LTB = -1, then a workspace query is assumed; the *> routine only calculates the optimal size of LTB, *> returns this value as the first entry of TB, and *> no error message related to LTB is issued by XERBLA. *> \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[out] IPIV2 *> \verbatim *> IPIV2 is INTEGER array, dimension (N) *> On exit, it contains the details of the interchanges, i.e., *> the row and column k of T 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 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 workspace of size LWORK *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The size of WORK. LWORK >= N, internally used to select NB *> such that LWORK >= N*NB. *> *> 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, band LU factorization failed on i-th column *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup doubleSYsolve * * ===================================================================== SUBROUTINE DSYSV_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, \$ IPIV, IPIV2, 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, LTB, LWORK, INFO * .. * .. Array Arguments .. INTEGER IPIV( * ), IPIV2( * ) DOUBLE PRECISION A( LDA, * ), B( LDB, * ), TB( * ), WORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. LOGICAL UPPER, TQUERY, WQUERY INTEGER LWKOPT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DSYTRF_AA_2STAGE, DSYTRS_AA_2STAGE, \$ XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) WQUERY = ( LWORK.EQ.-1 ) TQUERY = ( LTB.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( LTB.LT.( 4*N ) .AND. .NOT.TQUERY ) THEN INFO = -7 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -11 ELSE IF( LWORK.LT.N .AND. .NOT.WQUERY ) THEN INFO = -13 END IF * IF( INFO.EQ.0 ) THEN CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, -1, IPIV, \$ IPIV2, WORK, -1, INFO ) LWKOPT = INT( WORK(1) ) END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYSV_AA_2STAGE', -INFO ) RETURN ELSE IF( WQUERY .OR. TQUERY ) THEN RETURN END IF * * * Compute the factorization A = U**T*T*U or A = L*T*L**T. * CALL DSYTRF_AA_2STAGE( UPLO, N, A, LDA, TB, LTB, IPIV, IPIV2, \$ WORK, LWORK, INFO ) IF( INFO.EQ.0 ) THEN * * Solve the system A*X = B, overwriting B with X. * CALL DSYTRS_AA_2STAGE( UPLO, N, NRHS, A, LDA, TB, LTB, IPIV, \$ IPIV2, B, LDB, INFO ) * END IF * WORK( 1 ) = LWKOPT * RETURN * * End of DSYSV_AA_2STAGE * END