*> \brief \b DSYT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, * RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDAFAC, LDC, N * DOUBLE PRECISION RESID * .. * .. Array Arguments .. * INTEGER IPIV( * ) * DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ), * $ RWORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DSYT01 reconstructs a symmetric indefinite matrix A from its *> block L*D*L' or U*D*U' factorization and computes the residual *> norm( C - A ) / ( N * norm(A) * EPS ), *> where C is the reconstructed matrix and EPS is the machine epsilon. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> symmetric matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> The original symmetric matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N) *> \endverbatim *> *> \param[in] AFAC *> \verbatim *> AFAC is DOUBLE PRECISION array, dimension (LDAFAC,N) *> The factored form of the matrix A. AFAC contains the block *> diagonal matrix D and the multipliers used to obtain the *> factor L or U from the block L*D*L' or U*D*U' factorization *> as computed by DSYTRF. *> \endverbatim *> *> \param[in] LDAFAC *> \verbatim *> LDAFAC is INTEGER *> The leading dimension of the array AFAC. LDAFAC >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from DSYTRF. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDC,N) *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2016 * * @precisions fortran d -> s * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DSYT01_AASEN( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, $ LDC, RWORK, RESID ) * * -- LAPACK test routine (version 3.5.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2016 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDAFAC, LDC, N DOUBLE PRECISION RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) DOUBLE PRECISION A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ), $ RWORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANSY EXTERNAL LSAME, DLAMCH, DLANSY * .. * .. External Subroutines .. EXTERNAL DLASET, DLAVSY * .. * .. Intrinsic Functions .. INTRINSIC DBLE * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Determine EPS and the norm of A. * EPS = DLAMCH( 'Epsilon' ) ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK ) * * Initialize C to the tridiagonal matrix T. * CALL DLASET( 'Full', N, N, ZERO, ZERO, C, LDC ) CALL DLACPY( 'F', 1, N, AFAC( 1, 1 ), LDAFAC+1, C( 1, 1 ), LDC+1 ) IF( N.GT.1 ) THEN IF( LSAME( UPLO, 'U' ) ) THEN CALL DLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 1, 2 ), $ LDC+1 ) CALL DLACPY( 'F', 1, N-1, AFAC( 1, 2 ), LDAFAC+1, C( 2, 1 ), $ LDC+1 ) ELSE CALL DLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 1, 2 ), $ LDC+1 ) CALL DLACPY( 'F', 1, N-1, AFAC( 2, 1 ), LDAFAC+1, C( 2, 1 ), $ LDC+1 ) ENDIF ENDIF * * Call DTRMM to form the product U' * D (or L * D ). * IF( LSAME( UPLO, 'U' ) ) THEN CALL DTRMM( 'Left', UPLO, 'Transpose', 'Unit', N-1, N, $ ONE, AFAC( 1, 2 ), LDAFAC, C( 2, 1 ), LDC ) ELSE CALL DTRMM( 'Left', UPLO, 'No transpose', 'Unit', N-1, N, $ ONE, AFAC( 2, 1 ), LDAFAC, C( 2, 1 ), LDC ) END IF * * Call DTRMM again to multiply by U (or L ). * IF( LSAME( UPLO, 'U' ) ) THEN CALL DTRMM( 'Right', UPLO, 'No transpose', 'Unit', N, N-1, $ ONE, AFAC( 1, 2 ), LDAFAC, C( 1, 2 ), LDC ) ELSE CALL DTRMM( 'Right', UPLO, 'Transpose', 'Unit', N, N-1, $ ONE, AFAC( 2, 1 ), LDAFAC, C( 1, 2 ), LDC ) END IF * * Apply symmetric pivots * DO J = N, 1, -1 I = IPIV( J ) IF( I.NE.J ) $ CALL DSWAP( N, C( J, 1 ), LDC, C( I, 1 ), LDC ) END DO DO J = N, 1, -1 I = IPIV( J ) IF( I.NE.J ) $ CALL DSWAP( N, C( 1, J ), 1, C( 1, I ), 1 ) END DO * * * Compute the difference C - A . * IF( LSAME( UPLO, 'U' ) ) THEN DO J = 1, N DO I = 1, J C( I, J ) = C( I, J ) - A( I, J ) END DO END DO ELSE DO J = 1, N DO I = J, N C( I, J ) = C( I, J ) - A( I, J ) END DO END DO END IF * * Compute norm( C - A ) / ( N * norm(A) * EPS ) * RESID = DLANSY( '1', UPLO, N, C, LDC, RWORK ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS END IF * RETURN * * End of DSYT01 * END