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diff --git a/TESTING/LIN/dsyt01_aa.f b/TESTING/LIN/dsyt01_aa.f new file mode 100644 index 00000000..bc30df38 --- /dev/null +++ b/TESTING/LIN/dsyt01_aa.f @@ -0,0 +1,263 @@ +*> \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_AA( 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 |