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*> \brief \b DSYT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DSYT01_AA( 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 December 2016
*
* @precisions fortran d -> z c
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DSYT01_AA( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C,
$ LDC, RWORK, RESID )
*
* -- LAPACK test routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 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
*
* 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
ENDIF
*
* 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
|
