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*> \brief \b DPOT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
* RWORK, RCOND, RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER LDA, LDAINV, LDWORK, N
* DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
* $ WORK( LDWORK, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DPOT03 computes the residual for a symmetric matrix times its
*> inverse:
*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where 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,out] AINV
*> \verbatim
*> AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
*> On entry, the inverse of the matrix A, stored as a symmetric
*> matrix in the same format as A.
*> In this version, AINV is expanded into a full matrix and
*> multiplied by A, so the opposing triangle of AINV will be
*> changed; i.e., if the upper triangular part of AINV is
*> stored, the lower triangular part will be used as work space.
*> \endverbatim
*>
*> \param[in] LDAINV
*> \verbatim
*> LDAINV is INTEGER
*> The leading dimension of the array AINV. LDAINV >= max(1,N).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LDWORK,N)
*> \endverbatim
*>
*> \param[in] LDWORK
*> \verbatim
*> LDWORK is INTEGER
*> The leading dimension of the array WORK. LDWORK >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*> RCOND is DOUBLE PRECISION
*> The reciprocal of the condition number of A, computed as
*> ( 1/norm(A) ) / norm(AINV).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
$ RWORK, RCOND, RESID )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER LDA, LDAINV, LDWORK, N
DOUBLE PRECISION RCOND, RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
$ WORK( LDWORK, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION AINVNM, ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DLANGE, DLANSY
EXTERNAL LSAME, DLAMCH, DLANGE, DLANSY
* ..
* .. External Subroutines ..
EXTERNAL DSYMM
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RCOND = ONE
RESID = ZERO
RETURN
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
AINVNM = DLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
RCOND = ZERO
RESID = ONE / EPS
RETURN
END IF
RCOND = ( ONE / ANORM ) / AINVNM
*
* Expand AINV into a full matrix and call DSYMM to multiply
* AINV on the left by A.
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO 20 J = 1, N
DO 10 I = 1, J - 1
AINV( J, I ) = AINV( I, J )
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = J + 1, N
AINV( J, I ) = AINV( I, J )
30 CONTINUE
40 CONTINUE
END IF
CALL DSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
$ WORK, LDWORK )
*
* Add the identity matrix to WORK .
*
DO 50 I = 1, N
WORK( I, I ) = WORK( I, I ) + ONE
50 CONTINUE
*
* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
*
RESID = DLANGE( '1', N, N, WORK, LDWORK, RWORK )
*
RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
*
RETURN
*
* End of DPOT03
*
END
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