222 lines
5.8 KiB
Fortran
222 lines
5.8 KiB
Fortran
*> \brief \b SPOT03
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
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* RWORK, RCOND, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDA, LDAINV, LDWORK, N
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* REAL RCOND, RESID
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
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* $ WORK( LDWORK, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SPOT03 computes the residual for a symmetric matrix times its
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*> inverse:
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*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
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*> where EPS is the machine epsilon.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> symmetric matrix A is stored:
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows and columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,N)
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*> The original symmetric matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N)
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*> \endverbatim
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*>
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*> \param[in,out] AINV
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*> \verbatim
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*> AINV is REAL array, dimension (LDAINV,N)
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*> On entry, the inverse of the matrix A, stored as a symmetric
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*> matrix in the same format as A.
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*> In this version, AINV is expanded into a full matrix and
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*> multiplied by A, so the opposing triangle of AINV will be
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*> changed; i.e., if the upper triangular part of AINV is
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*> stored, the lower triangular part will be used as work space.
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*> \endverbatim
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*>
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*> \param[in] LDAINV
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*> \verbatim
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*> LDAINV is INTEGER
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*> The leading dimension of the array AINV. LDAINV >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LDWORK,N)
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*> \endverbatim
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*>
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*> \param[in] LDWORK
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*> \verbatim
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*> LDWORK is INTEGER
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*> The leading dimension of the array WORK. LDWORK >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RCOND
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*> \verbatim
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*> RCOND is REAL
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*> The reciprocal of the condition number of A, computed as
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*> ( 1/norm(A) ) / norm(AINV).
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is REAL
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*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2011
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SPOT03( UPLO, N, A, LDA, AINV, LDAINV, WORK, LDWORK,
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$ RWORK, RCOND, RESID )
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*
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* -- LAPACK test routine (version 3.4.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2011
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDA, LDAINV, LDWORK, N
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REAL RCOND, RESID
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AINV( LDAINV, * ), RWORK( * ),
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$ WORK( LDWORK, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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REAL AINVNM, ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SLAMCH, SLANGE, SLANSY
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EXTERNAL LSAME, SLAMCH, SLANGE, SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL SSYMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC REAL
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RCOND = ONE
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
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*
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EPS = SLAMCH( 'Epsilon' )
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ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
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AINVNM = SLANSY( '1', UPLO, N, AINV, LDAINV, RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCOND = ZERO
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RESID = ONE / EPS
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RETURN
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END IF
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RCOND = ( ONE / ANORM ) / AINVNM
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*
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* Expand AINV into a full matrix and call SSYMM to multiply
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* AINV on the left by A.
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 20 J = 1, N
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DO 10 I = 1, J - 1
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AINV( J, I ) = AINV( I, J )
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10 CONTINUE
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20 CONTINUE
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ELSE
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DO 40 J = 1, N
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DO 30 I = J + 1, N
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AINV( J, I ) = AINV( I, J )
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30 CONTINUE
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40 CONTINUE
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END IF
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CALL SSYMM( 'Left', UPLO, N, N, -ONE, A, LDA, AINV, LDAINV, ZERO,
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$ WORK, LDWORK )
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*
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* Add the identity matrix to WORK .
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*
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DO 50 I = 1, N
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WORK( I, I ) = WORK( I, I ) + ONE
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50 CONTINUE
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*
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* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = SLANGE( '1', N, N, WORK, LDWORK, RWORK )
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*
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RESID = ( ( RESID*RCOND ) / EPS ) / REAL( N )
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*
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RETURN
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*
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* End of SPOT03
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*
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END
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