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220 lines
6.0 KiB
220 lines
6.0 KiB
2 years ago
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*> \brief \b DTRT01
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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 DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
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* WORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, UPLO
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* INTEGER LDA, LDAINV, N
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* DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), WORK( * )
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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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*> DTRT01 computes the residual for a triangular matrix A times its
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*> inverse:
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*> RESID = norm( A*AINV - I ) / ( 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 matrix A is upper or lower triangular.
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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] DIAG
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*> \verbatim
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*> DIAG is CHARACTER*1
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*> Specifies whether or not the matrix A is unit triangular.
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*> = 'N': Non-unit triangular
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*> = 'U': Unit 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 order 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 DOUBLE PRECISION array, dimension (LDA,N)
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*> The triangular matrix A. If UPLO = 'U', the leading n by n
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*> upper triangular part of the array A contains the upper
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*> triangular matrix, and the strictly lower triangular part of
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*> A is not referenced. If UPLO = 'L', the leading n by n lower
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*> triangular part of the array A contains the lower triangular
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*> matrix, and the strictly upper triangular part of A is not
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*> referenced. If DIAG = 'U', the diagonal elements of A are
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*> also not referenced and are assumed to be 1.
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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 DOUBLE PRECISION array, dimension (LDAINV,N)
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*> On entry, the (triangular) inverse of the matrix A, in the
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*> same storage format as A.
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*> On exit, the contents of AINV are destroyed.
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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] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The reciprocal 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] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (N)
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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 DOUBLE PRECISION
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*> norm(A*AINV - I) / ( 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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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
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$ WORK, RESID )
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*
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* -- LAPACK test routine --
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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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*
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* .. Scalar Arguments ..
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CHARACTER DIAG, UPLO
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INTEGER LDA, LDAINV, N
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DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), AINV( LDAINV, * ), WORK( * )
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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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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER J
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DOUBLE PRECISION AINVNM, ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, DLANTR
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EXTERNAL LSAME, DLAMCH, DLANTR
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* ..
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* .. External Subroutines ..
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EXTERNAL DTRMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE
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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 = DLAMCH( 'Epsilon' )
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ANORM = DLANTR( '1', UPLO, DIAG, N, N, A, LDA, WORK )
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AINVNM = DLANTR( '1', UPLO, DIAG, N, N, AINV, LDAINV, WORK )
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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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* Set the diagonal of AINV to 1 if AINV has unit diagonal.
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*
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IF( LSAME( DIAG, 'U' ) ) THEN
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DO 10 J = 1, N
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AINV( J, J ) = ONE
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10 CONTINUE
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END IF
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*
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* Compute A * AINV, overwriting AINV.
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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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CALL DTRMV( 'Upper', 'No transpose', DIAG, J, A, LDA,
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$ AINV( 1, J ), 1 )
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20 CONTINUE
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ELSE
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DO 30 J = 1, N
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CALL DTRMV( 'Lower', 'No transpose', DIAG, N-J+1, A( J, J ),
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$ LDA, AINV( J, J ), 1 )
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30 CONTINUE
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END IF
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*
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* Subtract 1 from each diagonal element to form A*AINV - I.
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*
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DO 40 J = 1, N
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AINV( J, J ) = AINV( J, J ) - ONE
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40 CONTINUE
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*
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* Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = DLANTR( '1', UPLO, 'Non-unit', N, N, AINV, LDAINV, WORK )
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*
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RESID = ( ( RESID*RCOND ) / DBLE( N ) ) / EPS
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*
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RETURN
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*
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* End of DTRT01
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*
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END
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