204 lines
5.7 KiB
Fortran
204 lines
5.7 KiB
Fortran
*> \brief \b DTRT06
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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 DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
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* RAT )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, UPLO
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* INTEGER LDA, N
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* DOUBLE PRECISION RAT, RCOND, RCONDC
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), 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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*> DTRT06 computes a test ratio comparing RCOND (the reciprocal
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*> condition number of a triangular matrix A) and RCONDC, the estimate
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*> computed by DTRCON. Information about the triangular matrix A is
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*> used if one estimate is zero and the other is non-zero to decide if
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*> underflow in the estimate is justified.
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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] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The estimate of the reciprocal condition number obtained by
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*> forming the explicit inverse of the matrix A and computing
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*> RCOND = 1/( norm(A) * norm(inv(A)) ).
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*> \endverbatim
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*>
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*> \param[in] RCONDC
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*> \verbatim
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*> RCONDC is DOUBLE PRECISION
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*> The estimate of the reciprocal condition number computed by
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*> DTRCON.
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*> \endverbatim
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*>
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER
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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
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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[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] RAT
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*> \verbatim
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*> RAT is DOUBLE PRECISION
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*> The test ratio. If both RCOND and RCONDC are nonzero,
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*> RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
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*> If RAT = 0, the two estimates are exactly the same.
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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 double_lin
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*
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* =====================================================================
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SUBROUTINE DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA, WORK,
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$ RAT )
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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 DIAG, UPLO
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INTEGER LDA, N
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DOUBLE PRECISION RAT, RCOND, RCONDC
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), 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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DOUBLE PRECISION ANORM, BIGNUM, EPS, RMAX, RMIN, SMLNUM
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DLANTR
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EXTERNAL DLAMCH, DLANTR
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. External Subroutines ..
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EXTERNAL DLABAD
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* ..
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* .. Executable Statements ..
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*
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EPS = DLAMCH( 'Epsilon' )
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RMAX = MAX( RCOND, RCONDC )
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RMIN = MIN( RCOND, RCONDC )
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*
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* Do the easy cases first.
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*
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IF( RMIN.LT.ZERO ) THEN
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*
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* Invalid value for RCOND or RCONDC, return 1/EPS.
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*
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RAT = ONE / EPS
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*
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ELSE IF( RMIN.GT.ZERO ) THEN
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*
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* Both estimates are positive, return RMAX/RMIN - 1.
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*
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RAT = RMAX / RMIN - ONE
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*
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ELSE IF( RMAX.EQ.ZERO ) THEN
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*
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* Both estimates zero.
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*
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RAT = ZERO
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*
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ELSE
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*
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* One estimate is zero, the other is non-zero. If the matrix is
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* ill-conditioned, return the nonzero estimate multiplied by
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* 1/EPS; if the matrix is badly scaled, return the nonzero
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* estimate multiplied by BIGNUM/TMAX, where TMAX is the maximum
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* element in absolute value in A.
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*
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SMLNUM = DLAMCH( 'Safe minimum' )
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BIGNUM = ONE / SMLNUM
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CALL DLABAD( SMLNUM, BIGNUM )
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ANORM = DLANTR( 'M', UPLO, DIAG, N, N, A, LDA, WORK )
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*
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RAT = RMAX*( MIN( BIGNUM / MAX( ONE, ANORM ), ONE / EPS ) )
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END IF
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*
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RETURN
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*
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* End of DTRT06
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*
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END
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