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201 lines
5.5 KiB
201 lines
5.5 KiB
*> \brief \b CTBT06
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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 CTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
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* RWORK, RAT )
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*
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* .. Scalar Arguments ..
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* CHARACTER DIAG, UPLO
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* INTEGER KD, LDAB, N
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* REAL RAT, RCOND, RCONDC
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* ..
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* .. Array Arguments ..
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* REAL RWORK( * )
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* COMPLEX AB( LDAB, * )
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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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*> CTBT06 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 CTBCON. 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 REAL
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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 REAL
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*> The estimate of the reciprocal condition number computed by
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*> CTBCON.
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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] KD
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*> \verbatim
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*> KD is INTEGER
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*> The number of superdiagonals or subdiagonals of the
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*> triangular band matrix A. KD >= 0.
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*> \endverbatim
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*>
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*> \param[in] AB
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*> \verbatim
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*> AB is COMPLEX array, dimension (LDAB,N)
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*> The upper or lower triangular band matrix A, stored in the
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*> first kd+1 rows of the array. The j-th column of A is stored
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*> in the j-th column of the array AB as follows:
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
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*> \endverbatim
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*>
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*> \param[in] LDAB
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*> \verbatim
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*> LDAB is INTEGER
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*> The leading dimension of the array AB. LDAB >= KD+1.
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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] RAT
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*> \verbatim
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*> RAT is REAL
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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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*> \ingroup complex_lin
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*
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* =====================================================================
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SUBROUTINE CTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB, LDAB,
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$ RWORK, RAT )
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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 KD, LDAB, N
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REAL RAT, RCOND, RCONDC
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* ..
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* .. Array Arguments ..
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REAL RWORK( * )
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COMPLEX AB( LDAB, * )
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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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REAL ANORM, BIGNUM, EPS, RMAX, RMIN
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* ..
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* .. External Functions ..
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REAL CLANTB, SLAMCH
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EXTERNAL CLANTB, SLAMCH
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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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* .. Executable Statements ..
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*
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EPS = SLAMCH( '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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BIGNUM = ONE / SLAMCH( 'Safe minimum' )
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ANORM = CLANTB( 'M', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
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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 CTBT06
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*
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END
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