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215 lines
5.6 KiB
215 lines
5.6 KiB
*> \brief \b CBDT05
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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 CBDT05( M, N, A, LDA, S, NS, U, LDU,
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* VT, LDVT, WORK, RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDU, LDVT, N, NS
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL S( * )
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* COMPLEX A( LDA, * ), U( * ), VT( LDVT, * ), WORK( * )
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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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*> CBDT05 reconstructs a bidiagonal matrix B from its (partial) SVD:
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*> S = U' * B * V
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*> where U and V are orthogonal matrices and S is diagonal.
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*>
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*> The test ratio to test the singular value decomposition is
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*> RESID = norm( S - U' * B * V ) / ( n * norm(B) * EPS )
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*> where VT = V' and EPS is the machine precision.
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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] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrices A and U.
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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 columns of the matrices A and VT.
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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 COMPLEX array, dimension (LDA,N)
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*> The m by n 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,M).
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*> \endverbatim
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*>
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*> \param[in] S
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*> \verbatim
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*> S is REAL array, dimension (NS)
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*> The singular values from the (partial) SVD of B, sorted in
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*> decreasing order.
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*> \endverbatim
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*>
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*> \param[in] NS
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*> \verbatim
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*> NS is INTEGER
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*> The number of singular values/vectors from the (partial)
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*> SVD of B.
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*> \endverbatim
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*>
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*> \param[in] U
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*> \verbatim
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*> U is COMPLEX array, dimension (LDU,NS)
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*> The n by ns orthogonal matrix U in S = U' * B * V.
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*> \endverbatim
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*>
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*> \param[in] LDU
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*> \verbatim
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*> LDU is INTEGER
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*> The leading dimension of the array U. LDU >= max(1,N)
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*> \endverbatim
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*>
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*> \param[in] VT
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*> \verbatim
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*> VT is COMPLEX array, dimension (LDVT,N)
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*> The n by ns orthogonal matrix V in S = U' * B * V.
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*> \endverbatim
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*>
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*> \param[in] LDVT
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*> \verbatim
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*> LDVT is INTEGER
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*> The leading dimension of the array VT.
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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 COMPLEX array, dimension (M,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 REAL
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*> The test ratio: norm(S - U' * A * V) / ( n * norm(A) * 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_eig
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*
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* =====================================================================
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SUBROUTINE CBDT05( M, N, A, LDA, S, NS, U, LDU,
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$ VT, LDVT, 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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INTEGER LDA, LDU, LDVT, M, N, NS
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL S( * )
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COMPLEX A( LDA, * ), U( * ), VT( LDVT, * ), 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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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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COMPLEX CZERO, CONE
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PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
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$ CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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REAL ANORM, EPS
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* ..
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* .. Local Arrays ..
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REAL DUM( 1 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ISAMAX
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REAL SASUM, SCASUM, SLAMCH, CLANGE
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EXTERNAL LSAME, ISAMAX, SASUM, SCASUM, SLAMCH, CLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, REAL, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible.
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*
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RESID = ZERO
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IF( MIN( M, N ).LE.0 .OR. NS.LE.0 )
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$ RETURN
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*
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EPS = SLAMCH( 'Precision' )
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ANORM = CLANGE( 'M', M, N, A, LDA, DUM )
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*
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* Compute U' * A * V.
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*
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CALL CGEMM( 'N', 'C', M, NS, N, CONE, A, LDA, VT,
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$ LDVT, CZERO, WORK( 1+NS*NS ), M )
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CALL CGEMM( 'C', 'N', NS, NS, M, -CONE, U, LDU, WORK( 1+NS*NS ),
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$ M, CZERO, WORK, NS )
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*
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* norm(S - U' * B * V)
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*
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J = 0
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DO 10 I = 1, NS
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WORK( J+I ) = WORK( J+I ) + CMPLX( S( I ), ZERO )
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RESID = MAX( RESID, SCASUM( NS, WORK( J+1 ), 1 ) )
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J = J + NS
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10 CONTINUE
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*
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IF( ANORM.LE.ZERO ) THEN
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IF( RESID.NE.ZERO )
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$ RESID = ONE / EPS
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ELSE
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IF( ANORM.GE.RESID ) THEN
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RESID = ( RESID / ANORM ) / ( REAL( N )*EPS )
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ELSE
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IF( ANORM.LT.ONE ) THEN
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RESID = ( MIN( RESID, REAL( N )*ANORM ) / ANORM ) /
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$ ( REAL( N )*EPS )
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ELSE
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RESID = MIN( RESID / ANORM, REAL( N ) ) /
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$ ( REAL( N )*EPS )
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END IF
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END IF
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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 CBDT05
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*
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END
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