252 lines
6.5 KiB
Fortran
252 lines
6.5 KiB
Fortran
*> \brief \b DBDT04
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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 DBDT04( UPLO, N, D, E, S, NS, U, LDU, VT, LDVT,
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* WORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDU, LDVT, N, NS
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* DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION D( * ), E( * ), S( * ), U( LDU, * ),
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* $ VT( LDVT, * ), 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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*> DBDT04 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] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the matrix B is upper or lower bidiagonal.
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*> = 'U': Upper bidiagonal
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*> = 'L': Lower bidiagonal
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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 B.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (N)
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*> The n diagonal elements of the bidiagonal matrix B.
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is DOUBLE PRECISION array, dimension (N-1)
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*> The (n-1) superdiagonal elements of the bidiagonal matrix B
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*> if UPLO = 'U', or the (n-1) subdiagonal elements of B if
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*> UPLO = 'L'.
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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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (2*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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*> The test ratio: norm(S - U' * B * V) / ( n * norm(B) * 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 DBDT04( UPLO, N, D, E, S, NS, U, LDU, VT, LDVT, WORK,
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$ 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 UPLO
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INTEGER LDU, LDVT, N, NS
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DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION D( * ), E( * ), S( * ), U( LDU, * ),
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$ 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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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 I, J, K
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DOUBLE PRECISION BNORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER IDAMAX
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DOUBLE PRECISION DASUM, DLAMCH
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EXTERNAL LSAME, IDAMAX, DASUM, DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, DBLE, 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( N.LE.0 .OR. NS.LE.0 )
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$ RETURN
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*
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EPS = DLAMCH( 'Precision' )
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*
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* Compute S - U' * B * V.
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*
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BNORM = ZERO
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* B is upper bidiagonal.
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*
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K = 0
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DO 20 I = 1, NS
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DO 10 J = 1, N-1
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K = K + 1
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WORK( K ) = D( J )*VT( I, J ) + E( J )*VT( I, J+1 )
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10 CONTINUE
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K = K + 1
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WORK( K ) = D( N )*VT( I, N )
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20 CONTINUE
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BNORM = ABS( D( 1 ) )
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DO 30 I = 2, N
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BNORM = MAX( BNORM, ABS( D( I ) )+ABS( E( I-1 ) ) )
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30 CONTINUE
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ELSE
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*
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* B is lower bidiagonal.
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*
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K = 0
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DO 50 I = 1, NS
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K = K + 1
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WORK( K ) = D( 1 )*VT( I, 1 )
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DO 40 J = 1, N-1
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K = K + 1
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WORK( K ) = E( J )*VT( I, J ) + D( J+1 )*VT( I, J+1 )
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40 CONTINUE
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50 CONTINUE
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BNORM = ABS( D( N ) )
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DO 60 I = 1, N-1
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BNORM = MAX( BNORM, ABS( D( I ) )+ABS( E( I ) ) )
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60 CONTINUE
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END IF
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*
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CALL DGEMM( 'T', 'N', NS, NS, N, -ONE, U, LDU, WORK( 1 ),
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$ N, ZERO, WORK( 1+N*NS ), NS )
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*
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* norm(S - U' * B * V)
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*
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K = N*NS
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DO 70 I = 1, NS
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WORK( K+I ) = WORK( K+I ) + S( I )
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RESID = MAX( RESID, DASUM( NS, WORK( K+1 ), 1 ) )
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K = K + NS
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70 CONTINUE
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*
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IF( BNORM.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( BNORM.GE.RESID ) THEN
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RESID = ( RESID / BNORM ) / ( DBLE( N )*EPS )
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ELSE
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IF( BNORM.LT.ONE ) THEN
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RESID = ( MIN( RESID, DBLE( N )*BNORM ) / BNORM ) /
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$ ( DBLE( N )*EPS )
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ELSE
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RESID = MIN( RESID / BNORM, DBLE( N ) ) /
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$ ( DBLE( 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 DBDT04
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*
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END
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