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288 lines
8.1 KiB
288 lines
8.1 KiB
*> \brief \b SBDT01
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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 SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, WORK,
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* RESID )
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*
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* .. Scalar Arguments ..
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* INTEGER KD, LDA, LDPT, LDQ, M, N
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* REAL RESID
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), D( * ), E( * ), PT( LDPT, * ),
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* $ Q( LDQ, * ), 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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*> SBDT01 reconstructs a general matrix A from its bidiagonal form
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*> A = Q * B * P**T
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*> where Q (m by min(m,n)) and P**T (min(m,n) by n) are orthogonal
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*> matrices and B is bidiagonal.
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*>
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*> The test ratio to test the reduction is
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*> RESID = norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
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*> where 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 Q.
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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 P**T.
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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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*> If KD = 0, B is diagonal and the array E is not referenced.
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*> If KD = 1, the reduction was performed by xGEBRD; B is upper
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*> bidiagonal if M >= N, and lower bidiagonal if M < N.
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*> If KD = -1, the reduction was performed by xGBBRD; B is
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*> always upper bidiagonal.
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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 REAL 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] Q
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*> \verbatim
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*> Q is REAL array, dimension (LDQ,N)
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*> The m by min(m,n) orthogonal matrix Q in the reduction
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*> A = Q * B * P**T.
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*> \endverbatim
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*>
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*> \param[in] LDQ
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*> \verbatim
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*> LDQ is INTEGER
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*> The leading dimension of the array Q. LDQ >= max(1,M).
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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 REAL array, dimension (min(M,N))
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*> The 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 REAL array, dimension (min(M,N)-1)
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*> The superdiagonal elements of the bidiagonal matrix B if
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*> m >= n, or the subdiagonal elements of B if m < n.
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*> \endverbatim
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*>
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*> \param[in] PT
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*> \verbatim
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*> PT is REAL array, dimension (LDPT,N)
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*> The min(m,n) by n orthogonal matrix P**T in the reduction
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*> A = Q * B * P**T.
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*> \endverbatim
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*>
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*> \param[in] LDPT
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*> \verbatim
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*> LDPT is INTEGER
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*> The leading dimension of the array PT.
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*> LDPT >= max(1,min(M,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 REAL 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:
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*> norm(A - Q * B * P**T) / ( 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 single_eig
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*
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* =====================================================================
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SUBROUTINE SBDT01( M, N, KD, A, LDA, Q, LDQ, D, E, PT, LDPT, 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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INTEGER KD, LDA, LDPT, LDQ, M, N
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REAL RESID
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), D( * ), E( * ), PT( LDPT, * ),
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$ Q( LDQ, * ), 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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* ..
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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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* .. External Functions ..
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REAL SASUM, SLAMCH, SLANGE
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EXTERNAL SASUM, SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SCOPY, SGEMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, REAL
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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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IF( M.LE.0 .OR. N.LE.0 ) THEN
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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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* Compute A - Q * B * P**T one column at a time.
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*
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RESID = ZERO
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IF( KD.NE.0 ) THEN
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*
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* B is bidiagonal.
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*
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IF( KD.NE.0 .AND. M.GE.N ) THEN
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*
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* B is upper bidiagonal and M >= N.
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*
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DO 20 J = 1, N
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CALL SCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 10 I = 1, N - 1
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WORK( M+I ) = D( I )*PT( I, J ) + E( I )*PT( I+1, J )
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10 CONTINUE
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WORK( M+N ) = D( N )*PT( N, J )
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CALL SGEMV( 'No transpose', M, N, -ONE, Q, LDQ,
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$ WORK( M+1 ), 1, ONE, WORK, 1 )
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RESID = MAX( RESID, SASUM( M, WORK, 1 ) )
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20 CONTINUE
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ELSE IF( KD.LT.0 ) THEN
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*
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* B is upper bidiagonal and M < N.
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*
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DO 40 J = 1, N
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CALL SCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 30 I = 1, M - 1
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WORK( M+I ) = D( I )*PT( I, J ) + E( I )*PT( I+1, J )
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30 CONTINUE
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WORK( M+M ) = D( M )*PT( M, J )
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CALL SGEMV( 'No transpose', M, M, -ONE, Q, LDQ,
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$ WORK( M+1 ), 1, ONE, WORK, 1 )
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RESID = MAX( RESID, SASUM( M, WORK, 1 ) )
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40 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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DO 60 J = 1, N
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CALL SCOPY( M, A( 1, J ), 1, WORK, 1 )
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WORK( M+1 ) = D( 1 )*PT( 1, J )
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DO 50 I = 2, M
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WORK( M+I ) = E( I-1 )*PT( I-1, J ) +
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$ D( I )*PT( I, J )
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50 CONTINUE
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CALL SGEMV( 'No transpose', M, M, -ONE, Q, LDQ,
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$ WORK( M+1 ), 1, ONE, WORK, 1 )
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RESID = MAX( RESID, SASUM( M, WORK, 1 ) )
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60 CONTINUE
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END IF
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ELSE
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*
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* B is diagonal.
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*
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IF( M.GE.N ) THEN
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DO 80 J = 1, N
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CALL SCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 70 I = 1, N
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WORK( M+I ) = D( I )*PT( I, J )
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70 CONTINUE
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CALL SGEMV( 'No transpose', M, N, -ONE, Q, LDQ,
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$ WORK( M+1 ), 1, ONE, WORK, 1 )
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RESID = MAX( RESID, SASUM( M, WORK, 1 ) )
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80 CONTINUE
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ELSE
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DO 100 J = 1, N
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CALL SCOPY( M, A( 1, J ), 1, WORK, 1 )
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DO 90 I = 1, M
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WORK( M+I ) = D( I )*PT( I, J )
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90 CONTINUE
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CALL SGEMV( 'No transpose', M, M, -ONE, Q, LDQ,
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$ WORK( M+1 ), 1, ONE, WORK, 1 )
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RESID = MAX( RESID, SASUM( M, WORK, 1 ) )
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100 CONTINUE
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END IF
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END IF
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*
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* Compute norm(A - Q * B * P**T) / ( n * norm(A) * EPS )
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*
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ANORM = SLANGE( '1', M, N, A, LDA, WORK )
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EPS = SLAMCH( 'Precision' )
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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 SBDT01
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*
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END
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