784 lines
30 KiB
Fortran
784 lines
30 KiB
Fortran
*> \brief \b DGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots.
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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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*> \htmlonly
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*> Download DGSVJ1 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj1.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj1.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj1.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
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* EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION EPS, SFMIN, TOL
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* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
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* CHARACTER*1 JOBV
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ),
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* $ WORK( LWORK )
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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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*> DGSVJ1 is called from SGESVJ as a pre-processor and that is its main
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*> purpose. It applies Jacobi rotations in the same way as SGESVJ does, but
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*> it targets only particular pivots and it does not check convergence
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*> (stopping criterion). Few tunning parameters (marked by [TP]) are
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*> available for the implementer.
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*>
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*> Further Details
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*> ~~~~~~~~~~~~~~~
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*> DGSVJ1 applies few sweeps of Jacobi rotations in the column space of
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*> the input M-by-N matrix A. The pivot pairs are taken from the (1,2)
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*> off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The
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*> block-entries (tiles) of the (1,2) off-diagonal block are marked by the
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*> [x]'s in the following scheme:
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*>
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*> | * * * [x] [x] [x]|
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*> | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks.
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*> | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block.
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*> |[x] [x] [x] * * * |
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*> |[x] [x] [x] * * * |
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*> |[x] [x] [x] * * * |
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*>
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*> In terms of the columns of A, the first N1 columns are rotated 'against'
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*> the remaining N-N1 columns, trying to increase the angle between the
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*> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
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*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
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*> The number of sweeps is given in NSWEEP and the orthogonality threshold
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*> is given in TOL.
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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] JOBV
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*> \verbatim
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*> JOBV is CHARACTER*1
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*> Specifies whether the output from this procedure is used
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*> to compute the matrix V:
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*> = 'V': the product of the Jacobi rotations is accumulated
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*> by postmulyiplying the N-by-N array V.
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*> (See the description of V.)
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*> = 'A': the product of the Jacobi rotations is accumulated
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*> by postmulyiplying the MV-by-N array V.
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*> (See the descriptions of MV and V.)
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*> = 'N': the Jacobi rotations are not accumulated.
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*> \endverbatim
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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 input matrix A. M >= 0.
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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 input matrix A.
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*> M >= N >= 0.
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*> \endverbatim
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*>
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*> \param[in] N1
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*> \verbatim
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*> N1 is INTEGER
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*> N1 specifies the 2 x 2 block partition, the first N1 columns are
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*> rotated 'against' the remaining N-N1 columns of A.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, M-by-N matrix A, such that A*diag(D) represents
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*> the input matrix.
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*> On exit,
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*> A_onexit * D_onexit represents the input matrix A*diag(D)
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*> post-multiplied by a sequence of Jacobi rotations, where the
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*> rotation threshold and the total number of sweeps are given in
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*> TOL and NSWEEP, respectively.
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*> (See the descriptions of N1, D, TOL and NSWEEP.)
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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,out] D
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*> \verbatim
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*> D is DOUBLE PRECISION array, dimension (N)
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*> The array D accumulates the scaling factors from the fast scaled
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*> Jacobi rotations.
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*> On entry, A*diag(D) represents the input matrix.
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*> On exit, A_onexit*diag(D_onexit) represents the input matrix
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*> post-multiplied by a sequence of Jacobi rotations, where the
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*> rotation threshold and the total number of sweeps are given in
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*> TOL and NSWEEP, respectively.
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*> (See the descriptions of N1, A, TOL and NSWEEP.)
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*> \endverbatim
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*>
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*> \param[in,out] SVA
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*> \verbatim
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*> SVA is DOUBLE PRECISION array, dimension (N)
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*> On entry, SVA contains the Euclidean norms of the columns of
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*> the matrix A*diag(D).
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*> On exit, SVA contains the Euclidean norms of the columns of
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*> the matrix onexit*diag(D_onexit).
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*> \endverbatim
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*>
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*> \param[in] MV
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*> \verbatim
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*> MV is INTEGER
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*> If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
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*> sequence of Jacobi rotations.
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*> If JOBV = 'N', then MV is not referenced.
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*> \endverbatim
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*>
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*> \param[in,out] V
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*> \verbatim
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*> V is DOUBLE PRECISION array, dimension (LDV,N)
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*> If JOBV .EQ. 'V' then N rows of V are post-multipled by a
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*> sequence of Jacobi rotations.
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*> If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
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*> sequence of Jacobi rotations.
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*> If JOBV = 'N', then V is not referenced.
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*> \endverbatim
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*>
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*> \param[in] LDV
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*> \verbatim
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*> LDV is INTEGER
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*> The leading dimension of the array V, LDV >= 1.
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*> If JOBV = 'V', LDV .GE. N.
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*> If JOBV = 'A', LDV .GE. MV.
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*> \endverbatim
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*>
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*> \param[in] EPS
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*> \verbatim
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*> EPS is DOUBLE PRECISION
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*> EPS = DLAMCH('Epsilon')
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*> \endverbatim
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*>
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*> \param[in] SFMIN
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*> \verbatim
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*> SFMIN is DOUBLE PRECISION
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*> SFMIN = DLAMCH('Safe Minimum')
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*> \endverbatim
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*>
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*> \param[in] TOL
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*> \verbatim
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*> TOL is DOUBLE PRECISION
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*> TOL is the threshold for Jacobi rotations. For a pair
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*> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
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*> applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
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*> \endverbatim
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*>
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*> \param[in] NSWEEP
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*> \verbatim
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*> NSWEEP is INTEGER
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*> NSWEEP is the number of sweeps of Jacobi rotations to be
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*> performed.
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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 (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> LWORK is the dimension of WORK. LWORK .GE. M.
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0 : successful exit.
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*> < 0 : if INFO = -i, then the i-th argument had an illegal value
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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 September 2012
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*
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*> \ingroup doubleOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
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*
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* =====================================================================
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SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
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$ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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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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* September 2012
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION EPS, SFMIN, TOL
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INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
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CHARACTER*1 JOBV
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ),
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$ WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Local Parameters ..
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DOUBLE PRECISION ZERO, HALF, ONE
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PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0 )
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* ..
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* .. Local Scalars ..
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DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG,
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$ BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG,
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$ ROOTEPS, ROOTSFMIN, ROOTTOL, SMALL, SN, T,
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$ TEMP1, THETA, THSIGN
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INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK,
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$ ISWROT, jbc, jgl, KBL, MVL, NOTROT, nblc, nblr,
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$ p, PSKIPPED, q, ROWSKIP, SWBAND
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LOGICAL APPLV, ROTOK, RSVEC
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* ..
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* .. Local Arrays ..
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DOUBLE PRECISION FASTR( 5 )
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DDOT, DNRM2
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INTEGER IDAMAX
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LOGICAL LSAME
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EXTERNAL IDAMAX, LSAME, DDOT, DNRM2
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* ..
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* .. External Subroutines ..
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EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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APPLV = LSAME( JOBV, 'A' )
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RSVEC = LSAME( JOBV, 'V' )
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IF( .NOT.( RSVEC .OR. APPLV .OR. LSAME( JOBV, 'N' ) ) ) THEN
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INFO = -1
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ELSE IF( M.LT.0 ) THEN
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INFO = -2
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ELSE IF( ( N.LT.0 ) .OR. ( N.GT.M ) ) THEN
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INFO = -3
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ELSE IF( N1.LT.0 ) THEN
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INFO = -4
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ELSE IF( LDA.LT.M ) THEN
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INFO = -6
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ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN
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INFO = -9
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ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
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$ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
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INFO = -11
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ELSE IF( TOL.LE.EPS ) THEN
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INFO = -14
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ELSE IF( NSWEEP.LT.0 ) THEN
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INFO = -15
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ELSE IF( LWORK.LT.M ) THEN
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INFO = -17
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ELSE
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INFO = 0
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END IF
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*
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* #:(
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGSVJ1', -INFO )
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RETURN
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END IF
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*
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IF( RSVEC ) THEN
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MVL = N
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ELSE IF( APPLV ) THEN
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MVL = MV
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END IF
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RSVEC = RSVEC .OR. APPLV
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ROOTEPS = DSQRT( EPS )
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ROOTSFMIN = DSQRT( SFMIN )
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SMALL = SFMIN / EPS
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BIG = ONE / SFMIN
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ROOTBIG = ONE / ROOTSFMIN
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LARGE = BIG / DSQRT( DBLE( M*N ) )
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BIGTHETA = ONE / ROOTEPS
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ROOTTOL = DSQRT( TOL )
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*
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* .. Initialize the right singular vector matrix ..
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*
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* RSVEC = LSAME( JOBV, 'Y' )
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*
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EMPTSW = N1*( N-N1 )
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NOTROT = 0
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FASTR( 1 ) = ZERO
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*
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* .. Row-cyclic pivot strategy with de Rijk's pivoting ..
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*
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KBL = MIN0( 8, N )
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NBLR = N1 / KBL
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IF( ( NBLR*KBL ).NE.N1 )NBLR = NBLR + 1
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* .. the tiling is nblr-by-nblc [tiles]
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NBLC = ( N-N1 ) / KBL
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IF( ( NBLC*KBL ).NE.( N-N1 ) )NBLC = NBLC + 1
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BLSKIP = ( KBL**2 ) + 1
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*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
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ROWSKIP = MIN0( 5, KBL )
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*[TP] ROWSKIP is a tuning parameter.
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SWBAND = 0
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*[TP] SWBAND is a tuning parameter. It is meaningful and effective
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* if SGESVJ is used as a computational routine in the preconditioned
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* Jacobi SVD algorithm SGESVJ.
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*
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*
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* | * * * [x] [x] [x]|
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* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks.
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* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block.
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* |[x] [x] [x] * * * |
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* |[x] [x] [x] * * * |
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* |[x] [x] [x] * * * |
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*
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*
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DO 1993 i = 1, NSWEEP
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* .. go go go ...
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*
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MXAAPQ = ZERO
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MXSINJ = ZERO
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ISWROT = 0
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*
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NOTROT = 0
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PSKIPPED = 0
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*
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DO 2000 ibr = 1, NBLR
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igl = ( ibr-1 )*KBL + 1
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*
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*
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*........................................................
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* ... go to the off diagonal blocks
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igl = ( ibr-1 )*KBL + 1
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DO 2010 jbc = 1, NBLC
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jgl = N1 + ( jbc-1 )*KBL + 1
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* doing the block at ( ibr, jbc )
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IJBLSK = 0
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DO 2100 p = igl, MIN0( igl+KBL-1, N1 )
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AAPP = SVA( p )
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IF( AAPP.GT.ZERO ) THEN
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PSKIPPED = 0
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DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
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*
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AAQQ = SVA( q )
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IF( AAQQ.GT.ZERO ) THEN
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AAPP0 = AAPP
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*
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* .. M x 2 Jacobi SVD ..
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*
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* .. Safe Gram matrix computation ..
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*
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IF( AAQQ.GE.ONE ) THEN
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IF( AAPP.GE.AAQQ ) THEN
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ROTOK = ( SMALL*AAPP ).LE.AAQQ
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ELSE
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ROTOK = ( SMALL*AAQQ ).LE.AAPP
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END IF
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IF( AAPP.LT.( BIG / AAQQ ) ) THEN
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AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1,
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$ q ), 1 )*D( p )*D( q ) / AAQQ )
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$ / AAPP
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ELSE
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CALL DCOPY( M, A( 1, p ), 1, WORK, 1 )
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CALL DLASCL( 'G', 0, 0, AAPP, D( p ),
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$ M, 1, WORK, LDA, IERR )
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AAPQ = DDOT( M, WORK, 1, A( 1, q ),
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$ 1 )*D( q ) / AAQQ
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END IF
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ELSE
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IF( AAPP.GE.AAQQ ) THEN
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ROTOK = AAPP.LE.( AAQQ / SMALL )
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ELSE
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ROTOK = AAQQ.LE.( AAPP / SMALL )
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END IF
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IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
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AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1,
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$ q ), 1 )*D( p )*D( q ) / AAQQ )
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$ / AAPP
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ELSE
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CALL DCOPY( M, A( 1, q ), 1, WORK, 1 )
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CALL DLASCL( 'G', 0, 0, AAQQ, D( q ),
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$ M, 1, WORK, LDA, IERR )
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AAPQ = DDOT( M, WORK, 1, A( 1, p ),
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$ 1 )*D( p ) / AAPP
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END IF
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END IF
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MXAAPQ = DMAX1( MXAAPQ, DABS( AAPQ ) )
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* TO rotate or NOT to rotate, THAT is the question ...
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*
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IF( DABS( AAPQ ).GT.TOL ) THEN
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NOTROT = 0
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* ROTATED = ROTATED + 1
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PSKIPPED = 0
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ISWROT = ISWROT + 1
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*
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IF( ROTOK ) THEN
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*
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AQOAP = AAQQ / AAPP
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APOAQ = AAPP / AAQQ
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THETA = -HALF*DABS(AQOAP-APOAQ) / AAPQ
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IF( AAQQ.GT.AAPP0 )THETA = -THETA
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|
|
IF( DABS( THETA ).GT.BIGTHETA ) THEN
|
|
T = HALF / THETA
|
|
FASTR( 3 ) = T*D( p ) / D( q )
|
|
FASTR( 4 ) = -T*D( q ) / D( p )
|
|
CALL DROTM( M, A( 1, p ), 1,
|
|
$ A( 1, q ), 1, FASTR )
|
|
IF( RSVEC )CALL DROTM( MVL,
|
|
$ V( 1, p ), 1,
|
|
$ V( 1, q ), 1,
|
|
$ FASTR )
|
|
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
|
|
$ ONE+T*APOAQ*AAPQ ) )
|
|
AAPP = AAPP*DSQRT( DMAX1( ZERO,
|
|
$ ONE-T*AQOAP*AAPQ ) )
|
|
MXSINJ = DMAX1( MXSINJ, DABS( T ) )
|
|
ELSE
|
|
*
|
|
* .. choose correct signum for THETA and rotate
|
|
*
|
|
THSIGN = -DSIGN( ONE, AAPQ )
|
|
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN
|
|
T = ONE / ( THETA+THSIGN*
|
|
$ DSQRT( ONE+THETA*THETA ) )
|
|
CS = DSQRT( ONE / ( ONE+T*T ) )
|
|
SN = T*CS
|
|
MXSINJ = DMAX1( MXSINJ, DABS( SN ) )
|
|
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
|
|
$ ONE+T*APOAQ*AAPQ ) )
|
|
AAPP = AAPP*DSQRT( DMAX1( ZERO,
|
|
$ ONE-T*AQOAP*AAPQ ) )
|
|
|
|
APOAQ = D( p ) / D( q )
|
|
AQOAP = D( q ) / D( p )
|
|
IF( D( p ).GE.ONE ) THEN
|
|
*
|
|
IF( D( q ).GE.ONE ) THEN
|
|
FASTR( 3 ) = T*APOAQ
|
|
FASTR( 4 ) = -T*AQOAP
|
|
D( p ) = D( p )*CS
|
|
D( q ) = D( q )*CS
|
|
CALL DROTM( M, A( 1, p ), 1,
|
|
$ A( 1, q ), 1,
|
|
$ FASTR )
|
|
IF( RSVEC )CALL DROTM( MVL,
|
|
$ V( 1, p ), 1, V( 1, q ),
|
|
$ 1, FASTR )
|
|
ELSE
|
|
CALL DAXPY( M, -T*AQOAP,
|
|
$ A( 1, q ), 1,
|
|
$ A( 1, p ), 1 )
|
|
CALL DAXPY( M, CS*SN*APOAQ,
|
|
$ A( 1, p ), 1,
|
|
$ A( 1, q ), 1 )
|
|
IF( RSVEC ) THEN
|
|
CALL DAXPY( MVL, -T*AQOAP,
|
|
$ V( 1, q ), 1,
|
|
$ V( 1, p ), 1 )
|
|
CALL DAXPY( MVL,
|
|
$ CS*SN*APOAQ,
|
|
$ V( 1, p ), 1,
|
|
$ V( 1, q ), 1 )
|
|
END IF
|
|
D( p ) = D( p )*CS
|
|
D( q ) = D( q ) / CS
|
|
END IF
|
|
ELSE
|
|
IF( D( q ).GE.ONE ) THEN
|
|
CALL DAXPY( M, T*APOAQ,
|
|
$ A( 1, p ), 1,
|
|
$ A( 1, q ), 1 )
|
|
CALL DAXPY( M, -CS*SN*AQOAP,
|
|
$ A( 1, q ), 1,
|
|
$ A( 1, p ), 1 )
|
|
IF( RSVEC ) THEN
|
|
CALL DAXPY( MVL, T*APOAQ,
|
|
$ V( 1, p ), 1,
|
|
$ V( 1, q ), 1 )
|
|
CALL DAXPY( MVL,
|
|
$ -CS*SN*AQOAP,
|
|
$ V( 1, q ), 1,
|
|
$ V( 1, p ), 1 )
|
|
END IF
|
|
D( p ) = D( p ) / CS
|
|
D( q ) = D( q )*CS
|
|
ELSE
|
|
IF( D( p ).GE.D( q ) ) THEN
|
|
CALL DAXPY( M, -T*AQOAP,
|
|
$ A( 1, q ), 1,
|
|
$ A( 1, p ), 1 )
|
|
CALL DAXPY( M, CS*SN*APOAQ,
|
|
$ A( 1, p ), 1,
|
|
$ A( 1, q ), 1 )
|
|
D( p ) = D( p )*CS
|
|
D( q ) = D( q ) / CS
|
|
IF( RSVEC ) THEN
|
|
CALL DAXPY( MVL,
|
|
$ -T*AQOAP,
|
|
$ V( 1, q ), 1,
|
|
$ V( 1, p ), 1 )
|
|
CALL DAXPY( MVL,
|
|
$ CS*SN*APOAQ,
|
|
$ V( 1, p ), 1,
|
|
$ V( 1, q ), 1 )
|
|
END IF
|
|
ELSE
|
|
CALL DAXPY( M, T*APOAQ,
|
|
$ A( 1, p ), 1,
|
|
$ A( 1, q ), 1 )
|
|
CALL DAXPY( M,
|
|
$ -CS*SN*AQOAP,
|
|
$ A( 1, q ), 1,
|
|
$ A( 1, p ), 1 )
|
|
D( p ) = D( p ) / CS
|
|
D( q ) = D( q )*CS
|
|
IF( RSVEC ) THEN
|
|
CALL DAXPY( MVL,
|
|
$ T*APOAQ, V( 1, p ),
|
|
$ 1, V( 1, q ), 1 )
|
|
CALL DAXPY( MVL,
|
|
$ -CS*SN*AQOAP,
|
|
$ V( 1, q ), 1,
|
|
$ V( 1, p ), 1 )
|
|
END IF
|
|
END IF
|
|
END IF
|
|
END IF
|
|
END IF
|
|
|
|
ELSE
|
|
IF( AAPP.GT.AAQQ ) THEN
|
|
CALL DCOPY( M, A( 1, p ), 1, WORK,
|
|
$ 1 )
|
|
CALL DLASCL( 'G', 0, 0, AAPP, ONE,
|
|
$ M, 1, WORK, LDA, IERR )
|
|
CALL DLASCL( 'G', 0, 0, AAQQ, ONE,
|
|
$ M, 1, A( 1, q ), LDA,
|
|
$ IERR )
|
|
TEMP1 = -AAPQ*D( p ) / D( q )
|
|
CALL DAXPY( M, TEMP1, WORK, 1,
|
|
$ A( 1, q ), 1 )
|
|
CALL DLASCL( 'G', 0, 0, ONE, AAQQ,
|
|
$ M, 1, A( 1, q ), LDA,
|
|
$ IERR )
|
|
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO,
|
|
$ ONE-AAPQ*AAPQ ) )
|
|
MXSINJ = DMAX1( MXSINJ, SFMIN )
|
|
ELSE
|
|
CALL DCOPY( M, A( 1, q ), 1, WORK,
|
|
$ 1 )
|
|
CALL DLASCL( 'G', 0, 0, AAQQ, ONE,
|
|
$ M, 1, WORK, LDA, IERR )
|
|
CALL DLASCL( 'G', 0, 0, AAPP, ONE,
|
|
$ M, 1, A( 1, p ), LDA,
|
|
$ IERR )
|
|
TEMP1 = -AAPQ*D( q ) / D( p )
|
|
CALL DAXPY( M, TEMP1, WORK, 1,
|
|
$ A( 1, p ), 1 )
|
|
CALL DLASCL( 'G', 0, 0, ONE, AAPP,
|
|
$ M, 1, A( 1, p ), LDA,
|
|
$ IERR )
|
|
SVA( p ) = AAPP*DSQRT( DMAX1( ZERO,
|
|
$ ONE-AAPQ*AAPQ ) )
|
|
MXSINJ = DMAX1( MXSINJ, SFMIN )
|
|
END IF
|
|
END IF
|
|
* END IF ROTOK THEN ... ELSE
|
|
*
|
|
* In the case of cancellation in updating SVA(q)
|
|
* .. recompute SVA(q)
|
|
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS )
|
|
$ THEN
|
|
IF( ( AAQQ.LT.ROOTBIG ) .AND.
|
|
$ ( AAQQ.GT.ROOTSFMIN ) ) THEN
|
|
SVA( q ) = DNRM2( M, A( 1, q ), 1 )*
|
|
$ D( q )
|
|
ELSE
|
|
T = ZERO
|
|
AAQQ = ONE
|
|
CALL DLASSQ( M, A( 1, q ), 1, T,
|
|
$ AAQQ )
|
|
SVA( q ) = T*DSQRT( AAQQ )*D( q )
|
|
END IF
|
|
END IF
|
|
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN
|
|
IF( ( AAPP.LT.ROOTBIG ) .AND.
|
|
$ ( AAPP.GT.ROOTSFMIN ) ) THEN
|
|
AAPP = DNRM2( M, A( 1, p ), 1 )*
|
|
$ D( p )
|
|
ELSE
|
|
T = ZERO
|
|
AAPP = ONE
|
|
CALL DLASSQ( M, A( 1, p ), 1, T,
|
|
$ AAPP )
|
|
AAPP = T*DSQRT( AAPP )*D( p )
|
|
END IF
|
|
SVA( p ) = AAPP
|
|
END IF
|
|
* end of OK rotation
|
|
ELSE
|
|
NOTROT = NOTROT + 1
|
|
* SKIPPED = SKIPPED + 1
|
|
PSKIPPED = PSKIPPED + 1
|
|
IJBLSK = IJBLSK + 1
|
|
END IF
|
|
ELSE
|
|
NOTROT = NOTROT + 1
|
|
PSKIPPED = PSKIPPED + 1
|
|
IJBLSK = IJBLSK + 1
|
|
END IF
|
|
|
|
* IF ( NOTROT .GE. EMPTSW ) GO TO 2011
|
|
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) )
|
|
$ THEN
|
|
SVA( p ) = AAPP
|
|
NOTROT = 0
|
|
GO TO 2011
|
|
END IF
|
|
IF( ( i.LE.SWBAND ) .AND.
|
|
$ ( PSKIPPED.GT.ROWSKIP ) ) THEN
|
|
AAPP = -AAPP
|
|
NOTROT = 0
|
|
GO TO 2203
|
|
END IF
|
|
|
|
*
|
|
2200 CONTINUE
|
|
* end of the q-loop
|
|
2203 CONTINUE
|
|
|
|
SVA( p ) = AAPP
|
|
*
|
|
ELSE
|
|
IF( AAPP.EQ.ZERO )NOTROT = NOTROT +
|
|
$ MIN0( jgl+KBL-1, N ) - jgl + 1
|
|
IF( AAPP.LT.ZERO )NOTROT = 0
|
|
*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011
|
|
END IF
|
|
|
|
2100 CONTINUE
|
|
* end of the p-loop
|
|
2010 CONTINUE
|
|
* end of the jbc-loop
|
|
2011 CONTINUE
|
|
*2011 bailed out of the jbc-loop
|
|
DO 2012 p = igl, MIN0( igl+KBL-1, N )
|
|
SVA( p ) = DABS( SVA( p ) )
|
|
2012 CONTINUE
|
|
*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994
|
|
2000 CONTINUE
|
|
*2000 :: end of the ibr-loop
|
|
*
|
|
* .. update SVA(N)
|
|
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) )
|
|
$ THEN
|
|
SVA( N ) = DNRM2( M, A( 1, N ), 1 )*D( N )
|
|
ELSE
|
|
T = ZERO
|
|
AAPP = ONE
|
|
CALL DLASSQ( M, A( 1, N ), 1, T, AAPP )
|
|
SVA( N ) = T*DSQRT( AAPP )*D( N )
|
|
END IF
|
|
*
|
|
* Additional steering devices
|
|
*
|
|
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR.
|
|
$ ( ISWROT.LE.N ) ) )SWBAND = i
|
|
|
|
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DBLE( N )*TOL ) .AND.
|
|
$ ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
|
|
GO TO 1994
|
|
END IF
|
|
|
|
*
|
|
IF( NOTROT.GE.EMPTSW )GO TO 1994
|
|
|
|
1993 CONTINUE
|
|
* end i=1:NSWEEP loop
|
|
* #:) Reaching this point means that the procedure has completed the given
|
|
* number of sweeps.
|
|
INFO = NSWEEP - 1
|
|
GO TO 1995
|
|
1994 CONTINUE
|
|
* #:) Reaching this point means that during the i-th sweep all pivots were
|
|
* below the given threshold, causing early exit.
|
|
|
|
INFO = 0
|
|
* #:) INFO = 0 confirms successful iterations.
|
|
1995 CONTINUE
|
|
*
|
|
* Sort the vector D
|
|
*
|
|
DO 5991 p = 1, N - 1
|
|
q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1
|
|
IF( p.NE.q ) THEN
|
|
TEMP1 = SVA( p )
|
|
SVA( p ) = SVA( q )
|
|
SVA( q ) = TEMP1
|
|
TEMP1 = D( p )
|
|
D( p ) = D( q )
|
|
D( q ) = TEMP1
|
|
CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
|
|
IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 )
|
|
END IF
|
|
5991 CONTINUE
|
|
*
|
|
RETURN
|
|
* ..
|
|
* .. END OF DGSVJ1
|
|
* ..
|
|
END
|