remove redundant comments from generated C++ files. clean up with clang-format.
This commit is contained in:
Axel Kohlmeyer
@ -1,219 +1,18 @@
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/* fortran/dlalsd.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static doublereal c_b6 = 0.;
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static integer c__0 = 0;
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static doublereal c_b11 = 1.;
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/* > \brief \b DLALSD uses the singular value decomposition of A to solve the least squares problem. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DLALSD + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlalsd.
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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/dlalsd.
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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/dlalsd.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLALSD( UPLO, SMLSIZ, N, NRHS, D, E, B, LDB, RCOND, */
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/* RANK, WORK, IWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER UPLO */
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/* INTEGER INFO, LDB, N, NRHS, RANK, SMLSIZ */
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/* DOUBLE PRECISION RCOND */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER IWORK( * ) */
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/* DOUBLE PRECISION B( LDB, * ), D( * ), E( * ), WORK( * ) */
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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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/* > DLALSD uses the singular value decomposition of A to solve the least */
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/* > squares problem of finding X to minimize the Euclidean norm of each */
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/* > column of A*X-B, where A is N-by-N upper bidiagonal, and X and B */
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/* > are N-by-NRHS. The solution X overwrites B. */
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/* > */
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/* > The singular values of A smaller than RCOND times the largest */
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/* > singular value are treated as zero in solving the least squares */
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/* > problem; in this case a minimum norm solution is returned. */
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/* > The actual singular values are returned in D in ascending order. */
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/* > */
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/* > This code makes very mild assumptions about floating point */
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/* > arithmetic. It will work on machines with a guard digit in */
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/* > add/subtract, or on those binary machines without guard digits */
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/* > which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. */
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/* > It could conceivably fail on hexadecimal or decimal machines */
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/* > without guard digits, but we know of none. */
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/* > \endverbatim */
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/* Arguments: */
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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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/* > = 'U': D and E define an upper bidiagonal matrix. */
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/* > = 'L': D and E define a lower bidiagonal matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] SMLSIZ */
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/* > \verbatim */
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/* > SMLSIZ is INTEGER */
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/* > The maximum size of the subproblems at the bottom of the */
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/* > computation tree. */
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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 dimension of the bidiagonal matrix. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NRHS */
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/* > \verbatim */
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/* > NRHS is INTEGER */
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/* > The number of columns of B. NRHS must be at least 1. */
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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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/* > On entry D contains the main diagonal of the bidiagonal */
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/* > matrix. On exit, if INFO = 0, D contains its singular values. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] E */
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/* > \verbatim */
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/* > E is DOUBLE PRECISION array, dimension (N-1) */
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/* > Contains the super-diagonal entries of the bidiagonal matrix. */
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/* > On exit, E has been destroyed. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] B */
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/* > \verbatim */
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/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
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/* > On input, B contains the right hand sides of the least */
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/* > squares problem. On output, B contains the solution X. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDB */
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/* > \verbatim */
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/* > LDB is INTEGER */
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/* > The leading dimension of B in the calling subprogram. */
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/* > LDB must be at least max(1,N). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] RCOND */
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/* > \verbatim */
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/* > RCOND is DOUBLE PRECISION */
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/* > The singular values of A less than or equal to RCOND times */
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/* > the largest singular value are treated as zero in solving */
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/* > the least squares problem. If RCOND is negative, */
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/* > machine precision is used instead. */
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/* > For example, if diag(S)*X=B were the least squares problem, */
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/* > where diag(S) is a diagonal matrix of singular values, the */
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/* > solution would be X(i) = B(i) / S(i) if S(i) is greater than */
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/* > RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to */
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/* > RCOND*max(S). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] RANK */
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/* > \verbatim */
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/* > RANK is INTEGER */
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/* > The number of singular values of A greater than RCOND times */
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/* > the largest singular value. */
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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 at least */
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/* > (9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2), */
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/* > where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] IWORK */
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/* > \verbatim */
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/* > IWORK is INTEGER array, dimension at least */
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/* > (3*N*NLVL + 11*N) */
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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, the i-th argument had an illegal value. */
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/* > > 0: The algorithm failed to compute a singular value while */
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/* > working on the submatrix lying in rows and columns */
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/* > INFO/(N+1) through MOD(INFO,N+1). */
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/* > \endverbatim */
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/* Authors: */
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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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/* > \ingroup doubleOTHERcomputational */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Ming Gu and Ren-Cang Li, Computer Science Division, University of */
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/* > California at Berkeley, USA \n */
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/* > Osni Marques, LBNL/NERSC, USA \n */
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/* ===================================================================== */
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/* Subroutine */ int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer
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*nrhs, doublereal *d__, doublereal *e, doublereal *b, integer *ldb,
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doublereal *rcond, integer *rank, doublereal *work, integer *iwork,
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integer *info, ftnlen uplo_len)
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int dlalsd_(char *uplo, integer *smlsiz, integer *n, integer *nrhs, doublereal *d__, doublereal *e,
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doublereal *b, integer *ldb, doublereal *rcond, integer *rank, doublereal *work,
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integer *iwork, integer *info, ftnlen uplo_len)
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{
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/* System generated locals */
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integer b_dim1, b_offset, i__1, i__2;
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doublereal d__1;
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/* Builtin functions */
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double log(doublereal), d_lmp_sign(doublereal *, doublereal *);
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/* Local variables */
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integer c__, i__, j, k;
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doublereal r__;
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integer s, u, z__;
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@ -227,74 +26,42 @@ f"> */
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integer difl, difr;
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doublereal rcnd;
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integer perm, nsub;
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extern /* Subroutine */ int drot_(integer *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *);
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extern int drot_(integer *, doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *);
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integer nlvl, sqre, bxst;
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extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
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integer *, doublereal *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *, ftnlen, ftnlen),
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dcopy_(integer *, doublereal *, integer *, doublereal *, integer
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*);
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extern int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, doublereal *, integer *,
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ftnlen, ftnlen),
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dcopy_(integer *, doublereal *, integer *, doublereal *, integer *);
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integer poles, sizei, nsize, nwork, icmpq1, icmpq2;
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extern doublereal dlamch_(char *, ftnlen);
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extern /* Subroutine */ int dlasda_(integer *, integer *, integer *,
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integer *, doublereal *, doublereal *, doublereal *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *, integer *, integer *, integer *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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integer *), dlalsa_(integer *, integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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doublereal *, doublereal *, integer *, integer *, integer *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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integer *, integer *), dlascl_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, integer *, doublereal *,
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integer *, integer *, ftnlen);
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extern int dlasda_(integer *, integer *, integer *, integer *, doublereal *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *,
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doublereal *, doublereal *, integer *, integer *, integer *, integer *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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integer *),
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dlalsa_(integer *, integer *, integer *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, doublereal *, doublereal *, integer *, integer *, integer *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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integer *),
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dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *,
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doublereal *, integer *, integer *, ftnlen);
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extern integer idamax_(integer *, doublereal *, integer *);
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extern /* Subroutine */ int dlasdq_(char *, integer *, integer *, integer
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*, integer *, integer *, doublereal *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, integer *, ftnlen), dlacpy_(char *, integer *,
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integer *, doublereal *, integer *, doublereal *, integer *,
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ftnlen), dlartg_(doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *), dlaset_(char *, integer *, integer *,
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doublereal *, doublereal *, doublereal *, integer *, ftnlen),
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xerbla_(char *, integer *, ftnlen);
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extern int dlasdq_(char *, integer *, integer *, integer *, integer *, integer *, doublereal *,
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doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, integer *, ftnlen),
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dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *,
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ftnlen),
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dlartg_(doublereal *, doublereal *, doublereal *, doublereal *, doublereal *),
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dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *,
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ftnlen),
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xerbla_(char *, integer *, ftnlen);
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integer givcol;
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extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *,
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ftnlen);
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extern /* Subroutine */ int dlasrt_(char *, integer *, doublereal *,
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integer *, ftnlen);
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extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *, ftnlen);
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extern int dlasrt_(char *, integer *, doublereal *, integer *, ftnlen);
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doublereal orgnrm;
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integer givnum, givptr, smlszp;
|
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|
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|
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/* -- LAPACK computational 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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/* .. Array Arguments .. */
|
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/* .. */
|
||||
|
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/* ===================================================================== */
|
||||
|
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/* .. Parameters .. */
|
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/* .. */
|
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/* .. Local Scalars .. */
|
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/* .. */
|
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/* .. External Functions .. */
|
||||
/* .. */
|
||||
/* .. External Subroutines .. */
|
||||
/* .. */
|
||||
/* .. Intrinsic Functions .. */
|
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/* .. */
|
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/* .. Executable Statements .. */
|
||||
|
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/* Test the input parameters. */
|
||||
|
||||
/* Parameter adjustments */
|
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--d__;
|
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--e;
|
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b_dim1 = *ldb;
|
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@ -302,10 +69,7 @@ f"> */
|
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b -= b_offset;
|
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--work;
|
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--iwork;
|
||||
|
||||
/* Function Body */
|
||||
*info = 0;
|
||||
|
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if (*n < 0) {
|
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*info = -3;
|
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} else if (*nrhs < 1) {
|
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@ -318,38 +82,26 @@ f"> */
|
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xerbla_((char *)"DLALSD", &i__1, (ftnlen)6);
|
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return 0;
|
||||
}
|
||||
|
||||
eps = dlamch_((char *)"Epsilon", (ftnlen)7);
|
||||
|
||||
/* Set up the tolerance. */
|
||||
|
||||
if (*rcond <= 0. || *rcond >= 1.) {
|
||||
rcnd = eps;
|
||||
} else {
|
||||
rcnd = *rcond;
|
||||
}
|
||||
|
||||
*rank = 0;
|
||||
|
||||
/* Quick return if possible. */
|
||||
|
||||
if (*n == 0) {
|
||||
return 0;
|
||||
} else if (*n == 1) {
|
||||
if (d__[1] == 0.) {
|
||||
dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (
|
||||
ftnlen)1);
|
||||
dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1);
|
||||
} else {
|
||||
*rank = 1;
|
||||
dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[
|
||||
b_offset], ldb, info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &d__[1], &c_b11, &c__1, nrhs, &b[b_offset], ldb, info,
|
||||
(ftnlen)1);
|
||||
d__[1] = abs(d__[1]);
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Rotate the matrix if it is lower bidiagonal. */
|
||||
|
||||
if (*(unsigned char *)uplo == 'L') {
|
||||
i__1 = *n - 1;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
@ -358,13 +110,11 @@ f"> */
|
||||
e[i__] = sn * d__[i__ + 1];
|
||||
d__[i__ + 1] = cs * d__[i__ + 1];
|
||||
if (*nrhs == 1) {
|
||||
drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &
|
||||
c__1, &cs, &sn);
|
||||
drot_(&c__1, &b[i__ + b_dim1], &c__1, &b[i__ + 1 + b_dim1], &c__1, &cs, &sn);
|
||||
} else {
|
||||
work[(i__ << 1) - 1] = cs;
|
||||
work[i__ * 2] = sn;
|
||||
}
|
||||
/* L10: */
|
||||
}
|
||||
if (*nrhs > 1) {
|
||||
i__1 = *nrhs;
|
||||
@ -373,37 +123,25 @@ f"> */
|
||||
for (j = 1; j <= i__2; ++j) {
|
||||
cs = work[(j << 1) - 1];
|
||||
sn = work[j * 2];
|
||||
drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ *
|
||||
b_dim1], &c__1, &cs, &sn);
|
||||
/* L20: */
|
||||
drot_(&c__1, &b[j + i__ * b_dim1], &c__1, &b[j + 1 + i__ * b_dim1], &c__1, &cs,
|
||||
&sn);
|
||||
}
|
||||
/* L30: */
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* Scale. */
|
||||
|
||||
nm1 = *n - 1;
|
||||
orgnrm = dlanst_((char *)"M", n, &d__[1], &e[1], (ftnlen)1);
|
||||
if (orgnrm == 0.) {
|
||||
dlaset_((char *)"A", n, nrhs, &c_b6, &c_b6, &b[b_offset], ldb, (ftnlen)1);
|
||||
return 0;
|
||||
}
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, (
|
||||
ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1,
|
||||
info, (ftnlen)1);
|
||||
|
||||
/* If N is smaller than the minimum divide size SMLSIZ, then solve */
|
||||
/* the problem with another solver. */
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, &c__1, &d__[1], n, info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, &nm1, &c__1, &e[1], &nm1, info, (ftnlen)1);
|
||||
if (*n <= *smlsiz) {
|
||||
nwork = *n * *n + 1;
|
||||
dlaset_((char *)"A", n, n, &c_b6, &c_b11, &work[1], n, (ftnlen)1);
|
||||
dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, &
|
||||
work[1], n, &b[b_offset], ldb, &work[nwork], info, (ftnlen)1);
|
||||
dlasdq_((char *)"U", &c__0, n, n, &c__0, nrhs, &d__[1], &e[1], &work[1], n, &work[1], n,
|
||||
&b[b_offset], ldb, &work[nwork], info, (ftnlen)1);
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
@ -411,37 +149,23 @@ f"> */
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if (d__[i__] <= tol) {
|
||||
dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb,
|
||||
(ftnlen)1);
|
||||
dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &b[i__ + b_dim1], ldb, (ftnlen)1);
|
||||
} else {
|
||||
dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[
|
||||
i__ + b_dim1], ldb, info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &b[i__ + b_dim1], ldb,
|
||||
info, (ftnlen)1);
|
||||
++(*rank);
|
||||
}
|
||||
/* L40: */
|
||||
}
|
||||
dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, &
|
||||
c_b6, &work[nwork], n, (ftnlen)1, (ftnlen)1);
|
||||
dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b11, &work[1], n, &b[b_offset], ldb, &c_b6, &work[nwork], n,
|
||||
(ftnlen)1, (ftnlen)1);
|
||||
dlacpy_((char *)"A", n, nrhs, &work[nwork], n, &b[b_offset], ldb, (ftnlen)1);
|
||||
|
||||
/* Unscale. */
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n,
|
||||
info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (ftnlen)1);
|
||||
dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset],
|
||||
ldb, info, (ftnlen)1);
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1);
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Book-keeping and setting up some constants. */
|
||||
|
||||
nlvl = (integer) (log((doublereal) (*n) / (doublereal) (*smlsiz + 1)) /
|
||||
log(2.)) + 1;
|
||||
|
||||
nlvl = (integer)(log((doublereal)(*n) / (doublereal)(*smlsiz + 1)) / log(2.)) + 1;
|
||||
smlszp = *smlsiz + 1;
|
||||
|
||||
u = 1;
|
||||
vt = *smlsiz * *n + 1;
|
||||
difl = vt + smlszp * *n;
|
||||
@ -453,55 +177,35 @@ f"> */
|
||||
givnum = poles + (nlvl << 1) * *n;
|
||||
bx = givnum + (nlvl << 1) * *n;
|
||||
nwork = bx + *n * *nrhs;
|
||||
|
||||
sizei = *n + 1;
|
||||
k = sizei + *n;
|
||||
givptr = k + *n;
|
||||
perm = givptr + *n;
|
||||
givcol = perm + nlvl * *n;
|
||||
iwk = givcol + (nlvl * *n << 1);
|
||||
|
||||
st = 1;
|
||||
sqre = 0;
|
||||
icmpq1 = 1;
|
||||
icmpq2 = 0;
|
||||
nsub = 0;
|
||||
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if ((d__1 = d__[i__], abs(d__1)) < eps) {
|
||||
d__[i__] = d_lmp_sign(&eps, &d__[i__]);
|
||||
}
|
||||
/* L50: */
|
||||
}
|
||||
|
||||
i__1 = nm1;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if ((d__1 = e[i__], abs(d__1)) < eps || i__ == nm1) {
|
||||
++nsub;
|
||||
iwork[nsub] = st;
|
||||
|
||||
/* Subproblem found. First determine its size and then */
|
||||
/* apply divide and conquer on it. */
|
||||
|
||||
if (i__ < nm1) {
|
||||
|
||||
/* A subproblem with E(I) small for I < NM1. */
|
||||
|
||||
nsize = i__ - st + 1;
|
||||
iwork[sizei + nsub - 1] = nsize;
|
||||
} else if ((d__1 = e[i__], abs(d__1)) >= eps) {
|
||||
|
||||
/* A subproblem with E(NM1) not too small but I = NM1. */
|
||||
|
||||
nsize = *n - st + 1;
|
||||
iwork[sizei + nsub - 1] = nsize;
|
||||
} else {
|
||||
|
||||
/* A subproblem with E(NM1) small. This implies an */
|
||||
/* 1-by-1 subproblem at D(N), which is not solved */
|
||||
/* explicitly. */
|
||||
|
||||
nsize = i__ - st + 1;
|
||||
iwork[sizei + nsub - 1] = nsize;
|
||||
++nsub;
|
||||
@ -511,80 +215,50 @@ f"> */
|
||||
}
|
||||
st1 = st - 1;
|
||||
if (nsize == 1) {
|
||||
|
||||
/* This is a 1-by-1 subproblem and is not solved */
|
||||
/* explicitly. */
|
||||
|
||||
dcopy_(nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n);
|
||||
} else if (nsize <= *smlsiz) {
|
||||
|
||||
/* This is a small subproblem and is solved by DLASDQ. */
|
||||
|
||||
dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1],
|
||||
n, (ftnlen)1);
|
||||
dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[
|
||||
st], &work[vt + st1], n, &work[nwork], n, &b[st +
|
||||
b_dim1], ldb, &work[nwork], info, (ftnlen)1);
|
||||
dlaset_((char *)"A", &nsize, &nsize, &c_b6, &c_b11, &work[vt + st1], n, (ftnlen)1);
|
||||
dlasdq_((char *)"U", &c__0, &nsize, &nsize, &c__0, nrhs, &d__[st], &e[st], &work[vt + st1],
|
||||
n, &work[nwork], n, &b[st + b_dim1], ldb, &work[nwork], info, (ftnlen)1);
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx +
|
||||
st1], n, (ftnlen)1);
|
||||
dlacpy_((char *)"A", &nsize, nrhs, &b[st + b_dim1], ldb, &work[bx + st1], n, (ftnlen)1);
|
||||
} else {
|
||||
|
||||
/* A large problem. Solve it using divide and conquer. */
|
||||
|
||||
dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &
|
||||
work[u + st1], n, &work[vt + st1], &iwork[k + st1], &
|
||||
work[difl + st1], &work[difr + st1], &work[z__ + st1],
|
||||
&work[poles + st1], &iwork[givptr + st1], &iwork[
|
||||
givcol + st1], n, &iwork[perm + st1], &work[givnum +
|
||||
st1], &work[c__ + st1], &work[s + st1], &work[nwork],
|
||||
&iwork[iwk], info);
|
||||
dlasda_(&icmpq1, smlsiz, &nsize, &sqre, &d__[st], &e[st], &work[u + st1], n,
|
||||
&work[vt + st1], &iwork[k + st1], &work[difl + st1], &work[difr + st1],
|
||||
&work[z__ + st1], &work[poles + st1], &iwork[givptr + st1],
|
||||
&iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1],
|
||||
&work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info);
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
bxst = bx + st1;
|
||||
dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &
|
||||
work[bxst], n, &work[u + st1], n, &work[vt + st1], &
|
||||
iwork[k + st1], &work[difl + st1], &work[difr + st1],
|
||||
&work[z__ + st1], &work[poles + st1], &iwork[givptr +
|
||||
st1], &iwork[givcol + st1], n, &iwork[perm + st1], &
|
||||
work[givnum + st1], &work[c__ + st1], &work[s + st1],
|
||||
&work[nwork], &iwork[iwk], info);
|
||||
dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &b[st + b_dim1], ldb, &work[bxst], n,
|
||||
&work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1],
|
||||
&work[difr + st1], &work[z__ + st1], &work[poles + st1],
|
||||
&iwork[givptr + st1], &iwork[givcol + st1], n, &iwork[perm + st1],
|
||||
&work[givnum + st1], &work[c__ + st1], &work[s + st1], &work[nwork],
|
||||
&iwork[iwk], info);
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
}
|
||||
st = i__ + 1;
|
||||
}
|
||||
/* L60: */
|
||||
}
|
||||
|
||||
/* Apply the singular values and treat the tiny ones as zero. */
|
||||
|
||||
tol = rcnd * (d__1 = d__[idamax_(n, &d__[1], &c__1)], abs(d__1));
|
||||
|
||||
i__1 = *n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
|
||||
/* Some of the elements in D can be negative because 1-by-1 */
|
||||
/* subproblems were not solved explicitly. */
|
||||
|
||||
if ((d__1 = d__[i__], abs(d__1)) <= tol) {
|
||||
dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, (
|
||||
ftnlen)1);
|
||||
dlaset_((char *)"A", &c__1, nrhs, &c_b6, &c_b6, &work[bx + i__ - 1], n, (ftnlen)1);
|
||||
} else {
|
||||
++(*rank);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[
|
||||
bx + i__ - 1], n, info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &d__[i__], &c_b11, &c__1, nrhs, &work[bx + i__ - 1], n, info,
|
||||
(ftnlen)1);
|
||||
}
|
||||
d__[i__] = (d__1 = d__[i__], abs(d__1));
|
||||
/* L70: */
|
||||
}
|
||||
|
||||
/* Now apply back the right singular vectors. */
|
||||
|
||||
icmpq2 = 1;
|
||||
i__1 = nsub;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
@ -595,38 +269,24 @@ f"> */
|
||||
if (nsize == 1) {
|
||||
dcopy_(nrhs, &work[bxst], n, &b[st + b_dim1], ldb);
|
||||
} else if (nsize <= *smlsiz) {
|
||||
dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n,
|
||||
&work[bxst], n, &c_b6, &b[st + b_dim1], ldb, (ftnlen)1, (
|
||||
ftnlen)1);
|
||||
dgemm_((char *)"T", (char *)"N", &nsize, nrhs, &nsize, &c_b11, &work[vt + st1], n, &work[bxst], n,
|
||||
&c_b6, &b[st + b_dim1], ldb, (ftnlen)1, (ftnlen)1);
|
||||
} else {
|
||||
dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st +
|
||||
b_dim1], ldb, &work[u + st1], n, &work[vt + st1], &iwork[
|
||||
k + st1], &work[difl + st1], &work[difr + st1], &work[z__
|
||||
+ st1], &work[poles + st1], &iwork[givptr + st1], &iwork[
|
||||
givcol + st1], n, &iwork[perm + st1], &work[givnum + st1],
|
||||
&work[c__ + st1], &work[s + st1], &work[nwork], &iwork[
|
||||
iwk], info);
|
||||
dlalsa_(&icmpq2, smlsiz, &nsize, nrhs, &work[bxst], n, &b[st + b_dim1], ldb,
|
||||
&work[u + st1], n, &work[vt + st1], &iwork[k + st1], &work[difl + st1],
|
||||
&work[difr + st1], &work[z__ + st1], &work[poles + st1], &iwork[givptr + st1],
|
||||
&iwork[givcol + st1], n, &iwork[perm + st1], &work[givnum + st1],
|
||||
&work[c__ + st1], &work[s + st1], &work[nwork], &iwork[iwk], info);
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
}
|
||||
/* L80: */
|
||||
}
|
||||
|
||||
/* Unscale and sort the singular values. */
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (
|
||||
ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &c_b11, &orgnrm, n, &c__1, &d__[1], n, info, (ftnlen)1);
|
||||
dlasrt_((char *)"D", n, &d__[1], info, (ftnlen)1);
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb,
|
||||
info, (ftnlen)1);
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b11, n, nrhs, &b[b_offset], ldb, info, (ftnlen)1);
|
||||
return 0;
|
||||
|
||||
/* End of DLALSD */
|
||||
|
||||
} /* dlalsd_ */
|
||||
|
||||
}
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
}
|
||||
#endif
|
||||
|
||||
Reference in New Issue
Block a user