convert linalg library from Fortran to C++
This commit is contained in:
Axel Kohlmeyer
514
lib/linalg/dlasd6.cpp
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514
lib/linalg/dlasd6.cpp
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/* fortran/dlasd6.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__0 = 0;
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static doublereal c_b7 = 1.;
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static integer c__1 = 1;
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static integer c_n1 = -1;
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/* > \brief \b DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two smaller o
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nes by appending a row. Used by sbdsdc. */
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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 DLASD6 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd6.
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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/dlasd6.
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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/dlasd6.
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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 DLASD6( ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, */
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/* IDXQ, PERM, GIVPTR, GIVCOL, LDGCOL, GIVNUM, */
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/* LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, */
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/* IWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, */
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/* $ NR, SQRE */
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/* DOUBLE PRECISION ALPHA, BETA, C, S */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER GIVCOL( LDGCOL, * ), IDXQ( * ), IWORK( * ), */
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/* $ PERM( * ) */
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/* DOUBLE PRECISION D( * ), DIFL( * ), DIFR( * ), */
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/* $ GIVNUM( LDGNUM, * ), POLES( LDGNUM, * ), */
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/* $ VF( * ), VL( * ), WORK( * ), Z( * ) */
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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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/* > DLASD6 computes the SVD of an updated upper bidiagonal matrix B */
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/* > obtained by merging two smaller ones by appending a row. This */
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/* > routine is used only for the problem which requires all singular */
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/* > values and optionally singular vector matrices in factored form. */
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/* > B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE. */
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/* > A related subroutine, DLASD1, handles the case in which all singular */
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/* > values and singular vectors of the bidiagonal matrix are desired. */
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/* > */
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/* > DLASD6 computes the SVD as follows: */
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/* > */
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/* > ( D1(in) 0 0 0 ) */
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/* > B = U(in) * ( Z1**T a Z2**T b ) * VT(in) */
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/* > ( 0 0 D2(in) 0 ) */
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/* > */
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/* > = U(out) * ( D(out) 0) * VT(out) */
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/* > */
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/* > where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M */
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/* > with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros */
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/* > elsewhere; and the entry b is empty if SQRE = 0. */
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/* > */
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/* > The singular values of B can be computed using D1, D2, the first */
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/* > components of all the right singular vectors of the lower block, and */
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/* > the last components of all the right singular vectors of the upper */
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/* > block. These components are stored and updated in VF and VL, */
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/* > respectively, in DLASD6. Hence U and VT are not explicitly */
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/* > referenced. */
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/* > */
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/* > The singular values are stored in D. The algorithm consists of two */
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/* > stages: */
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/* > */
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/* > The first stage consists of deflating the size of the problem */
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/* > when there are multiple singular values or if there is a zero */
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/* > in the Z vector. For each such occurrence the dimension of the */
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/* > secular equation problem is reduced by one. This stage is */
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/* > performed by the routine DLASD7. */
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/* > */
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/* > The second stage consists of calculating the updated */
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/* > singular values. This is done by finding the roots of the */
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/* > secular equation via the routine DLASD4 (as called by DLASD8). */
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/* > This routine also updates VF and VL and computes the distances */
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/* > between the updated singular values and the old singular */
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/* > values. */
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/* > */
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/* > DLASD6 is called from DLASDA. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] ICOMPQ */
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/* > \verbatim */
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/* > ICOMPQ is INTEGER */
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/* > Specifies whether singular vectors are to be computed in */
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/* > factored form: */
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/* > = 0: Compute singular values only. */
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/* > = 1: Compute singular vectors in factored form as well. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NL */
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/* > \verbatim */
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/* > NL is INTEGER */
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/* > The row dimension of the upper block. NL >= 1. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] NR */
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/* > \verbatim */
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/* > NR is INTEGER */
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/* > The row dimension of the lower block. NR >= 1. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] SQRE */
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/* > \verbatim */
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/* > SQRE is INTEGER */
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/* > = 0: the lower block is an NR-by-NR square matrix. */
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/* > = 1: the lower block is an NR-by-(NR+1) rectangular matrix. */
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/* > */
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/* > The bidiagonal matrix has row dimension N = NL + NR + 1, */
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/* > and column dimension M = N + SQRE. */
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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 ( NL+NR+1 ). */
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/* > On entry D(1:NL,1:NL) contains the singular values of the */
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/* > upper block, and D(NL+2:N) contains the singular values */
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/* > of the lower block. On exit D(1:N) contains the singular */
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/* > values of the modified matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] VF */
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/* > \verbatim */
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/* > VF is DOUBLE PRECISION array, dimension ( M ) */
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/* > On entry, VF(1:NL+1) contains the first components of all */
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/* > right singular vectors of the upper block; and VF(NL+2:M) */
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/* > contains the first components of all right singular vectors */
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/* > of the lower block. On exit, VF contains the first components */
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/* > of all right singular vectors of the bidiagonal matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] VL */
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/* > \verbatim */
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/* > VL is DOUBLE PRECISION array, dimension ( M ) */
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/* > On entry, VL(1:NL+1) contains the last components of all */
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/* > right singular vectors of the upper block; and VL(NL+2:M) */
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/* > contains the last components of all right singular vectors of */
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/* > the lower block. On exit, VL contains the last components of */
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/* > all right singular vectors of the bidiagonal matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] ALPHA */
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/* > \verbatim */
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/* > ALPHA is DOUBLE PRECISION */
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/* > Contains the diagonal element associated with the added row. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] BETA */
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/* > \verbatim */
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/* > BETA is DOUBLE PRECISION */
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/* > Contains the off-diagonal element associated with the added */
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/* > row. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] IDXQ */
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/* > \verbatim */
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/* > IDXQ is INTEGER array, dimension ( N ) */
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/* > This contains the permutation which will reintegrate the */
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/* > subproblem just solved back into sorted order, i.e. */
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/* > D( IDXQ( I = 1, N ) ) will be in ascending order. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] PERM */
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/* > \verbatim */
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/* > PERM is INTEGER array, dimension ( N ) */
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/* > The permutations (from deflation and sorting) to be applied */
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/* > to each block. Not referenced if ICOMPQ = 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] GIVPTR */
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/* > \verbatim */
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/* > GIVPTR is INTEGER */
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/* > The number of Givens rotations which took place in this */
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/* > subproblem. Not referenced if ICOMPQ = 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] GIVCOL */
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/* > \verbatim */
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/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 ) */
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/* > Each pair of numbers indicates a pair of columns to take place */
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/* > in a Givens rotation. Not referenced if ICOMPQ = 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDGCOL */
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/* > \verbatim */
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/* > LDGCOL is INTEGER */
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/* > leading dimension of GIVCOL, must be at least N. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] GIVNUM */
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/* > \verbatim */
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/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
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/* > Each number indicates the C or S value to be used in the */
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/* > corresponding Givens rotation. Not referenced if ICOMPQ = 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDGNUM */
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/* > \verbatim */
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/* > LDGNUM is INTEGER */
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/* > The leading dimension of GIVNUM and POLES, must be at least N. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] POLES */
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/* > \verbatim */
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/* > POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 ) */
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/* > On exit, POLES(1,*) is an array containing the new singular */
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/* > values obtained from solving the secular equation, and */
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/* > POLES(2,*) is an array containing the poles in the secular */
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/* > equation. Not referenced if ICOMPQ = 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] DIFL */
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/* > \verbatim */
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/* > DIFL is DOUBLE PRECISION array, dimension ( N ) */
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/* > On exit, DIFL(I) is the distance between I-th updated */
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/* > (undeflated) singular value and the I-th (undeflated) old */
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/* > singular value. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] DIFR */
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/* > \verbatim */
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/* > DIFR is DOUBLE PRECISION array, */
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/* > dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and */
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/* > dimension ( K ) if ICOMPQ = 0. */
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/* > On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not */
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/* > defined and will not be referenced. */
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/* > */
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/* > If ICOMPQ = 1, DIFR(1:K,2) is an array containing the */
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/* > normalizing factors for the right singular vector matrix. */
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/* > */
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/* > See DLASD8 for details on DIFL and DIFR. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] Z */
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/* > \verbatim */
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/* > Z is DOUBLE PRECISION array, dimension ( M ) */
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/* > The first elements of this array contain the components */
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/* > of the deflation-adjusted updating row vector. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] K */
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/* > \verbatim */
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/* > K is INTEGER */
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/* > Contains the dimension of the non-deflated matrix, */
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/* > This is the order of the related secular equation. 1 <= K <=N. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] C */
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/* > \verbatim */
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/* > C is DOUBLE PRECISION */
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/* > C contains garbage if SQRE =0 and the C-value of a Givens */
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/* > rotation related to the right null space if SQRE = 1. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] S */
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/* > \verbatim */
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/* > S is DOUBLE PRECISION */
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/* > S contains garbage if SQRE =0 and the S-value of a Givens */
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/* > rotation related to the right null space if SQRE = 1. */
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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 ( 4 * M ) */
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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 ( 3 * 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: if INFO = 1, a singular value did not converge */
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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 OTHERauxiliary */
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/* > \par Contributors: */
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/* ================== */
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/* > */
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/* > Ming Gu and Huan Ren, Computer Science Division, University of */
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/* > California at Berkeley, USA */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int dlasd6_(integer *icompq, integer *nl, integer *nr,
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integer *sqre, doublereal *d__, doublereal *vf, doublereal *vl,
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doublereal *alpha, doublereal *beta, integer *idxq, integer *perm,
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integer *givptr, integer *givcol, integer *ldgcol, doublereal *givnum,
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integer *ldgnum, doublereal *poles, doublereal *difl, doublereal *
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||||
difr, doublereal *z__, integer *k, doublereal *c__, doublereal *s,
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doublereal *work, integer *iwork, integer *info)
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{
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||||
/* System generated locals */
|
||||
integer givcol_dim1, givcol_offset, givnum_dim1, givnum_offset,
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poles_dim1, poles_offset, i__1;
|
||||
doublereal d__1, d__2;
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||||
|
||||
/* Local variables */
|
||||
integer i__, m, n, n1, n2, iw, idx, idxc, idxp, ivfw, ivlw;
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||||
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
|
||||
doublereal *, integer *), dlasd7_(integer *, integer *, integer *,
|
||||
integer *, integer *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, integer *, integer *,
|
||||
integer *, integer *, integer *, integer *, integer *, doublereal
|
||||
*, integer *, doublereal *, doublereal *, integer *), dlasd8_(
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||||
integer *, integer *, doublereal *, doublereal *, doublereal *,
|
||||
doublereal *, doublereal *, doublereal *, integer *, doublereal *,
|
||||
doublereal *, integer *), dlascl_(char *, integer *, integer *,
|
||||
doublereal *, doublereal *, integer *, integer *, doublereal *,
|
||||
integer *, integer *, ftnlen), dlamrg_(integer *, integer *,
|
||||
doublereal *, integer *, integer *, integer *);
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||||
integer isigma;
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||||
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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doublereal orgnrm;
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||||
|
||||
|
||||
/* -- LAPACK auxiliary routine -- */
|
||||
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
||||
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
||||
|
||||
/* .. Scalar Arguments .. */
|
||||
/* .. */
|
||||
/* .. Array Arguments .. */
|
||||
/* .. */
|
||||
|
||||
/* ===================================================================== */
|
||||
|
||||
/* .. Parameters .. */
|
||||
/* .. */
|
||||
/* .. Local Scalars .. */
|
||||
/* .. */
|
||||
/* .. External Subroutines .. */
|
||||
/* .. */
|
||||
/* .. Intrinsic Functions .. */
|
||||
/* .. */
|
||||
/* .. Executable Statements .. */
|
||||
|
||||
/* Test the input parameters. */
|
||||
|
||||
/* Parameter adjustments */
|
||||
--d__;
|
||||
--vf;
|
||||
--vl;
|
||||
--idxq;
|
||||
--perm;
|
||||
givcol_dim1 = *ldgcol;
|
||||
givcol_offset = 1 + givcol_dim1;
|
||||
givcol -= givcol_offset;
|
||||
poles_dim1 = *ldgnum;
|
||||
poles_offset = 1 + poles_dim1;
|
||||
poles -= poles_offset;
|
||||
givnum_dim1 = *ldgnum;
|
||||
givnum_offset = 1 + givnum_dim1;
|
||||
givnum -= givnum_offset;
|
||||
--difl;
|
||||
--difr;
|
||||
--z__;
|
||||
--work;
|
||||
--iwork;
|
||||
|
||||
/* Function Body */
|
||||
*info = 0;
|
||||
n = *nl + *nr + 1;
|
||||
m = n + *sqre;
|
||||
|
||||
if (*icompq < 0 || *icompq > 1) {
|
||||
*info = -1;
|
||||
} else if (*nl < 1) {
|
||||
*info = -2;
|
||||
} else if (*nr < 1) {
|
||||
*info = -3;
|
||||
} else if (*sqre < 0 || *sqre > 1) {
|
||||
*info = -4;
|
||||
} else if (*ldgcol < n) {
|
||||
*info = -14;
|
||||
} else if (*ldgnum < n) {
|
||||
*info = -16;
|
||||
}
|
||||
if (*info != 0) {
|
||||
i__1 = -(*info);
|
||||
xerbla_((char *)"DLASD6", &i__1, (ftnlen)6);
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* The following values are for bookkeeping purposes only. They are */
|
||||
/* integer pointers which indicate the portion of the workspace */
|
||||
/* used by a particular array in DLASD7 and DLASD8. */
|
||||
|
||||
isigma = 1;
|
||||
iw = isigma + n;
|
||||
ivfw = iw + m;
|
||||
ivlw = ivfw + m;
|
||||
|
||||
idx = 1;
|
||||
idxc = idx + n;
|
||||
idxp = idxc + n;
|
||||
|
||||
/* Scale. */
|
||||
|
||||
/* Computing MAX */
|
||||
d__1 = abs(*alpha), d__2 = abs(*beta);
|
||||
orgnrm = max(d__1,d__2);
|
||||
d__[*nl + 1] = 0.;
|
||||
i__1 = n;
|
||||
for (i__ = 1; i__ <= i__1; ++i__) {
|
||||
if ((d__1 = d__[i__], abs(d__1)) > orgnrm) {
|
||||
orgnrm = (d__1 = d__[i__], abs(d__1));
|
||||
}
|
||||
/* L10: */
|
||||
}
|
||||
dlascl_((char *)"G", &c__0, &c__0, &orgnrm, &c_b7, &n, &c__1, &d__[1], &n, info, (
|
||||
ftnlen)1);
|
||||
*alpha /= orgnrm;
|
||||
*beta /= orgnrm;
|
||||
|
||||
/* Sort and Deflate singular values. */
|
||||
|
||||
dlasd7_(icompq, nl, nr, sqre, k, &d__[1], &z__[1], &work[iw], &vf[1], &
|
||||
work[ivfw], &vl[1], &work[ivlw], alpha, beta, &work[isigma], &
|
||||
iwork[idx], &iwork[idxp], &idxq[1], &perm[1], givptr, &givcol[
|
||||
givcol_offset], ldgcol, &givnum[givnum_offset], ldgnum, c__, s,
|
||||
info);
|
||||
|
||||
/* Solve Secular Equation, compute DIFL, DIFR, and update VF, VL. */
|
||||
|
||||
dlasd8_(icompq, k, &d__[1], &z__[1], &vf[1], &vl[1], &difl[1], &difr[1],
|
||||
ldgnum, &work[isigma], &work[iw], info);
|
||||
|
||||
/* Report the possible convergence failure. */
|
||||
|
||||
if (*info != 0) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
/* Save the poles if ICOMPQ = 1. */
|
||||
|
||||
if (*icompq == 1) {
|
||||
dcopy_(k, &d__[1], &c__1, &poles[poles_dim1 + 1], &c__1);
|
||||
dcopy_(k, &work[isigma], &c__1, &poles[(poles_dim1 << 1) + 1], &c__1);
|
||||
}
|
||||
|
||||
/* Unscale. */
|
||||
|
||||
dlascl_((char *)"G", &c__0, &c__0, &c_b7, &orgnrm, &n, &c__1, &d__[1], &n, info, (
|
||||
ftnlen)1);
|
||||
|
||||
/* Prepare the IDXQ sorting permutation. */
|
||||
|
||||
n1 = *k;
|
||||
n2 = n - *k;
|
||||
dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &idxq[1]);
|
||||
|
||||
return 0;
|
||||
|
||||
/* End of DLASD6 */
|
||||
|
||||
} /* dlasd6_ */
|
||||
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
Reference in New Issue
Block a user