599 lines
20 KiB
C++
599 lines
20 KiB
C++
/* fortran/dlalsa.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 doublereal c_b7 = 1.;
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static doublereal c_b8 = 0.;
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static integer c__2 = 2;
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/* > \brief \b DLALSA computes the SVD of the coefficient matrix in compact form. Used by sgelsd. */
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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 DLALSA + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlalsa.
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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/dlalsa.
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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/dlalsa.
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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 DLALSA( ICOMPQ, SMLSIZ, N, NRHS, B, LDB, BX, LDBX, U, */
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/* LDU, VT, K, DIFL, DIFR, Z, POLES, GIVPTR, */
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/* GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, */
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/* IWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER ICOMPQ, INFO, LDB, LDBX, LDGCOL, LDU, N, NRHS, */
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/* $ SMLSIZ */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), */
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/* $ K( * ), PERM( LDGCOL, * ) */
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/* DOUBLE PRECISION B( LDB, * ), BX( LDBX, * ), C( * ), */
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/* $ DIFL( LDU, * ), DIFR( LDU, * ), */
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/* $ GIVNUM( LDU, * ), POLES( LDU, * ), S( * ), */
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/* $ U( LDU, * ), VT( LDU, * ), WORK( * ), */
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/* $ Z( LDU, * ) */
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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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/* > DLALSA is an itermediate step in solving the least squares problem */
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/* > by computing the SVD of the coefficient matrix in compact form (The */
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/* > singular vectors are computed as products of simple orthorgonal */
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/* > matrices.). */
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/* > */
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/* > If ICOMPQ = 0, DLALSA applies the inverse of the left singular vector */
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/* > matrix of an upper bidiagonal matrix to the right hand side; and if */
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/* > ICOMPQ = 1, DLALSA applies the right singular vector matrix to the */
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/* > right hand side. The singular vector matrices were generated in */
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/* > compact form by DLALSA. */
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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 the left or the right singular vector */
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/* > matrix is involved. */
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/* > = 0: Left singular vector matrix */
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/* > = 1: Right singular vector 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 row and column dimensions of the upper bidiagonal matrix. */
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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 and BX. NRHS must be at least 1. */
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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 in rows 1 through M. */
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/* > On output, B contains the solution X in rows 1 through N. */
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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,MAX( M, N ) ). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] BX */
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/* > \verbatim */
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/* > BX is DOUBLE PRECISION array, dimension ( LDBX, NRHS ) */
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/* > On exit, the result of applying the left or right singular */
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/* > vector matrix to B. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDBX */
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/* > \verbatim */
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/* > LDBX is INTEGER */
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/* > The leading dimension of BX. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] U */
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/* > \verbatim */
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/* > U is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ ). */
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/* > On entry, U contains the left singular vector matrices of all */
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/* > subproblems at the bottom level. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDU */
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/* > \verbatim */
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/* > LDU is INTEGER, LDU = > N. */
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/* > The leading dimension of arrays U, VT, DIFL, DIFR, */
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/* > POLES, GIVNUM, and Z. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] VT */
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/* > \verbatim */
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/* > VT is DOUBLE PRECISION array, dimension ( LDU, SMLSIZ+1 ). */
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/* > On entry, VT**T contains the right singular vector matrices of */
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/* > all subproblems at the bottom level. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] K */
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/* > \verbatim */
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/* > K is INTEGER array, dimension ( N ). */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DIFL */
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/* > \verbatim */
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/* > DIFL is DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
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/* > where NLVL = INT(log_2 (N/(SMLSIZ+1))) + 1. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DIFR */
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/* > \verbatim */
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/* > DIFR is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
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/* > On entry, DIFL(*, I) and DIFR(*, 2 * I -1) record */
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/* > distances between singular values on the I-th level and */
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/* > singular values on the (I -1)-th level, and DIFR(*, 2 * I) */
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/* > record the normalizing factors of the right singular vectors */
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/* > matrices of subproblems on I-th level. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] Z */
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/* > \verbatim */
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/* > Z is DOUBLE PRECISION array, dimension ( LDU, NLVL ). */
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/* > On entry, Z(1, I) contains the components of the deflation- */
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/* > adjusted updating row vector for subproblems on the I-th */
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/* > level. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] POLES */
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/* > \verbatim */
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/* > POLES is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
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/* > On entry, POLES(*, 2 * I -1: 2 * I) contains the new and old */
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/* > singular values involved in the secular equations on the I-th */
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/* > level. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVPTR */
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/* > \verbatim */
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/* > GIVPTR is INTEGER array, dimension ( N ). */
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/* > On entry, GIVPTR( I ) records the number of Givens */
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/* > rotations performed on the I-th problem on the computation */
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/* > tree. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVCOL */
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/* > \verbatim */
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/* > GIVCOL is INTEGER array, dimension ( LDGCOL, 2 * NLVL ). */
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/* > On entry, for each I, GIVCOL(*, 2 * I - 1: 2 * I) records the */
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/* > locations of Givens rotations performed on the I-th level on */
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/* > the computation tree. */
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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, LDGCOL = > N. */
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/* > The leading dimension of arrays GIVCOL and PERM. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] PERM */
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/* > \verbatim */
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/* > PERM is INTEGER array, dimension ( LDGCOL, NLVL ). */
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/* > On entry, PERM(*, I) records permutations done on the I-th */
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/* > level of the computation tree. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] GIVNUM */
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/* > \verbatim */
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/* > GIVNUM is DOUBLE PRECISION array, dimension ( LDU, 2 * NLVL ). */
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/* > On entry, GIVNUM(*, 2 *I -1 : 2 * I) records the C- and S- */
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/* > values of Givens rotations performed on the I-th level on the */
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/* > computation tree. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] C */
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/* > \verbatim */
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/* > C is DOUBLE PRECISION array, dimension ( N ). */
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/* > On entry, if the I-th subproblem is not square, */
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/* > C( I ) contains the C-value of a Givens rotation related to */
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/* > the right null space of the I-th subproblem. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] S */
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/* > \verbatim */
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/* > S is DOUBLE PRECISION array, dimension ( N ). */
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/* > On entry, if the I-th subproblem is not square, */
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/* > S( I ) contains the S-value of a Givens rotation related to */
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/* > the right null space of the I-th subproblem. */
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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 (N) */
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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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/* > \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 dlalsa_(integer *icompq, integer *smlsiz, integer *n,
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integer *nrhs, doublereal *b, integer *ldb, doublereal *bx, integer *
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ldbx, doublereal *u, integer *ldu, doublereal *vt, integer *k,
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doublereal *difl, doublereal *difr, doublereal *z__, doublereal *
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poles, integer *givptr, integer *givcol, integer *ldgcol, integer *
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perm, doublereal *givnum, doublereal *c__, doublereal *s, doublereal *
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work, integer *iwork, integer *info)
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{
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/* System generated locals */
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integer givcol_dim1, givcol_offset, perm_dim1, perm_offset, b_dim1,
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b_offset, bx_dim1, bx_offset, difl_dim1, difl_offset, difr_dim1,
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difr_offset, givnum_dim1, givnum_offset, poles_dim1, poles_offset,
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u_dim1, u_offset, vt_dim1, vt_offset, z_dim1, z_offset, i__1,
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i__2;
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/* Builtin functions */
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integer pow_lmp_ii(integer *, integer *);
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/* Local variables */
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integer i__, j, i1, ic, lf, nd, ll, nl, nr, im1, nlf, nrf, lvl, ndb1,
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nlp1, lvl2, nrp1, nlvl, sqre;
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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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integer inode, ndiml, ndimr;
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *), dlals0_(integer *, integer *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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integer *, integer *, integer *, integer *, integer *, doublereal
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*, integer *, doublereal *, doublereal *, doublereal *,
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doublereal *, integer *, doublereal *, doublereal *, doublereal *,
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integer *), dlasdt_(integer *, integer *, integer *, integer *,
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integer *, integer *, integer *), xerbla_(char *, integer *,
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ftnlen);
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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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/* .. Scalar Arguments .. */
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/* .. */
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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 Subroutines .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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b_dim1 = *ldb;
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b_offset = 1 + b_dim1;
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b -= b_offset;
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bx_dim1 = *ldbx;
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bx_offset = 1 + bx_dim1;
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bx -= bx_offset;
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givnum_dim1 = *ldu;
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givnum_offset = 1 + givnum_dim1;
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givnum -= givnum_offset;
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poles_dim1 = *ldu;
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poles_offset = 1 + poles_dim1;
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poles -= poles_offset;
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z_dim1 = *ldu;
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z_offset = 1 + z_dim1;
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z__ -= z_offset;
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difr_dim1 = *ldu;
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difr_offset = 1 + difr_dim1;
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difr -= difr_offset;
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difl_dim1 = *ldu;
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difl_offset = 1 + difl_dim1;
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difl -= difl_offset;
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vt_dim1 = *ldu;
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vt_offset = 1 + vt_dim1;
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vt -= vt_offset;
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u_dim1 = *ldu;
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u_offset = 1 + u_dim1;
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u -= u_offset;
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--k;
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--givptr;
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perm_dim1 = *ldgcol;
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perm_offset = 1 + perm_dim1;
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perm -= perm_offset;
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givcol_dim1 = *ldgcol;
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givcol_offset = 1 + givcol_dim1;
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givcol -= givcol_offset;
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--c__;
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--s;
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--work;
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--iwork;
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/* Function Body */
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*info = 0;
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if (*icompq < 0 || *icompq > 1) {
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*info = -1;
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} else if (*smlsiz < 3) {
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*info = -2;
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} else if (*n < *smlsiz) {
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*info = -3;
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} else if (*nrhs < 1) {
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*info = -4;
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} else if (*ldb < *n) {
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*info = -6;
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} else if (*ldbx < *n) {
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*info = -8;
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} else if (*ldu < *n) {
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*info = -10;
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} else if (*ldgcol < *n) {
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*info = -19;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DLALSA", &i__1, (ftnlen)6);
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return 0;
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}
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/* Book-keeping and setting up the computation tree. */
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inode = 1;
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ndiml = inode + *n;
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ndimr = ndiml + *n;
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dlasdt_(n, &nlvl, &nd, &iwork[inode], &iwork[ndiml], &iwork[ndimr],
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smlsiz);
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/* The following code applies back the left singular vector factors. */
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/* For applying back the right singular vector factors, go to 50. */
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if (*icompq == 1) {
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goto L50;
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}
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/* The nodes on the bottom level of the tree were solved */
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/* by DLASDQ. The corresponding left and right singular vector */
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/* matrices are in explicit form. First apply back the left */
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/* singular vector matrices. */
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ndb1 = (nd + 1) / 2;
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i__1 = nd;
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for (i__ = ndb1; i__ <= i__1; ++i__) {
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/* IC : center row of each node */
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/* NL : number of rows of left subproblem */
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/* NR : number of rows of right subproblem */
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/* NLF: starting row of the left subproblem */
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/* NRF: starting row of the right subproblem */
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i1 = i__ - 1;
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ic = iwork[inode + i1];
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nl = iwork[ndiml + i1];
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nr = iwork[ndimr + i1];
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nlf = ic - nl;
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nrf = ic + 1;
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dgemm_((char *)"T", (char *)"N", &nl, nrhs, &nl, &c_b7, &u[nlf + u_dim1], ldu, &b[nlf
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+ b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, (ftnlen)1, (
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ftnlen)1);
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dgemm_((char *)"T", (char *)"N", &nr, nrhs, &nr, &c_b7, &u[nrf + u_dim1], ldu, &b[nrf
|
|
+ b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, (ftnlen)1, (
|
|
ftnlen)1);
|
|
/* L10: */
|
|
}
|
|
|
|
/* Next copy the rows of B that correspond to unchanged rows */
|
|
/* in the bidiagonal matrix to BX. */
|
|
|
|
i__1 = nd;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
ic = iwork[inode + i__ - 1];
|
|
dcopy_(nrhs, &b[ic + b_dim1], ldb, &bx[ic + bx_dim1], ldbx);
|
|
/* L20: */
|
|
}
|
|
|
|
/* Finally go through the left singular vector matrices of all */
|
|
/* the other subproblems bottom-up on the tree. */
|
|
|
|
j = pow_lmp_ii(&c__2, &nlvl);
|
|
sqre = 0;
|
|
|
|
for (lvl = nlvl; lvl >= 1; --lvl) {
|
|
lvl2 = (lvl << 1) - 1;
|
|
|
|
/* find the first node LF and last node LL on */
|
|
/* the current level LVL */
|
|
|
|
if (lvl == 1) {
|
|
lf = 1;
|
|
ll = 1;
|
|
} else {
|
|
i__1 = lvl - 1;
|
|
lf = pow_lmp_ii(&c__2, &i__1);
|
|
ll = (lf << 1) - 1;
|
|
}
|
|
i__1 = ll;
|
|
for (i__ = lf; i__ <= i__1; ++i__) {
|
|
im1 = i__ - 1;
|
|
ic = iwork[inode + im1];
|
|
nl = iwork[ndiml + im1];
|
|
nr = iwork[ndimr + im1];
|
|
nlf = ic - nl;
|
|
nrf = ic + 1;
|
|
--j;
|
|
dlals0_(icompq, &nl, &nr, &sqre, nrhs, &bx[nlf + bx_dim1], ldbx, &
|
|
b[nlf + b_dim1], ldb, &perm[nlf + lvl * perm_dim1], &
|
|
givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
|
|
givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
|
|
poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
|
|
lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
|
|
j], &s[j], &work[1], info);
|
|
/* L30: */
|
|
}
|
|
/* L40: */
|
|
}
|
|
goto L90;
|
|
|
|
/* ICOMPQ = 1: applying back the right singular vector factors. */
|
|
|
|
L50:
|
|
|
|
/* First now go through the right singular vector matrices of all */
|
|
/* the tree nodes top-down. */
|
|
|
|
j = 0;
|
|
i__1 = nlvl;
|
|
for (lvl = 1; lvl <= i__1; ++lvl) {
|
|
lvl2 = (lvl << 1) - 1;
|
|
|
|
/* Find the first node LF and last node LL on */
|
|
/* the current level LVL. */
|
|
|
|
if (lvl == 1) {
|
|
lf = 1;
|
|
ll = 1;
|
|
} else {
|
|
i__2 = lvl - 1;
|
|
lf = pow_lmp_ii(&c__2, &i__2);
|
|
ll = (lf << 1) - 1;
|
|
}
|
|
i__2 = lf;
|
|
for (i__ = ll; i__ >= i__2; --i__) {
|
|
im1 = i__ - 1;
|
|
ic = iwork[inode + im1];
|
|
nl = iwork[ndiml + im1];
|
|
nr = iwork[ndimr + im1];
|
|
nlf = ic - nl;
|
|
nrf = ic + 1;
|
|
if (i__ == ll) {
|
|
sqre = 0;
|
|
} else {
|
|
sqre = 1;
|
|
}
|
|
++j;
|
|
dlals0_(icompq, &nl, &nr, &sqre, nrhs, &b[nlf + b_dim1], ldb, &bx[
|
|
nlf + bx_dim1], ldbx, &perm[nlf + lvl * perm_dim1], &
|
|
givptr[j], &givcol[nlf + lvl2 * givcol_dim1], ldgcol, &
|
|
givnum[nlf + lvl2 * givnum_dim1], ldu, &poles[nlf + lvl2 *
|
|
poles_dim1], &difl[nlf + lvl * difl_dim1], &difr[nlf +
|
|
lvl2 * difr_dim1], &z__[nlf + lvl * z_dim1], &k[j], &c__[
|
|
j], &s[j], &work[1], info);
|
|
/* L60: */
|
|
}
|
|
/* L70: */
|
|
}
|
|
|
|
/* The nodes on the bottom level of the tree were solved */
|
|
/* by DLASDQ. The corresponding right singular vector */
|
|
/* matrices are in explicit form. Apply them back. */
|
|
|
|
ndb1 = (nd + 1) / 2;
|
|
i__1 = nd;
|
|
for (i__ = ndb1; i__ <= i__1; ++i__) {
|
|
i1 = i__ - 1;
|
|
ic = iwork[inode + i1];
|
|
nl = iwork[ndiml + i1];
|
|
nr = iwork[ndimr + i1];
|
|
nlp1 = nl + 1;
|
|
if (i__ == nd) {
|
|
nrp1 = nr;
|
|
} else {
|
|
nrp1 = nr + 1;
|
|
}
|
|
nlf = ic - nl;
|
|
nrf = ic + 1;
|
|
dgemm_((char *)"T", (char *)"N", &nlp1, nrhs, &nlp1, &c_b7, &vt[nlf + vt_dim1], ldu, &
|
|
b[nlf + b_dim1], ldb, &c_b8, &bx[nlf + bx_dim1], ldbx, (
|
|
ftnlen)1, (ftnlen)1);
|
|
dgemm_((char *)"T", (char *)"N", &nrp1, nrhs, &nrp1, &c_b7, &vt[nrf + vt_dim1], ldu, &
|
|
b[nrf + b_dim1], ldb, &c_b8, &bx[nrf + bx_dim1], ldbx, (
|
|
ftnlen)1, (ftnlen)1);
|
|
/* L80: */
|
|
}
|
|
|
|
L90:
|
|
|
|
return 0;
|
|
|
|
/* End of DLALSA */
|
|
|
|
} /* dlalsa_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|