989 lines
37 KiB
C++
989 lines
37 KiB
C++
/* fortran/dgelss.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__6 = 6;
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static integer c_n1 = -1;
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static integer c__0 = 0;
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static doublereal c_b46 = 0.;
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static integer c__1 = 1;
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static doublereal c_b79 = 1.;
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/* > \brief <b> DGELSS solves overdetermined or underdetermined systems for GE matrices</b> */
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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 DGELSS + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelss.
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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/dgelss.
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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/dgelss.
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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 DGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, */
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/* WORK, LWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK */
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/* DOUBLE PRECISION RCOND */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), 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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/* > DGELSS computes the minimum norm solution to a real linear least */
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/* > squares problem: */
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/* > */
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/* > Minimize 2-norm(| b - A*x |). */
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/* > */
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/* > using the singular value decomposition (SVD) of A. A is an M-by-N */
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/* > matrix which may be rank-deficient. */
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/* > */
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/* > Several right hand side vectors b and solution vectors x can be */
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/* > handled in a single call; they are stored as the columns of the */
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/* > M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix */
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/* > X. */
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/* > */
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/* > The effective rank of A is determined by treating as zero those */
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/* > singular values which are less than RCOND times the largest singular */
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/* > value. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of rows of the matrix A. M >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of columns of the matrix A. 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 right hand sides, i.e., the number of columns */
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/* > of the matrices B and X. NRHS >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
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/* > On entry, the M-by-N matrix A. */
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/* > On exit, the first min(m,n) rows of A are overwritten with */
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/* > its right singular vectors, stored rowwise. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= max(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] B */
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/* > \verbatim */
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/* > B is DOUBLE PRECISION array, dimension (LDB,NRHS) */
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/* > On entry, the M-by-NRHS right hand side matrix B. */
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/* > On exit, B is overwritten by the N-by-NRHS solution */
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/* > matrix X. If m >= n and RANK = n, the residual */
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/* > sum-of-squares for the solution in the i-th column is given */
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/* > by the sum of squares of elements n+1:m in that column. */
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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 the array B. LDB >= max(1,max(M,N)). */
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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 array, dimension (min(M,N)) */
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/* > The singular values of A in decreasing order. */
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/* > The condition number of A in the 2-norm = S(1)/S(min(m,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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/* > RCOND is used to determine the effective rank of A. */
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/* > Singular values S(i) <= RCOND*S(1) are treated as zero. */
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/* > If RCOND < 0, machine precision is used instead. */
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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 effective rank of A, i.e., the number of singular values */
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/* > which are greater than RCOND*S(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 (MAX(1,LWORK)) */
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/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LWORK */
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/* > \verbatim */
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/* > LWORK is INTEGER */
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/* > The dimension of the array WORK. LWORK >= 1, and also: */
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/* > LWORK >= 3*min(M,N) + max( 2*min(M,N), max(M,N), NRHS ) */
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/* > For good performance, LWORK should generally be larger. */
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/* > */
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/* > If LWORK = -1, then a workspace query is assumed; the routine */
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/* > only calculates the optimal size of the WORK array, returns */
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/* > this value as the first entry of the WORK array, and no error */
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/* > message related to LWORK is issued by XERBLA. */
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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 for computing the SVD failed to converge; */
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/* > if INFO = i, i off-diagonal elements of an intermediate */
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/* > bidiagonal form did not converge to zero. */
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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 doubleGEsolve */
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/* ===================================================================== */
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/* Subroutine */ int dgelss_(integer *m, integer *n, integer *nrhs,
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doublereal *a, integer *lda, doublereal *b, integer *ldb, doublereal *
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s, doublereal *rcond, integer *rank, doublereal *work, integer *lwork,
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integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4;
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doublereal d__1;
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/* Local variables */
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integer i__, bl, ie, il, mm;
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doublereal dum[1], eps, thr, anrm, bnrm;
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integer itau, lwork_dgebrd__, lwork_dgelqf__, lwork_dgeqrf__,
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lwork_dorgbr__, lwork_dormbr__, lwork_dormlq__, lwork_dormqr__;
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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 iascl, ibscl;
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extern /* Subroutine */ int dgemv_(char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, ftnlen), drscl_(integer *,
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doublereal *, doublereal *, integer *);
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integer chunk;
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doublereal sfmin;
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integer minmn;
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
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doublereal *, integer *);
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integer maxmn, itaup, itauq, mnthr, iwork;
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extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dgebrd_(
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integer *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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integer *);
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extern doublereal dlamch_(char *, ftnlen), dlange_(char *, integer *,
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integer *, doublereal *, integer *, doublereal *, ftnlen);
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integer bdspac;
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extern /* Subroutine */ int dgelqf_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *, integer *),
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dlascl_(char *, integer *, integer *, doublereal *, doublereal *,
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integer *, integer *, doublereal *, integer *, integer *, ftnlen),
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dgeqrf_(integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, integer *), dlacpy_(char *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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integer *, ftnlen), dlaset_(char *, integer *, integer *,
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doublereal *, doublereal *, doublereal *, integer *, ftnlen),
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xerbla_(char *, integer *, ftnlen), dbdsqr_(char *, integer *,
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integer *, integer *, integer *, doublereal *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, integer *, ftnlen), dorgbr_(char *,
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integer *, integer *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, integer *, ftnlen);
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doublereal bignum;
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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extern /* Subroutine */ int dormbr_(char *, char *, char *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, integer *,
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ftnlen, ftnlen, ftnlen), dormlq_(char *, char *, integer *,
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integer *, integer *, doublereal *, integer *, doublereal *,
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doublereal *, integer *, doublereal *, integer *, integer *,
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ftnlen, ftnlen);
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integer ldwork;
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extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, integer *, ftnlen, ftnlen);
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integer minwrk, maxwrk;
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doublereal smlnum;
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logical lquery;
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/* -- LAPACK driver 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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/* .. Local Arrays .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input arguments */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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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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--s;
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--work;
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/* Function Body */
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*info = 0;
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minmn = min(*m,*n);
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maxmn = max(*m,*n);
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lquery = *lwork == -1;
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if (*m < 0) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*nrhs < 0) {
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*info = -3;
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} else if (*lda < max(1,*m)) {
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*info = -5;
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} else if (*ldb < max(1,maxmn)) {
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*info = -7;
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}
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/* Compute workspace */
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/* (Note: Comments in the code beginning (char *)"Workspace:" describe the */
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/* minimal amount of workspace needed at that point in the code, */
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/* as well as the preferred amount for good performance. */
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/* NB refers to the optimal block size for the immediately */
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/* following subroutine, as returned by ILAENV.) */
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if (*info == 0) {
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minwrk = 1;
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maxwrk = 1;
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if (minmn > 0) {
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mm = *m;
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mnthr = ilaenv_(&c__6, (char *)"DGELSS", (char *)" ", m, n, nrhs, &c_n1, (ftnlen)
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6, (ftnlen)1);
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if (*m >= *n && *m >= mnthr) {
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/* Path 1a - overdetermined, with many more rows than */
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/* columns */
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/* Compute space needed for DGEQRF */
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dgeqrf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info);
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lwork_dgeqrf__ = (integer) dum[0];
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/* Compute space needed for DORMQR */
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dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum, &b[
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b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (ftnlen)
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1);
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lwork_dormqr__ = (integer) dum[0];
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mm = *n;
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/* Computing MAX */
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i__1 = maxwrk, i__2 = *n + lwork_dgeqrf__;
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maxwrk = max(i__1,i__2);
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/* Computing MAX */
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i__1 = maxwrk, i__2 = *n + lwork_dormqr__;
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maxwrk = max(i__1,i__2);
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}
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if (*m >= *n) {
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/* Path 1 - overdetermined or exactly determined */
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/* Compute workspace needed for DBDSQR */
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/* Computing MAX */
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i__1 = 1, i__2 = *n * 5;
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bdspac = max(i__1,i__2);
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/* Compute space needed for DGEBRD */
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dgebrd_(&mm, n, &a[a_offset], lda, &s[1], dum, dum, dum, dum,
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&c_n1, info);
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lwork_dgebrd__ = (integer) dum[0];
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/* Compute space needed for DORMBR */
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dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, dum, &
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b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (
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ftnlen)1, (ftnlen)1);
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lwork_dormbr__ = (integer) dum[0];
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/* Compute space needed for DORGBR */
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dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, dum, dum, &c_n1,
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info, (ftnlen)1);
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lwork_dorgbr__ = (integer) dum[0];
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/* Compute total workspace needed */
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/* Computing MAX */
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i__1 = maxwrk, i__2 = *n * 3 + lwork_dgebrd__;
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maxwrk = max(i__1,i__2);
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/* Computing MAX */
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i__1 = maxwrk, i__2 = *n * 3 + lwork_dormbr__;
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maxwrk = max(i__1,i__2);
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/* Computing MAX */
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i__1 = maxwrk, i__2 = *n * 3 + lwork_dorgbr__;
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maxwrk = max(i__1,i__2);
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maxwrk = max(maxwrk,bdspac);
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/* Computing MAX */
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i__1 = maxwrk, i__2 = *n * *nrhs;
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maxwrk = max(i__1,i__2);
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/* Computing MAX */
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i__1 = *n * 3 + mm, i__2 = *n * 3 + *nrhs, i__1 = max(i__1,
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i__2);
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minwrk = max(i__1,bdspac);
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maxwrk = max(minwrk,maxwrk);
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}
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if (*n > *m) {
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/* Compute workspace needed for DBDSQR */
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/* Computing MAX */
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i__1 = 1, i__2 = *m * 5;
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bdspac = max(i__1,i__2);
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/* Computing MAX */
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i__1 = *m * 3 + *nrhs, i__2 = *m * 3 + *n, i__1 = max(i__1,
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i__2);
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minwrk = max(i__1,bdspac);
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if (*n >= mnthr) {
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/* Path 2a - underdetermined, with many more columns */
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/* than rows */
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/* Compute space needed for DGELQF */
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dgelqf_(m, n, &a[a_offset], lda, dum, dum, &c_n1, info);
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lwork_dgelqf__ = (integer) dum[0];
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/* Compute space needed for DGEBRD */
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dgebrd_(m, m, &a[a_offset], lda, &s[1], dum, dum, dum,
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dum, &c_n1, info);
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lwork_dgebrd__ = (integer) dum[0];
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/* Compute space needed for DORMBR */
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dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, dum,
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&b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (
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ftnlen)1, (ftnlen)1);
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lwork_dormbr__ = (integer) dum[0];
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/* Compute space needed for DORGBR */
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dorgbr_((char *)"P", m, m, m, &a[a_offset], lda, dum, dum, &c_n1,
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info, (ftnlen)1);
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lwork_dorgbr__ = (integer) dum[0];
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/* Compute space needed for DORMLQ */
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dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, dum, &b[
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b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (
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ftnlen)1);
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lwork_dormlq__ = (integer) dum[0];
|
|
/* Compute total workspace needed */
|
|
maxwrk = *m + lwork_dgelqf__;
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
|
|
lwork_dgebrd__;
|
|
maxwrk = max(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
|
|
lwork_dormbr__;
|
|
maxwrk = max(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 2) +
|
|
lwork_dorgbr__;
|
|
maxwrk = max(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + *m + bdspac;
|
|
maxwrk = max(i__1,i__2);
|
|
if (*nrhs > 1) {
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + *m + *m * *nrhs;
|
|
maxwrk = max(i__1,i__2);
|
|
} else {
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * *m + (*m << 1);
|
|
maxwrk = max(i__1,i__2);
|
|
}
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m + lwork_dormlq__;
|
|
maxwrk = max(i__1,i__2);
|
|
} else {
|
|
|
|
/* Path 2 - underdetermined */
|
|
|
|
/* Compute space needed for DGEBRD */
|
|
dgebrd_(m, n, &a[a_offset], lda, &s[1], dum, dum, dum,
|
|
dum, &c_n1, info);
|
|
lwork_dgebrd__ = (integer) dum[0];
|
|
/* Compute space needed for DORMBR */
|
|
dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &a[a_offset], lda, dum,
|
|
&b[b_offset], ldb, dum, &c_n1, info, (ftnlen)1, (
|
|
ftnlen)1, (ftnlen)1);
|
|
lwork_dormbr__ = (integer) dum[0];
|
|
/* Compute space needed for DORGBR */
|
|
dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, dum, dum, &c_n1,
|
|
info, (ftnlen)1);
|
|
lwork_dorgbr__ = (integer) dum[0];
|
|
maxwrk = *m * 3 + lwork_dgebrd__;
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * 3 + lwork_dormbr__;
|
|
maxwrk = max(i__1,i__2);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *m * 3 + lwork_dorgbr__;
|
|
maxwrk = max(i__1,i__2);
|
|
maxwrk = max(maxwrk,bdspac);
|
|
/* Computing MAX */
|
|
i__1 = maxwrk, i__2 = *n * *nrhs;
|
|
maxwrk = max(i__1,i__2);
|
|
}
|
|
}
|
|
maxwrk = max(minwrk,maxwrk);
|
|
}
|
|
work[1] = (doublereal) maxwrk;
|
|
|
|
if (*lwork < minwrk && ! lquery) {
|
|
*info = -12;
|
|
}
|
|
}
|
|
|
|
if (*info != 0) {
|
|
i__1 = -(*info);
|
|
xerbla_((char *)"DGELSS", &i__1, (ftnlen)6);
|
|
return 0;
|
|
} else if (lquery) {
|
|
return 0;
|
|
}
|
|
|
|
/* Quick return if possible */
|
|
|
|
if (*m == 0 || *n == 0) {
|
|
*rank = 0;
|
|
return 0;
|
|
}
|
|
|
|
/* Get machine parameters */
|
|
|
|
eps = dlamch_((char *)"P", (ftnlen)1);
|
|
sfmin = dlamch_((char *)"S", (ftnlen)1);
|
|
smlnum = sfmin / eps;
|
|
bignum = 1. / smlnum;
|
|
dlabad_(&smlnum, &bignum);
|
|
|
|
/* Scale A if max element outside range [SMLNUM,BIGNUM] */
|
|
|
|
anrm = dlange_((char *)"M", m, n, &a[a_offset], lda, &work[1], (ftnlen)1);
|
|
iascl = 0;
|
|
if (anrm > 0. && anrm < smlnum) {
|
|
|
|
/* Scale matrix norm up to SMLNUM */
|
|
|
|
dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
|
|
info, (ftnlen)1);
|
|
iascl = 1;
|
|
} else if (anrm > bignum) {
|
|
|
|
/* Scale matrix norm down to BIGNUM */
|
|
|
|
dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
|
|
info, (ftnlen)1);
|
|
iascl = 2;
|
|
} else if (anrm == 0.) {
|
|
|
|
/* Matrix all zero. Return zero solution. */
|
|
|
|
i__1 = max(*m,*n);
|
|
dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[b_offset], ldb, (ftnlen)
|
|
1);
|
|
dlaset_((char *)"F", &minmn, &c__1, &c_b46, &c_b46, &s[1], &minmn, (ftnlen)1);
|
|
*rank = 0;
|
|
goto L70;
|
|
}
|
|
|
|
/* Scale B if max element outside range [SMLNUM,BIGNUM] */
|
|
|
|
bnrm = dlange_((char *)"M", m, nrhs, &b[b_offset], ldb, &work[1], (ftnlen)1);
|
|
ibscl = 0;
|
|
if (bnrm > 0. && bnrm < smlnum) {
|
|
|
|
/* Scale matrix norm up to SMLNUM */
|
|
|
|
dlascl_((char *)"G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
|
|
info, (ftnlen)1);
|
|
ibscl = 1;
|
|
} else if (bnrm > bignum) {
|
|
|
|
/* Scale matrix norm down to BIGNUM */
|
|
|
|
dlascl_((char *)"G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
|
|
info, (ftnlen)1);
|
|
ibscl = 2;
|
|
}
|
|
|
|
/* Overdetermined case */
|
|
|
|
if (*m >= *n) {
|
|
|
|
/* Path 1 - overdetermined or exactly determined */
|
|
|
|
mm = *m;
|
|
if (*m >= mnthr) {
|
|
|
|
/* Path 1a - overdetermined, with many more rows than columns */
|
|
|
|
mm = *n;
|
|
itau = 1;
|
|
iwork = itau + *n;
|
|
|
|
/* Compute A=Q*R */
|
|
/* (Workspace: need 2*N, prefer N+N*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dgeqrf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__1,
|
|
info);
|
|
|
|
/* Multiply B by transpose(Q) */
|
|
/* (Workspace: need N+NRHS, prefer N+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dormqr_((char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itau], &b[
|
|
b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, (
|
|
ftnlen)1);
|
|
|
|
/* Zero out below R */
|
|
|
|
if (*n > 1) {
|
|
i__1 = *n - 1;
|
|
i__2 = *n - 1;
|
|
dlaset_((char *)"L", &i__1, &i__2, &c_b46, &c_b46, &a[a_dim1 + 2],
|
|
lda, (ftnlen)1);
|
|
}
|
|
}
|
|
|
|
ie = 1;
|
|
itauq = ie + *n;
|
|
itaup = itauq + *n;
|
|
iwork = itaup + *n;
|
|
|
|
/* Bidiagonalize R in A */
|
|
/* (Workspace: need 3*N+MM, prefer 3*N+(MM+N)*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dgebrd_(&mm, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
|
|
work[itaup], &work[iwork], &i__1, info);
|
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors of R */
|
|
/* (Workspace: need 3*N+NRHS, prefer 3*N+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dormbr_((char *)"Q", (char *)"L", (char *)"T", &mm, nrhs, n, &a[a_offset], lda, &work[itauq],
|
|
&b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, (
|
|
ftnlen)1, (ftnlen)1);
|
|
|
|
/* Generate right bidiagonalizing vectors of R in A */
|
|
/* (Workspace: need 4*N-1, prefer 3*N+(N-1)*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dorgbr_((char *)"P", n, n, n, &a[a_offset], lda, &work[itaup], &work[iwork], &
|
|
i__1, info, (ftnlen)1);
|
|
iwork = ie + *n;
|
|
|
|
/* Perform bidiagonal QR iteration */
|
|
/* multiply B by transpose of left singular vectors */
|
|
/* compute right singular vectors in A */
|
|
/* (Workspace: need BDSPAC) */
|
|
|
|
dbdsqr_((char *)"U", n, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset], lda,
|
|
dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (ftnlen)1);
|
|
if (*info != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Multiply B by reciprocals of singular values */
|
|
|
|
/* Computing MAX */
|
|
d__1 = *rcond * s[1];
|
|
thr = max(d__1,sfmin);
|
|
if (*rcond < 0.) {
|
|
/* Computing MAX */
|
|
d__1 = eps * s[1];
|
|
thr = max(d__1,sfmin);
|
|
}
|
|
*rank = 0;
|
|
i__1 = *n;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (s[i__] > thr) {
|
|
drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
|
|
++(*rank);
|
|
} else {
|
|
dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1],
|
|
ldb, (ftnlen)1);
|
|
}
|
|
/* L10: */
|
|
}
|
|
|
|
/* Multiply B by right singular vectors */
|
|
/* (Workspace: need N, prefer N*NRHS) */
|
|
|
|
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
|
|
dgemm_((char *)"T", (char *)"N", n, nrhs, n, &c_b79, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (ftnlen)
|
|
1);
|
|
dlacpy_((char *)"G", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (ftnlen)1)
|
|
;
|
|
} else if (*nrhs > 1) {
|
|
chunk = *lwork / *n;
|
|
i__1 = *nrhs;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *nrhs - i__ + 1;
|
|
bl = min(i__3,chunk);
|
|
dgemm_((char *)"T", (char *)"N", n, &bl, n, &c_b79, &a[a_offset], lda, &b[i__
|
|
* b_dim1 + 1], ldb, &c_b46, &work[1], n, (ftnlen)1, (
|
|
ftnlen)1);
|
|
dlacpy_((char *)"G", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1], ldb, (
|
|
ftnlen)1);
|
|
/* L20: */
|
|
}
|
|
} else {
|
|
dgemv_((char *)"T", n, n, &c_b79, &a[a_offset], lda, &b[b_offset], &c__1,
|
|
&c_b46, &work[1], &c__1, (ftnlen)1);
|
|
dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
|
|
}
|
|
|
|
} else /* if(complicated condition) */ {
|
|
/* Computing MAX */
|
|
i__2 = *m, i__1 = (*m << 1) - 4, i__2 = max(i__2,i__1), i__2 = max(
|
|
i__2,*nrhs), i__1 = *n - *m * 3;
|
|
if (*n >= mnthr && *lwork >= (*m << 2) + *m * *m + max(i__2,i__1)) {
|
|
|
|
/* Path 2a - underdetermined, with many more columns than rows */
|
|
/* and sufficient workspace for an efficient algorithm */
|
|
|
|
ldwork = *m;
|
|
/* Computing MAX */
|
|
/* Computing MAX */
|
|
i__3 = *m, i__4 = (*m << 1) - 4, i__3 = max(i__3,i__4), i__3 =
|
|
max(i__3,*nrhs), i__4 = *n - *m * 3;
|
|
i__2 = (*m << 2) + *m * *lda + max(i__3,i__4), i__1 = *m * *lda +
|
|
*m + *m * *nrhs;
|
|
if (*lwork >= max(i__2,i__1)) {
|
|
ldwork = *lda;
|
|
}
|
|
itau = 1;
|
|
iwork = *m + 1;
|
|
|
|
/* Compute A=L*Q */
|
|
/* (Workspace: need 2*M, prefer M+M*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
dgelqf_(m, n, &a[a_offset], lda, &work[itau], &work[iwork], &i__2,
|
|
info);
|
|
il = iwork;
|
|
|
|
/* Copy L to WORK(IL), zeroing out above it */
|
|
|
|
dlacpy_((char *)"L", m, m, &a[a_offset], lda, &work[il], &ldwork, (ftnlen)
|
|
1);
|
|
i__2 = *m - 1;
|
|
i__1 = *m - 1;
|
|
dlaset_((char *)"U", &i__2, &i__1, &c_b46, &c_b46, &work[il + ldwork], &
|
|
ldwork, (ftnlen)1);
|
|
ie = il + ldwork * *m;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize L in WORK(IL) */
|
|
/* (Workspace: need M*M+5*M, prefer M*M+4*M+2*M*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
dgebrd_(m, m, &work[il], &ldwork, &s[1], &work[ie], &work[itauq],
|
|
&work[itaup], &work[iwork], &i__2, info);
|
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors of L */
|
|
/* (Workspace: need M*M+4*M+NRHS, prefer M*M+4*M+NRHS*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, m, &work[il], &ldwork, &work[
|
|
itauq], &b[b_offset], ldb, &work[iwork], &i__2, info, (
|
|
ftnlen)1, (ftnlen)1, (ftnlen)1);
|
|
|
|
/* Generate right bidiagonalizing vectors of R in WORK(IL) */
|
|
/* (Workspace: need M*M+5*M-1, prefer M*M+4*M+(M-1)*NB) */
|
|
|
|
i__2 = *lwork - iwork + 1;
|
|
dorgbr_((char *)"P", m, m, m, &work[il], &ldwork, &work[itaup], &work[
|
|
iwork], &i__2, info, (ftnlen)1);
|
|
iwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, */
|
|
/* computing right singular vectors of L in WORK(IL) and */
|
|
/* multiplying B by transpose of left singular vectors */
|
|
/* (Workspace: need M*M+M+BDSPAC) */
|
|
|
|
dbdsqr_((char *)"U", m, m, &c__0, nrhs, &s[1], &work[ie], &work[il], &
|
|
ldwork, &a[a_offset], lda, &b[b_offset], ldb, &work[iwork]
|
|
, info, (ftnlen)1);
|
|
if (*info != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Multiply B by reciprocals of singular values */
|
|
|
|
/* Computing MAX */
|
|
d__1 = *rcond * s[1];
|
|
thr = max(d__1,sfmin);
|
|
if (*rcond < 0.) {
|
|
/* Computing MAX */
|
|
d__1 = eps * s[1];
|
|
thr = max(d__1,sfmin);
|
|
}
|
|
*rank = 0;
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
if (s[i__] > thr) {
|
|
drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
|
|
++(*rank);
|
|
} else {
|
|
dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1]
|
|
, ldb, (ftnlen)1);
|
|
}
|
|
/* L30: */
|
|
}
|
|
iwork = ie;
|
|
|
|
/* Multiply B by right singular vectors of L in WORK(IL) */
|
|
/* (Workspace: need M*M+2*M, prefer M*M+M+M*NRHS) */
|
|
|
|
if (*lwork >= *ldb * *nrhs + iwork - 1 && *nrhs > 1) {
|
|
dgemm_((char *)"T", (char *)"N", m, nrhs, m, &c_b79, &work[il], &ldwork, &b[
|
|
b_offset], ldb, &c_b46, &work[iwork], ldb, (ftnlen)1,
|
|
(ftnlen)1);
|
|
dlacpy_((char *)"G", m, nrhs, &work[iwork], ldb, &b[b_offset], ldb, (
|
|
ftnlen)1);
|
|
} else if (*nrhs > 1) {
|
|
chunk = (*lwork - iwork + 1) / *m;
|
|
i__2 = *nrhs;
|
|
i__1 = chunk;
|
|
for (i__ = 1; i__1 < 0 ? i__ >= i__2 : i__ <= i__2; i__ +=
|
|
i__1) {
|
|
/* Computing MIN */
|
|
i__3 = *nrhs - i__ + 1;
|
|
bl = min(i__3,chunk);
|
|
dgemm_((char *)"T", (char *)"N", m, &bl, m, &c_b79, &work[il], &ldwork, &
|
|
b[i__ * b_dim1 + 1], ldb, &c_b46, &work[iwork], m,
|
|
(ftnlen)1, (ftnlen)1);
|
|
dlacpy_((char *)"G", m, &bl, &work[iwork], m, &b[i__ * b_dim1 + 1]
|
|
, ldb, (ftnlen)1);
|
|
/* L40: */
|
|
}
|
|
} else {
|
|
dgemv_((char *)"T", m, m, &c_b79, &work[il], &ldwork, &b[b_dim1 + 1],
|
|
&c__1, &c_b46, &work[iwork], &c__1, (ftnlen)1);
|
|
dcopy_(m, &work[iwork], &c__1, &b[b_dim1 + 1], &c__1);
|
|
}
|
|
|
|
/* Zero out below first M rows of B */
|
|
|
|
i__1 = *n - *m;
|
|
dlaset_((char *)"F", &i__1, nrhs, &c_b46, &c_b46, &b[*m + 1 + b_dim1],
|
|
ldb, (ftnlen)1);
|
|
iwork = itau + *m;
|
|
|
|
/* Multiply transpose(Q) by B */
|
|
/* (Workspace: need M+NRHS, prefer M+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dormlq_((char *)"L", (char *)"T", n, nrhs, m, &a[a_offset], lda, &work[itau], &b[
|
|
b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1, (
|
|
ftnlen)1);
|
|
|
|
} else {
|
|
|
|
/* Path 2 - remaining underdetermined cases */
|
|
|
|
ie = 1;
|
|
itauq = ie + *m;
|
|
itaup = itauq + *m;
|
|
iwork = itaup + *m;
|
|
|
|
/* Bidiagonalize A */
|
|
/* (Workspace: need 3*M+N, prefer 3*M+(M+N)*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dgebrd_(m, n, &a[a_offset], lda, &s[1], &work[ie], &work[itauq], &
|
|
work[itaup], &work[iwork], &i__1, info);
|
|
|
|
/* Multiply B by transpose of left bidiagonalizing vectors */
|
|
/* (Workspace: need 3*M+NRHS, prefer 3*M+NRHS*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dormbr_((char *)"Q", (char *)"L", (char *)"T", m, nrhs, n, &a[a_offset], lda, &work[itauq]
|
|
, &b[b_offset], ldb, &work[iwork], &i__1, info, (ftnlen)1,
|
|
(ftnlen)1, (ftnlen)1);
|
|
|
|
/* Generate right bidiagonalizing vectors in A */
|
|
/* (Workspace: need 4*M, prefer 3*M+M*NB) */
|
|
|
|
i__1 = *lwork - iwork + 1;
|
|
dorgbr_((char *)"P", m, n, m, &a[a_offset], lda, &work[itaup], &work[
|
|
iwork], &i__1, info, (ftnlen)1);
|
|
iwork = ie + *m;
|
|
|
|
/* Perform bidiagonal QR iteration, */
|
|
/* computing right singular vectors of A in A and */
|
|
/* multiplying B by transpose of left singular vectors */
|
|
/* (Workspace: need BDSPAC) */
|
|
|
|
dbdsqr_((char *)"L", m, n, &c__0, nrhs, &s[1], &work[ie], &a[a_offset],
|
|
lda, dum, &c__1, &b[b_offset], ldb, &work[iwork], info, (
|
|
ftnlen)1);
|
|
if (*info != 0) {
|
|
goto L70;
|
|
}
|
|
|
|
/* Multiply B by reciprocals of singular values */
|
|
|
|
/* Computing MAX */
|
|
d__1 = *rcond * s[1];
|
|
thr = max(d__1,sfmin);
|
|
if (*rcond < 0.) {
|
|
/* Computing MAX */
|
|
d__1 = eps * s[1];
|
|
thr = max(d__1,sfmin);
|
|
}
|
|
*rank = 0;
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
if (s[i__] > thr) {
|
|
drscl_(nrhs, &s[i__], &b[i__ + b_dim1], ldb);
|
|
++(*rank);
|
|
} else {
|
|
dlaset_((char *)"F", &c__1, nrhs, &c_b46, &c_b46, &b[i__ + b_dim1]
|
|
, ldb, (ftnlen)1);
|
|
}
|
|
/* L50: */
|
|
}
|
|
|
|
/* Multiply B by right singular vectors of A */
|
|
/* (Workspace: need N, prefer N*NRHS) */
|
|
|
|
if (*lwork >= *ldb * *nrhs && *nrhs > 1) {
|
|
dgemm_((char *)"T", (char *)"N", n, nrhs, m, &c_b79, &a[a_offset], lda, &b[
|
|
b_offset], ldb, &c_b46, &work[1], ldb, (ftnlen)1, (
|
|
ftnlen)1);
|
|
dlacpy_((char *)"F", n, nrhs, &work[1], ldb, &b[b_offset], ldb, (
|
|
ftnlen)1);
|
|
} else if (*nrhs > 1) {
|
|
chunk = *lwork / *n;
|
|
i__1 = *nrhs;
|
|
i__2 = chunk;
|
|
for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ +=
|
|
i__2) {
|
|
/* Computing MIN */
|
|
i__3 = *nrhs - i__ + 1;
|
|
bl = min(i__3,chunk);
|
|
dgemm_((char *)"T", (char *)"N", n, &bl, m, &c_b79, &a[a_offset], lda, &b[
|
|
i__ * b_dim1 + 1], ldb, &c_b46, &work[1], n, (
|
|
ftnlen)1, (ftnlen)1);
|
|
dlacpy_((char *)"F", n, &bl, &work[1], n, &b[i__ * b_dim1 + 1],
|
|
ldb, (ftnlen)1);
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
dgemv_((char *)"T", m, n, &c_b79, &a[a_offset], lda, &b[b_offset], &
|
|
c__1, &c_b46, &work[1], &c__1, (ftnlen)1);
|
|
dcopy_(n, &work[1], &c__1, &b[b_offset], &c__1);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Undo scaling */
|
|
|
|
if (iascl == 1) {
|
|
dlascl_((char *)"G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
|
|
info, (ftnlen)1);
|
|
dlascl_((char *)"G", &c__0, &c__0, &smlnum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, info, (ftnlen)1);
|
|
} else if (iascl == 2) {
|
|
dlascl_((char *)"G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
|
|
info, (ftnlen)1);
|
|
dlascl_((char *)"G", &c__0, &c__0, &bignum, &anrm, &minmn, &c__1, &s[1], &
|
|
minmn, info, (ftnlen)1);
|
|
}
|
|
if (ibscl == 1) {
|
|
dlascl_((char *)"G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
|
|
info, (ftnlen)1);
|
|
} else if (ibscl == 2) {
|
|
dlascl_((char *)"G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
|
|
info, (ftnlen)1);
|
|
}
|
|
|
|
L70:
|
|
work[1] = (doublereal) maxwrk;
|
|
return 0;
|
|
|
|
/* End of DGELSS */
|
|
|
|
} /* dgelss_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|