355 lines
10 KiB
C++
355 lines
10 KiB
C++
/* fortran/dgeqrf.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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static integer c__3 = 3;
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static integer c__2 = 2;
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/* > \brief \b DGEQRF */
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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 DGEQRF + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqrf.
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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/dgeqrf.
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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/dgeqrf.
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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 DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER INFO, LDA, LWORK, M, N */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION A( LDA, * ), TAU( * ), 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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/* > DGEQRF computes a QR factorization of a real M-by-N matrix A: */
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/* > */
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/* > A = Q * ( R ), */
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/* > ( 0 ) */
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/* > */
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/* > where: */
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/* > */
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/* > Q is a M-by-M orthogonal matrix; */
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/* > R is an upper-triangular N-by-N matrix; */
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/* > 0 is a (M-N)-by-N zero matrix, if M > N. */
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/* > */
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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,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 elements on and above the diagonal of the array */
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/* > contain the min(M,N)-by-N upper trapezoidal matrix R (R is */
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/* > upper triangular if m >= n); the elements below the diagonal, */
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/* > with the array TAU, represent the orthogonal matrix Q as a */
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/* > product of min(m,n) elementary reflectors (see Further */
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/* > Details). */
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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[out] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION array, dimension (min(M,N)) */
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/* > The scalar factors of the elementary reflectors (see Further */
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/* > Details). */
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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. */
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/* > LWORK >= 1, if MIN(M,N) = 0, and LWORK >= N, otherwise. */
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/* > For optimum performance LWORK >= N*NB, where NB is */
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/* > the optimal blocksize. */
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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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/* > \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 doubleGEcomputational */
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/* > \par Further Details: */
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/* ===================== */
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/* > */
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/* > \verbatim */
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/* > */
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/* > The matrix Q is represented as a product of elementary reflectors */
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/* > */
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/* > Q = H(1) H(2) . . . H(k), where k = min(m,n). */
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/* > */
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/* > Each H(i) has the form */
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/* > */
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/* > H(i) = I - tau * v * v**T */
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/* > */
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/* > where tau is a real scalar, and v is a real vector with */
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/* > v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
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/* > and tau in TAU(i). */
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/* > \endverbatim */
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/* > */
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/* ===================================================================== */
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/* Subroutine */ int dgeqrf_(integer *m, integer *n, doublereal *a, integer *
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lda, doublereal *tau, doublereal *work, integer *lwork, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
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/* Local variables */
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integer i__, k, ib, nb, nx, iws, nbmin, iinfo;
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extern /* Subroutine */ int dgeqr2_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *), dlarfb_(char *,
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char *, char *, char *, integer *, integer *, integer *,
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doublereal *, integer *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, integer *, ftnlen, ftnlen, ftnlen,
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ftnlen), dlarft_(char *, char *, integer *, integer *, doublereal
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*, integer *, doublereal *, doublereal *, integer *, ftnlen,
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ftnlen), xerbla_(char *, integer *, ftnlen);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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integer ldwork, lwkopt;
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logical lquery;
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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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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. External 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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--tau;
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--work;
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/* Function Body */
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k = min(*m,*n);
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*info = 0;
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nb = ilaenv_(&c__1, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen)
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1);
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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 (*lda < max(1,*m)) {
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*info = -4;
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} else if (! lquery) {
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if (*lwork <= 0 || *m > 0 && *lwork < max(1,*n)) {
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*info = -7;
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}
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DGEQRF", &i__1, (ftnlen)6);
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return 0;
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} else if (lquery) {
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if (k == 0) {
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lwkopt = 1;
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} else {
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lwkopt = *n * nb;
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}
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work[1] = (doublereal) lwkopt;
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return 0;
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}
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/* Quick return if possible */
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if (k == 0) {
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work[1] = 1.;
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return 0;
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}
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nbmin = 2;
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nx = 0;
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iws = *n;
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if (nb > 1 && nb < k) {
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/* Determine when to cross over from blocked to unblocked code. */
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/* Computing MAX */
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i__1 = 0, i__2 = ilaenv_(&c__3, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &c_n1, (
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ftnlen)6, (ftnlen)1);
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nx = max(i__1,i__2);
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if (nx < k) {
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/* Determine if workspace is large enough for blocked code. */
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ldwork = *n;
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iws = ldwork * nb;
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if (*lwork < iws) {
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/* Not enough workspace to use optimal NB: reduce NB and */
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/* determine the minimum value of NB. */
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nb = *lwork / ldwork;
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/* Computing MAX */
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i__1 = 2, i__2 = ilaenv_(&c__2, (char *)"DGEQRF", (char *)" ", m, n, &c_n1, &
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c_n1, (ftnlen)6, (ftnlen)1);
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nbmin = max(i__1,i__2);
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}
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}
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}
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if (nb >= nbmin && nb < k && nx < k) {
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/* Use blocked code initially */
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i__1 = k - nx;
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i__2 = nb;
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for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
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/* Computing MIN */
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i__3 = k - i__ + 1;
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ib = min(i__3,nb);
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/* Compute the QR factorization of the current block */
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/* A(i:m,i:i+ib-1) */
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i__3 = *m - i__ + 1;
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dgeqr2_(&i__3, &ib, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[
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1], &iinfo);
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if (i__ + ib <= *n) {
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/* Form the triangular factor of the block reflector */
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/* H = H(i) H(i+1) . . . H(i+ib-1) */
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i__3 = *m - i__ + 1;
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dlarft_((char *)"Forward", (char *)"Columnwise", &i__3, &ib, &a[i__ + i__ *
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a_dim1], lda, &tau[i__], &work[1], &ldwork, (ftnlen)7,
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(ftnlen)10);
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/* Apply H**T to A(i:m,i+ib:n) from the left */
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i__3 = *m - i__ + 1;
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i__4 = *n - i__ - ib + 1;
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dlarfb_((char *)"Left", (char *)"Transpose", (char *)"Forward", (char *)"Columnwise", &i__3, &
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i__4, &ib, &a[i__ + i__ * a_dim1], lda, &work[1], &
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ldwork, &a[i__ + (i__ + ib) * a_dim1], lda, &work[ib
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+ 1], &ldwork, (ftnlen)4, (ftnlen)9, (ftnlen)7, (
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ftnlen)10);
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}
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/* L10: */
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}
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} else {
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i__ = 1;
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}
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/* Use unblocked code to factor the last or only block. */
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if (i__ <= k) {
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i__2 = *m - i__ + 1;
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i__1 = *n - i__ + 1;
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dgeqr2_(&i__2, &i__1, &a[i__ + i__ * a_dim1], lda, &tau[i__], &work[1]
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, &iinfo);
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}
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work[1] = (doublereal) iws;
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return 0;
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/* End of DGEQRF */
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} /* dgeqrf_ */
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#ifdef __cplusplus
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}
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#endif
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