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references/igraph-1.0.1/vendor/lapack/dgeqr2.c
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/* -- translated by f2c (version 20240504).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
/* > \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorit
hm.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DGEQR2 + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
INTEGER INFO, LDA, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
> \par Purpose:
=============
>
> \verbatim
>
> DGEQR2 computes a QR factorization of a real m by n matrix A:
> A = Q * R.
> \endverbatim
Arguments:
==========
> \param[in] M
> \verbatim
> M is INTEGER
> The number of rows of the matrix A. M >= 0.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The number of columns of the matrix A. N >= 0.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA,N)
> On entry, the m by n matrix A.
> On exit, the elements on and above the diagonal of the array
> contain the min(m,n) by n upper trapezoidal matrix R (R is
> upper triangular if m >= n); the elements below the diagonal,
> with the array TAU, represent the orthogonal matrix Q as a
> product of elementary reflectors (see Further Details).
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,M).
> \endverbatim
>
> \param[out] TAU
> \verbatim
> TAU is DOUBLE PRECISION array, dimension (min(M,N))
> The scalar factors of the elementary reflectors (see Further
> Details).
> \endverbatim
>
> \param[out] WORK
> \verbatim
> WORK is DOUBLE PRECISION array, dimension (N)
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleGEcomputational
> \par Further Details:
=====================
>
> \verbatim
>
> The matrix Q is represented as a product of elementary reflectors
>
> Q = H(1) H(2) . . . H(k), where k = min(m,n).
>
> Each H(i) has the form
>
> H(i) = I - tau * v * v**T
>
> where tau is a real scalar, and v is a real vector with
> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
> and tau in TAU(i).
> \endverbatim
>
=====================================================================
Subroutine */ int igraphdgeqr2_(integer *m, integer *n, doublereal *a, integer *
lda, doublereal *tau, doublereal *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, k;
doublereal aii;
extern /* Subroutine */ int igraphdlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *), igraphdlarfg_(integer *, doublereal *,
doublereal *, integer *, doublereal *), igraphxerbla_(char *, integer *,
ftnlen);
/* -- LAPACK computational routine (version 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
Test the input arguments
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DGEQR2", &i__1, (ftnlen)6);
return 0;
}
k = min(*m,*n);
i__1 = k;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Generate elementary reflector H(i) to annihilate A(i+1:m,i) */
i__2 = *m - i__ + 1;
/* Computing MIN */
i__3 = i__ + 1;
igraphdlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1]
, &c__1, &tau[i__]);
if (i__ < *n) {
/* Apply H(i) to A(i:m,i+1:n) from the left */
aii = a[i__ + i__ * a_dim1];
a[i__ + i__ * a_dim1] = 1.;
i__2 = *m - i__ + 1;
i__3 = *n - i__;
igraphdlarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[
i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]);
a[i__ + i__ * a_dim1] = aii;
}
/* L10: */
}
return 0;
/* End of DGEQR2 */
} /* igraphdgeqr2_ */