246 lines
7.0 KiB
C++
246 lines
7.0 KiB
C++
/* fortran/dgelq2.f -- translated by f2c (version 20200916).
|
|
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
|
|
*/
|
|
|
|
#ifdef __cplusplus
|
|
extern "C" {
|
|
#endif
|
|
#include "lmp_f2c.h"
|
|
|
|
/* > \brief \b DGELQ2 computes the LQ 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 DGELQ2 + dependencies */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelq2.
|
|
f"> */
|
|
/* > [TGZ]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgelq2.
|
|
f"> */
|
|
/* > [ZIP]</a> */
|
|
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgelq2.
|
|
f"> */
|
|
/* > [TXT]</a> */
|
|
/* > \endhtmlonly */
|
|
|
|
/* Definition: */
|
|
/* =========== */
|
|
|
|
/* SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO ) */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* INTEGER INFO, LDA, M, N */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) */
|
|
/* .. */
|
|
|
|
|
|
/* > \par Purpose: */
|
|
/* ============= */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > DGELQ2 computes an LQ factorization of a real m-by-n matrix A: */
|
|
/* > */
|
|
/* > A = ( L 0 ) * Q */
|
|
/* > */
|
|
/* > where: */
|
|
/* > */
|
|
/* > Q is a n-by-n orthogonal matrix; */
|
|
/* > L is a lower-triangular m-by-m matrix; */
|
|
/* > 0 is a m-by-(n-m) zero matrix, if m < n. */
|
|
/* > */
|
|
/* > \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 below the diagonal of the array */
|
|
/* > contain the m by min(m,n) lower trapezoidal matrix L (L is */
|
|
/* > lower triangular if m <= n); the elements above 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 (M) */
|
|
/* > \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. */
|
|
|
|
/* > \ingroup doubleGEcomputational */
|
|
|
|
/* > \par Further Details: */
|
|
/* ===================== */
|
|
/* > */
|
|
/* > \verbatim */
|
|
/* > */
|
|
/* > The matrix Q is represented as a product of elementary reflectors */
|
|
/* > */
|
|
/* > Q = H(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), */
|
|
/* > and tau in TAU(i). */
|
|
/* > \endverbatim */
|
|
/* > */
|
|
/* ===================================================================== */
|
|
/* Subroutine */ int dgelq2_(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 dlarf_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *, ftnlen), dlarfg_(integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *), xerbla_(char *, integer *,
|
|
ftnlen);
|
|
|
|
|
|
/* -- LAPACK computational routine -- */
|
|
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
|
|
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
|
|
|
|
/* .. Scalar Arguments .. */
|
|
/* .. */
|
|
/* .. Array Arguments .. */
|
|
/* .. */
|
|
|
|
/* ===================================================================== */
|
|
|
|
/* .. Parameters .. */
|
|
/* .. */
|
|
/* .. Local Scalars .. */
|
|
/* .. */
|
|
/* .. External Subroutines .. */
|
|
/* .. */
|
|
/* .. Intrinsic Functions .. */
|
|
/* .. */
|
|
/* .. Executable Statements .. */
|
|
|
|
/* Test the input 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);
|
|
xerbla_((char *)"DGELQ2", &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,i+1:n) */
|
|
|
|
i__2 = *n - i__ + 1;
|
|
/* Computing MIN */
|
|
i__3 = i__ + 1;
|
|
dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1]
|
|
, lda, &tau[i__]);
|
|
if (i__ < *m) {
|
|
|
|
/* Apply H(i) to A(i+1:m,i:n) from the right */
|
|
|
|
aii = a[i__ + i__ * a_dim1];
|
|
a[i__ + i__ * a_dim1] = 1.;
|
|
i__2 = *m - i__;
|
|
i__3 = *n - i__ + 1;
|
|
dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[
|
|
i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen)
|
|
5);
|
|
a[i__ + i__ * a_dim1] = aii;
|
|
}
|
|
/* L10: */
|
|
}
|
|
return 0;
|
|
|
|
/* End of DGELQ2 */
|
|
|
|
} /* dgelq2_ */
|
|
|
|
#ifdef __cplusplus
|
|
}
|
|
#endif
|