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/* dgerq2.f -- translated by f2c (version 20061008).
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"
#include "blaswrap.h"
/* Subroutine */ int dgerq2_(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;
/* Local variables */
integer i__, k;
doublereal aii;
extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *), dlarfp_(integer *, doublereal *,
doublereal *, integer *, doublereal *), xerbla_(char *, integer *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGERQ2 computes an RQ factorization of a real m by n matrix A: */
/* A = R * Q. */
/* Arguments */
/* ========= */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the m by n matrix A. */
/* On exit, if m <= n, the upper triangle of the subarray */
/* A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; */
/* if m >= n, the elements on and above the (m-n)-th subdiagonal */
/* contain the m by n upper trapezoidal matrix R; the remaining */
/* elements, with the array TAU, represent the orthogonal matrix */
/* Q as a product of elementary reflectors (see Further */
/* Details). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (M) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* 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' */
/* where tau is a real scalar, and v is a real vector with */
/* v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */
/* A(m-k+i,1:n-k+i-1), and tau in TAU(i). */
/* ===================================================================== */
/* .. 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_("DGERQ2", &i__1);
return 0;
}
k = min(*m,*n);
for (i__ = k; i__ >= 1; --i__) {
/* Generate elementary reflector H(i) to annihilate */
/* A(m-k+i,1:n-k+i-1) */
i__1 = *n - k + i__;
dlarfp_(&i__1, &a[*m - k + i__ + (*n - k + i__) * a_dim1], &a[*m - k
+ i__ + a_dim1], lda, &tau[i__]);
/* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right */
aii = a[*m - k + i__ + (*n - k + i__) * a_dim1];
a[*m - k + i__ + (*n - k + i__) * a_dim1] = 1.;
i__1 = *m - k + i__ - 1;
i__2 = *n - k + i__;
dlarf_("Right", &i__1, &i__2, &a[*m - k + i__ + a_dim1], lda, &tau[
i__], &a[a_offset], lda, &work[1]);
a[*m - k + i__ + (*n - k + i__) * a_dim1] = aii;
/* L10: */
}
return 0;
/* End of DGERQ2 */
} /* dgerq2_ */
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