138 lines
3.7 KiB
C
138 lines
3.7 KiB
C
|
|
#include "hypre_lapack.h"
|
|
#include "f2c.h"
|
|
|
|
/* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer *
|
|
lda, doublereal *tau, doublereal *work, integer *info)
|
|
{
|
|
/* -- LAPACK routine (version 3.0) --
|
|
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
|
|
Courant Institute, Argonne National Lab, and Rice University
|
|
February 29, 1992
|
|
|
|
|
|
Purpose
|
|
=======
|
|
|
|
DGELQ2 computes an LQ factorization of a real m by n matrix A:
|
|
A = L * 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, 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).
|
|
|
|
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(k) . . . H(2) H(1), 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(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).
|
|
|
|
=====================================================================
|
|
|
|
|
|
Test the input arguments
|
|
|
|
Parameter adjustments */
|
|
/* System generated locals */
|
|
integer a_dim1, a_offset, i__1, i__2, i__3;
|
|
/* Local variables */
|
|
static integer i__, k;
|
|
extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
|
|
doublereal *, integer *, doublereal *, doublereal *, integer *,
|
|
doublereal *), dlarfg_(integer *, doublereal *,
|
|
doublereal *, integer *, doublereal *), xerbla_(char *, integer *);
|
|
static doublereal aii;
|
|
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
|
|
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
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_("DGELQ2", &i__1);
|
|
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)
|
|
|
|
Computing MIN */
|
|
i__2 = i__ + 1;
|
|
i__3 = *n - i__ + 1;
|
|
dlarfg_(&i__3, &a_ref(i__, i__), &a_ref(i__, min(i__2,*n)), lda, &tau[
|
|
i__]);
|
|
if (i__ < *m) {
|
|
|
|
/* Apply H(i) to A(i+1:m,i:n) from the right */
|
|
|
|
aii = a_ref(i__, i__);
|
|
a_ref(i__, i__) = 1.;
|
|
i__2 = *m - i__;
|
|
i__3 = *n - i__ + 1;
|
|
dlarf_("Right", &i__2, &i__3, &a_ref(i__, i__), lda, &tau[i__], &
|
|
a_ref(i__ + 1, i__), lda, &work[1]);
|
|
a_ref(i__, i__) = aii;
|
|
}
|
|
/* L10: */
|
|
}
|
|
return 0;
|
|
|
|
/* End of DGELQ2 */
|
|
|
|
} /* dgelq2_ */
|
|
|
|
#undef a_ref
|
|
|
|
|