141 lines
3.8 KiB
C
141 lines
3.8 KiB
C
#include "hypre_lapack.h"
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#include "f2c.h"
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/* Subroutine */ int dgeqr2_(integer *m, integer *n, doublereal *a, integer *
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lda, doublereal *tau, doublereal *work, integer *info)
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{
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/* -- LAPACK routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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February 29, 1992
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Purpose
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=======
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DGEQR2 computes a QR factorization of a real m by n matrix A:
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A = Q * R.
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Arguments
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=========
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M (input) INTEGER
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The number of rows of the matrix A. M >= 0.
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N (input) INTEGER
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The number of columns of the matrix A. N >= 0.
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A (input/output) 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 elementary reflectors (see Further Details).
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LDA (input) INTEGER
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The leading dimension of the array A. LDA >= max(1,M).
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TAU (output) 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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WORK (workspace) DOUBLE PRECISION array, dimension (N)
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INFO (output) 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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Further Details
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===============
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The matrix Q is represented as a product of elementary reflectors
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Q = H(1) H(2) . . . H(k), where k = min(m,n).
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Each H(i) has the form
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H(i) = I - tau * v * v'
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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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=====================================================================
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Test the input arguments
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Parameter adjustments */
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/* Table of constant values */
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static integer c__1 = 1;
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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static integer i__, k;
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extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
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doublereal *, integer *, doublereal *, doublereal *, integer *,
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doublereal *), dlarfg_(integer *, doublereal *,
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doublereal *, integer *, doublereal *), xerbla_(char *, integer *);
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static doublereal aii;
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#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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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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*info = 0;
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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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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGEQR2", &i__1);
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return 0;
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}
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k = min(*m,*n);
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i__1 = k;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
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Computing MIN */
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i__2 = i__ + 1;
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i__3 = *m - i__ + 1;
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dlarfg_(&i__3, &a_ref(i__, i__), &a_ref(min(i__2,*m), i__), &c__1, &
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tau[i__]);
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if (i__ < *n) {
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/* Apply H(i) to A(i:m,i+1:n) from the left */
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aii = a_ref(i__, i__);
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a_ref(i__, i__) = 1.;
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i__2 = *m - i__ + 1;
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i__3 = *n - i__;
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dlarf_("Left", &i__2, &i__3, &a_ref(i__, i__), &c__1, &tau[i__], &
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a_ref(i__, i__ + 1), lda, &work[1]);
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a_ref(i__, i__) = aii;
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}
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/* L10: */
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}
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return 0;
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/* End of DGEQR2 */
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} /* dgeqr2_ */
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#undef a_ref
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