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145 lines
3.9 KiB
C
145 lines
3.9 KiB
C
#include "clapack.h"
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/* Subroutine */ int dgelq2_(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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/* 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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integer i__, k;
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doublereal aii;
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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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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DGELQ2 computes an LQ factorization of a real m by n matrix A: */
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/* A = L * Q. */
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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 below the diagonal of the array */
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/* contain the m by min(m,n) lower trapezoidal matrix L (L is */
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/* lower triangular if m <= n); the elements above 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 (M) */
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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(k) . . . H(2) H(1), 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:n) is stored on exit in A(i,i+1:n), */
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/* and tau in TAU(i). */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input arguments */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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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_("DGELQ2", &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,i+1:n) */
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i__2 = *n - i__ + 1;
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/* Computing MIN */
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i__3 = i__ + 1;
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dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3, *n)* a_dim1]
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, lda, &tau[i__]);
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if (i__ < *m) {
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/* Apply H(i) to A(i+1:m,i:n) from the right */
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aii = a[i__ + i__ * a_dim1];
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a[i__ + i__ * a_dim1] = 1.;
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i__2 = *m - i__;
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i__3 = *n - i__ + 1;
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dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[
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i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]);
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a[i__ + i__ * a_dim1] = 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 DGELQ2 */
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} /* dgelq2_ */
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