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/* lapack/single/sgerq2.f -- translated by f2c (version 20050501).
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 "v3p_netlib.h"
/*< SUBROUTINE SGERQ2( M, N, A, LDA, TAU, WORK, INFO ) >*/
/* Subroutine */ int sgerq2_(integer *m, integer *n, real *a, integer *lda,
real *tau, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
integer i__, k;
real aii;
extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *,
integer *, real *, real *, integer *, real *, ftnlen), xerbla_(
char *, integer *, ftnlen), slarfg_(integer *, real *, real *,
integer *, real *);
/* -- 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 */
/* .. Scalar Arguments .. */
/*< INTEGER INFO, LDA, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< REAL A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* SGERQ2 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) REAL 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) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors (see Further */
/* Details). */
/* WORK (workspace) REAL 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 .. */
/*< REAL ONE >*/
/*< PARAMETER ( ONE = 1.0E+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, K >*/
/*< REAL AII >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL SLARF, SLARFG, XERBLA >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC MAX, MIN >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
*info = 0;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 ) THEN >*/
} else if (*n < 0) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -4 >*/
*info = -4;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'SGERQ2', -INFO ) >*/
i__1 = -(*info);
xerbla_("SGERQ2", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< K = MIN( M, N ) >*/
k = min(*m,*n);
/*< DO 10 I = K, 1, -1 >*/
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__;
slarfg_(&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 ) >*/
aii = a[*m - k + i__ + (*n - k + i__) * a_dim1];
/*< A( M-K+I, N-K+I ) = ONE >*/
a[*m - k + i__ + (*n - k + i__) * a_dim1] = (float)1.;
/*< >*/
i__1 = *m - k + i__ - 1;
i__2 = *n - k + i__;
slarf_("Right", &i__1, &i__2, &a[*m - k + i__ + a_dim1], lda, &tau[
i__], &a[a_offset], lda, &work[1], (ftnlen)5);
/*< A( M-K+I, N-K+I ) = AII >*/
a[*m - k + i__ + (*n - k + i__) * a_dim1] = aii;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< RETURN >*/
return 0;
/* End of SGERQ2 */
/*< END >*/
} /* sgerq2_ */
#ifdef __cplusplus
}
#endif
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