/* stzrqf.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"
/* Table of constant values */
static integer c__1 = 1;
static real c_b8 = 1.f;
/* Subroutine */ int stzrqf_(integer *m, integer *n, real *a, integer *lda,
real *tau, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
real r__1;
/* Local variables */
integer i__, k, m1;
extern /* Subroutine */ int sger_(integer *, integer *, real *, real *,
integer *, real *, integer *, real *, integer *), sgemv_(char *,
integer *, integer *, real *, real *, integer *, real *, integer *
, real *, real *, integer *), scopy_(integer *, real *,
integer *, real *, integer *), saxpy_(integer *, real *, real *,
integer *, real *, integer *), xerbla_(char *, integer *),
slarfp_(integer *, real *, real *, integer *, real *);
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine STZRZF. */
/* STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A */
/* to upper triangular form by means of orthogonal transformations. */
/* The upper trapezoidal matrix A is factored as */
/* A = ( R 0 ) * Z, */
/* where Z is an N-by-N orthogonal matrix and R is an M-by-M upper */
/* triangular matrix. */
/* 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 >= M. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the leading M-by-N upper trapezoidal part of the */
/* array A must contain the matrix to be factorized. */
/* On exit, the leading M-by-M upper triangular part of A */
/* contains the upper triangular matrix R, and elements M+1 to */
/* N of the first M rows of A, with the array TAU, represent the */
/* orthogonal matrix Z as a product of M elementary reflectors. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* TAU (output) REAL array, dimension (M) */
/* The scalar factors of the elementary reflectors. */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* Further Details */
/* =============== */
/* The factorization is obtained by Householder's method. The kth */
/* transformation matrix, Z( k ), which is used to introduce zeros into */
/* the ( m - k + 1 )th row of A, is given in the form */
/* Z( k ) = ( I 0 ), */
/* ( 0 T( k ) ) */
/* where */
/* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ), */
/* ( 0 ) */
/* ( z( k ) ) */
/* tau is a scalar and z( k ) is an ( n - m ) element vector. */
/* tau and z( k ) are chosen to annihilate the elements of the kth row */
/* of X. */
/* The scalar tau is returned in the kth element of TAU and the vector */
/* u( k ) in the kth row of A, such that the elements of z( k ) are */
/* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in */
/* the upper triangular part of A. */
/* Z is given by */
/* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
/* Function Body */
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < *m) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("STZRQF", &i__1);
return 0;
}
/* Perform the factorization. */
if (*m == 0) {
return 0;
}
if (*m == *n) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tau[i__] = 0.f;
/* L10: */
}
} else {
/* Computing MIN */
i__1 = *m + 1;
m1 = min(i__1,*n);
for (k = *m; k >= 1; --k) {
/* Use a Householder reflection to zero the kth row of A. */
/* First set up the reflection. */
i__1 = *n - *m + 1;
slarfp_(&i__1, &a[k + k * a_dim1], &a[k + m1 * a_dim1], lda, &tau[
k]);
if (tau[k] != 0.f && k > 1) {
/* We now perform the operation A := A*P( k ). */
/* Use the first ( k - 1 ) elements of TAU to store a( k ), */
/* where a( k ) consists of the first ( k - 1 ) elements of */
/* the kth column of A. Also let B denote the first */
/* ( k - 1 ) rows of the last ( n - m ) columns of A. */
i__1 = k - 1;
scopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &tau[1], &c__1);
/* Form w = a( k ) + B*z( k ) in TAU. */
i__1 = k - 1;
i__2 = *n - *m;
sgemv_("No transpose", &i__1, &i__2, &c_b8, &a[m1 * a_dim1 +
1], lda, &a[k + m1 * a_dim1], lda, &c_b8, &tau[1], &
c__1);
/* Now form a( k ) := a( k ) - tau*w */
/* and B := B - tau*w*z( k )'. */
i__1 = k - 1;
r__1 = -tau[k];
saxpy_(&i__1, &r__1, &tau[1], &c__1, &a[k * a_dim1 + 1], &
c__1);
i__1 = k - 1;
i__2 = *n - *m;
r__1 = -tau[k];
sger_(&i__1, &i__2, &r__1, &tau[1], &c__1, &a[k + m1 * a_dim1]
, lda, &a[m1 * a_dim1 + 1], lda);
}
/* L20: */
}
}
return 0;
/* End of STZRQF */
} /* stzrqf_ */
