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/* ../../../dependencies/lapack/src/dlatrz.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"
/* Subroutine */ int dlatrz_(integer *m, integer *n, integer *l, doublereal *
a, integer *lda, doublereal *tau, doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
/* Local variables */
static integer i__;
extern /* Subroutine */ int dlarz_(char *, integer *, integer *, integer *
, doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, ftnlen), dlarfg_(integer *, doublereal *,
doublereal *, integer *, doublereal *);
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* June 30, 1999 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix */
/* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means */
/* of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal */
/* matrix and, R and A1 are M-by-M upper triangular matrices. */
/* 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. */
/* L (input) INTEGER */
/* The number of columns of the matrix A containing the */
/* meaningful part of the Householder vectors. N-M >= L >= 0. */
/* A (input/output) DOUBLE PRECISION 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 N-L+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) DOUBLE PRECISION array, dimension (M) */
/* The scalar factors of the elementary reflectors. */
/* WORK (workspace) DOUBLE PRECISION array, dimension (M) */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA */
/* 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 l element vector. tau and z( k ) */
/* are chosen to annihilate the elements of the kth row of A2. */
/* The scalar tau is returned in the kth element of TAU and the vector */
/* u( k ) in the kth row of A2, such that the elements of z( k ) are */
/* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in */
/* the upper triangular part of A1. */
/* Z is given by */
/* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/* Quick return if possible */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--tau;
--work;
/* Function Body */
if (*m == 0) {
return 0;
} else if (*m == *n) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
tau[i__] = 0.;
/* L10: */
}
return 0;
}
for (i__ = *m; i__ >= 1; --i__) {
/* Generate elementary reflector H(i) to annihilate */
/* [ A(i,i) A(i,n-l+1:n) ] */
i__1 = *l + 1;
dlarfg_(&i__1, &a[i__ + i__ * a_dim1], &a[i__ + (*n - *l + 1) *
a_dim1], lda, &tau[i__]);
/* Apply H(i) to A(1:i-1,i:n) from the right */
i__1 = i__ - 1;
i__2 = *n - i__ + 1;
dlarz_("Right", &i__1, &i__2, l, &a[i__ + (*n - *l + 1) * a_dim1],
lda, &tau[i__], &a[i__ * a_dim1 + 1], lda, &work[1], (ftnlen)
5);
/* L20: */
}
return 0;
/* End of DLATRZ */
} /* dlatrz_ */
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