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/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* This file belongs to the template_lapack part of the Ergo source
* code. The source files in the template_lapack directory are modified
* versions of files originally distributed as CLAPACK, see the
* Copyright/license notice in the file template_lapack/COPYING.
*/
#ifndef TEMPLATE_LAPACK_LARFG_HEADER
#define TEMPLATE_LAPACK_LARFG_HEADER
#include "template_lapack_lapy2.h"
template<class Treal>
int template_lapack_larfg(const integer *n, Treal *alpha, Treal *x,
const integer *incx, Treal *tau)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
DLARFG generates a real elementary reflector H of order n, such
that
H * ( alpha ) = ( beta ), H' * H = I.
( x ) ( 0 )
where alpha and beta are scalars, and x is an (n-1)-element real
vector. H is represented in the form
H = I - tau * ( 1 ) * ( 1 v' ) ,
( v )
where tau is a real scalar and v is a real (n-1)-element
vector.
If the elements of x are all zero, then tau = 0 and H is taken to be
the unit matrix.
Otherwise 1 <= tau <= 2.
Arguments
=========
N (input) INTEGER
The order of the elementary reflector.
ALPHA (input/output) DOUBLE PRECISION
On entry, the value alpha.
On exit, it is overwritten with the value beta.
X (input/output) DOUBLE PRECISION array, dimension
(1+(N-2)*abs(INCX))
On entry, the vector x.
On exit, it is overwritten with the vector v.
INCX (input) INTEGER
The increment between elements of X. INCX > 0.
TAU (output) DOUBLE PRECISION
The value tau.
=====================================================================
Parameter adjustments */
/* System generated locals */
integer i__1;
Treal d__1;
/* Local variables */
Treal beta;
integer j;
Treal xnorm;
Treal safmin, rsafmn;
integer knt;
--x;
/* Function Body */
if (*n <= 1) {
*tau = 0.;
return 0;
}
i__1 = *n - 1;
xnorm = template_blas_nrm2(&i__1, &x[1], incx);
if (xnorm == 0.) {
/* H = I */
*tau = 0.;
} else {
/* general case */
d__1 = template_lapack_lapy2(alpha, &xnorm);
beta = -template_lapack_d_sign(&d__1, alpha);
safmin = template_lapack_lamch("S", (Treal)0) / template_lapack_lamch("E", (Treal)0);
if (absMACRO(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
rsafmn = 1. / safmin;
knt = 0;
L10:
++knt;
i__1 = *n - 1;
template_blas_scal(&i__1, &rsafmn, &x[1], incx);
beta *= rsafmn;
*alpha *= rsafmn;
if (absMACRO(beta) < safmin) {
goto L10;
}
/* New BETA is at most 1, at least SAFMIN */
i__1 = *n - 1;
xnorm = template_blas_nrm2(&i__1, &x[1], incx);
d__1 = template_lapack_lapy2(alpha, &xnorm);
beta = -template_lapack_d_sign(&d__1, alpha);
*tau = (beta - *alpha) / beta;
i__1 = *n - 1;
d__1 = 1. / (*alpha - beta);
template_blas_scal(&i__1, &d__1, &x[1], incx);
/* If ALPHA is subnormal, it may lose relative accuracy */
*alpha = beta;
i__1 = knt;
for (j = 1; j <= i__1; ++j) {
*alpha *= safmin;
/* L20: */
}
} else {
*tau = (beta - *alpha) / beta;
i__1 = *n - 1;
d__1 = 1. / (*alpha - beta);
template_blas_scal(&i__1, &d__1, &x[1], incx);
*alpha = beta;
}
}
return 0;
/* End of DLARFG */
} /* dlarfg_ */
#endif
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