hypre/lapack/dlarfg.c

178 lines
4.9 KiB
C

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#include "../blas/hypre_blas.h"
#include "hypre_lapack.h"
#include "f2c.h"
/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x,
integer *incx, doublereal *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;
doublereal d__1;
/* Builtin functions */
double d_sign(doublereal *, doublereal *);
/* Local variables */
static doublereal beta;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static integer j;
extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
integer *);
static doublereal xnorm;
extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
static doublereal safmin, rsafmn;
static integer knt;
--x;
/* Function Body */
if (*n <= 1) {
*tau = 0.;
return 0;
}
i__1 = *n - 1;
xnorm = dnrm2_(&i__1, &x[1], incx);
if (xnorm == 0.) {
/* H = I */
*tau = 0.;
} else {
/* general case */
d__1 = dlapy2_(alpha, &xnorm);
beta = -d_sign(&d__1, alpha);
safmin = dlamch_("S") / dlamch_("E");
if (abs(beta) < safmin) {
/* XNORM, BETA may be inaccurate; scale X and recompute them */
rsafmn = 1. / safmin;
knt = 0;
L10:
++knt;
i__1 = *n - 1;
dscal_(&i__1, &rsafmn, &x[1], incx);
beta *= rsafmn;
*alpha *= rsafmn;
if (abs(beta) < safmin) {
goto L10;
}
/* New BETA is at most 1, at least SAFMIN */
i__1 = *n - 1;
xnorm = dnrm2_(&i__1, &x[1], incx);
d__1 = dlapy2_(alpha, &xnorm);
beta = -d_sign(&d__1, alpha);
*tau = (beta - *alpha) / beta;
i__1 = *n - 1;
d__1 = 1. / (*alpha - beta);
dscal_(&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);
dscal_(&i__1, &d__1, &x[1], incx);
*alpha = beta;
}
}
return 0;
/* End of DLARFG */
} /* dlarfg_ */