155 lines
3.7 KiB
C
155 lines
3.7 KiB
C
#include "blaswrap.h"
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#ifdef _cpluscplus
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extern "C" {
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#endif
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#include "f2c.h"
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/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x,
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integer *incx, doublereal *tau)
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{
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/* -- LAPACK auxiliary routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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September 30, 1994
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Purpose
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=======
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DLARFG generates a real elementary reflector H of order n, such
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that
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H * ( alpha ) = ( beta ), H' * H = I.
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( x ) ( 0 )
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where alpha and beta are scalars, and x is an (n-1)-element real
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vector. H is represented in the form
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H = I - tau * ( 1 ) * ( 1 v' ) ,
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( v )
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where tau is a real scalar and v is a real (n-1)-element
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vector.
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If the elements of x are all zero, then tau = 0 and H is taken to be
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the unit matrix.
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Otherwise 1 <= tau <= 2.
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Arguments
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=========
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N (input) INTEGER
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The order of the elementary reflector.
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ALPHA (input/output) DOUBLE PRECISION
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On entry, the value alpha.
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On exit, it is overwritten with the value beta.
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X (input/output) DOUBLE PRECISION array, dimension
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(1+(N-2)*abs(INCX))
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On entry, the vector x.
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On exit, it is overwritten with the vector v.
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INCX (input) INTEGER
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The increment between elements of X. INCX > 0.
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TAU (output) DOUBLE PRECISION
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The value tau.
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=====================================================================
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Parameter adjustments */
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/* System generated locals */
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integer i__1;
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doublereal d__1;
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/* Builtin functions */
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double d_sign(doublereal *, doublereal *);
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/* Local variables */
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static doublereal beta;
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extern doublereal dnrm2_(integer *, doublereal *, integer *);
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static integer j;
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
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integer *);
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static doublereal xnorm;
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extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
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static doublereal safmin, rsafmn;
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static integer knt;
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--x;
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/* Function Body */
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if (*n <= 1) {
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*tau = 0.;
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return 0;
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}
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i__1 = *n - 1;
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xnorm = dnrm2_(&i__1, &x[1], incx);
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if (xnorm == 0.) {
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/* H = I */
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*tau = 0.;
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} else {
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/* general case */
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d__1 = dlapy2_(alpha, &xnorm);
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beta = -d_sign(&d__1, alpha);
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safmin = dlamch_("S") / dlamch_("E");
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if (abs(beta) < safmin) {
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/* XNORM, BETA may be inaccurate; scale X and recompute them */
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rsafmn = 1. / safmin;
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knt = 0;
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L10:
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++knt;
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i__1 = *n - 1;
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dscal_(&i__1, &rsafmn, &x[1], incx);
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beta *= rsafmn;
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*alpha *= rsafmn;
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if (abs(beta) < safmin) {
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goto L10;
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}
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/* New BETA is at most 1, at least SAFMIN */
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i__1 = *n - 1;
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xnorm = dnrm2_(&i__1, &x[1], incx);
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d__1 = dlapy2_(alpha, &xnorm);
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beta = -d_sign(&d__1, alpha);
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*tau = (beta - *alpha) / beta;
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i__1 = *n - 1;
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d__1 = 1. / (*alpha - beta);
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dscal_(&i__1, &d__1, &x[1], incx);
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/* If ALPHA is subnormal, it may lose relative accuracy */
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*alpha = beta;
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i__1 = knt;
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for (j = 1; j <= i__1; ++j) {
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*alpha *= safmin;
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/* L20: */
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}
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} else {
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*tau = (beta - *alpha) / beta;
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i__1 = *n - 1;
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d__1 = 1. / (*alpha - beta);
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dscal_(&i__1, &d__1, &x[1], incx);
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*alpha = beta;
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}
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}
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return 0;
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/* End of DLARFG */
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} /* dlarfg_ */
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#ifdef _cpluscplus
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}
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#endif
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