Add graph references

2026-06-28 13:49:01 +01:00
parent 0a9807e448
commit a11edf0c53
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+/*  -- translated by f2c (version 20240504).
+   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"
+
+/* > \brief \b DLARFG generates an elementary reflector (Householder matrix).   
+
+    =========== DOCUMENTATION ===========   
+
+   Online html documentation available at   
+              http://www.netlib.org/lapack/explore-html/   
+
+   > \htmlonly   
+   > Download DLARFG + dependencies   
+   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.
+f">   
+   > [TGZ]</a>   
+   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.
+f">   
+   > [ZIP]</a>   
+   > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.
+f">   
+   > [TXT]</a>   
+   > \endhtmlonly   
+
+    Definition:   
+    ===========   
+
+         SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )   
+
+         INTEGER            INCX, N   
+         DOUBLE PRECISION   ALPHA, TAU   
+         DOUBLE PRECISION   X( * )   
+
+
+   > \par Purpose:   
+    =============   
+   >   
+   > \verbatim   
+   >   
+   > DLARFG generates a real elementary reflector H of order n, such   
+   > that   
+   >   
+   >       H * ( alpha ) = ( beta ),   H**T * 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**T ) ,   
+   >                     ( 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.   
+   > \endverbatim   
+
+    Arguments:   
+    ==========   
+
+   > \param[in] N   
+   > \verbatim   
+   >          N is INTEGER   
+   >          The order of the elementary reflector.   
+   > \endverbatim   
+   >   
+   > \param[in,out] ALPHA   
+   > \verbatim   
+   >          ALPHA is DOUBLE PRECISION   
+   >          On entry, the value alpha.   
+   >          On exit, it is overwritten with the value beta.   
+   > \endverbatim   
+   >   
+   > \param[in,out] X   
+   > \verbatim   
+   >          X is DOUBLE PRECISION array, dimension   
+   >                         (1+(N-2)*abs(INCX))   
+   >          On entry, the vector x.   
+   >          On exit, it is overwritten with the vector v.   
+   > \endverbatim   
+   >   
+   > \param[in] INCX   
+   > \verbatim   
+   >          INCX is INTEGER   
+   >          The increment between elements of X. INCX > 0.   
+   > \endverbatim   
+   >   
+   > \param[out] TAU   
+   > \verbatim   
+   >          TAU is DOUBLE PRECISION   
+   >          The value tau.   
+   > \endverbatim   
+
+    Authors:   
+    ========   
+
+   > \author Univ. of Tennessee   
+   > \author Univ. of California Berkeley   
+   > \author Univ. of Colorado Denver   
+   > \author NAG Ltd.   
+
+   > \date September 2012   
+
+   > \ingroup doubleOTHERauxiliary   
+
+    =====================================================================   
+   Subroutine */ int igraphdlarfg_(integer *n, doublereal *alpha, doublereal *x, 
+	integer *incx, doublereal *tau)
+{
+    /* System generated locals */
+    integer i__1;
+    doublereal d__1;
+
+    /* Builtin functions */
+    double d_sign(doublereal *, doublereal *);
+
+    /* Local variables */
+    integer j, knt;
+    doublereal beta;
+    extern doublereal igraphdnrm2_(integer *, doublereal *, integer *);
+    extern /* Subroutine */ int igraphdscal_(integer *, doublereal *, doublereal *, 
+	    integer *);
+    doublereal xnorm;
+    extern doublereal igraphdlapy2_(doublereal *, doublereal *), igraphdlamch_(char *);
+    doublereal safmin, rsafmn;
+
+
+/*  -- LAPACK auxiliary routine (version 3.4.2) --   
+    -- LAPACK is a software package provided by Univ. of Tennessee,    --   
+    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--   
+       September 2012   
+
+
+    =====================================================================   
+
+
+       Parameter adjustments */
+    --x;
+
+    /* Function Body */
+    if (*n <= 1) {
+	*tau = 0.;
+	return 0;
+    }
+
+    i__1 = *n - 1;
+    xnorm = igraphdnrm2_(&i__1, &x[1], incx);
+
+    if (xnorm == 0.) {
+
+/*        H  =  I */
+
+	*tau = 0.;
+    } else {
+
+/*        general case */
+
+	d__1 = igraphdlapy2_(alpha, &xnorm);
+	beta = -d_sign(&d__1, alpha);
+	safmin = igraphdlamch_("S") / igraphdlamch_("E");
+	knt = 0;
+	if (abs(beta) < safmin) {
+
+/*           XNORM, BETA may be inaccurate; scale X and recompute them */
+
+	    rsafmn = 1. / safmin;
+L10:
+	    ++knt;
+	    i__1 = *n - 1;
+	    igraphdscal_(&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 = igraphdnrm2_(&i__1, &x[1], incx);
+	    d__1 = igraphdlapy2_(alpha, &xnorm);
+	    beta = -d_sign(&d__1, alpha);
+	}
+	*tau = (beta - *alpha) / beta;
+	i__1 = *n - 1;
+	d__1 = 1. / (*alpha - beta);
+	igraphdscal_(&i__1, &d__1, &x[1], incx);
+
+/*        If ALPHA is subnormal, it may lose relative accuracy */
+
+	i__1 = knt;
+	for (j = 1; j <= i__1; ++j) {
+	    beta *= safmin;
+/* L20: */
+	}
+	*alpha = beta;
+    }
+
+    return 0;
+
+/*     End of DLARFG */
+
+} /* igraphdlarfg_ */
+