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references/igraph-1.0.1/vendor/lapack/dlacn2.c
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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"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b11 = 1.;
/* > \brief \b DLACN2 estimates the 1-norm of a square matrix, using reverse communication for evaluating matr
ix-vector products.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLACN2 + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlacn2.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlacn2.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlacn2.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLACN2( N, V, X, ISGN, EST, KASE, ISAVE )
INTEGER KASE, N
DOUBLE PRECISION EST
INTEGER ISGN( * ), ISAVE( 3 )
DOUBLE PRECISION V( * ), X( * )
> \par Purpose:
=============
>
> \verbatim
>
> DLACN2 estimates the 1-norm of a square, real matrix A.
> Reverse communication is used for evaluating matrix-vector products.
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix. N >= 1.
> \endverbatim
>
> \param[out] V
> \verbatim
> V is DOUBLE PRECISION array, dimension (N)
> On the final return, V = A*W, where EST = norm(V)/norm(W)
> (W is not returned).
> \endverbatim
>
> \param[in,out] X
> \verbatim
> X is DOUBLE PRECISION array, dimension (N)
> On an intermediate return, X should be overwritten by
> A * X, if KASE=1,
> A**T * X, if KASE=2,
> and DLACN2 must be re-called with all the other parameters
> unchanged.
> \endverbatim
>
> \param[out] ISGN
> \verbatim
> ISGN is INTEGER array, dimension (N)
> \endverbatim
>
> \param[in,out] EST
> \verbatim
> EST is DOUBLE PRECISION
> On entry with KASE = 1 or 2 and ISAVE(1) = 3, EST should be
> unchanged from the previous call to DLACN2.
> On exit, EST is an estimate (a lower bound) for norm(A).
> \endverbatim
>
> \param[in,out] KASE
> \verbatim
> KASE is INTEGER
> On the initial call to DLACN2, KASE should be 0.
> On an intermediate return, KASE will be 1 or 2, indicating
> whether X should be overwritten by A * X or A**T * X.
> On the final return from DLACN2, KASE will again be 0.
> \endverbatim
>
> \param[in,out] ISAVE
> \verbatim
> ISAVE is INTEGER array, dimension (3)
> ISAVE is used to save variables between calls to DLACN2
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup doubleOTHERauxiliary
> \par Further Details:
=====================
>
> \verbatim
>
> Originally named SONEST, dated March 16, 1988.
>
> This is a thread safe version of DLACON, which uses the array ISAVE
> in place of a SAVE statement, as follows:
>
> DLACON DLACN2
> JUMP ISAVE(1)
> J ISAVE(2)
> ITER ISAVE(3)
> \endverbatim
> \par Contributors:
==================
>
> Nick Higham, University of Manchester
> \par References:
================
>
> N.J. Higham, "FORTRAN codes for estimating the one-norm of
> a real or complex matrix, with applications to condition estimation",
> ACM Trans. Math. Soft., vol. 14, no. 4, pp. 381-396, December 1988.
>
=====================================================================
Subroutine */ int igraphdlacn2_(integer *n, doublereal *v, doublereal *x,
integer *isgn, doublereal *est, integer *kase, integer *isave)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Builtin functions */
double d_sign(doublereal *, doublereal *);
integer i_dnnt(doublereal *);
/* Local variables */
integer i__;
doublereal temp;
extern doublereal igraphdasum_(integer *, doublereal *, integer *);
integer jlast;
extern /* Subroutine */ int igraphdcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
extern integer igraphidamax_(integer *, doublereal *, integer *);
doublereal altsgn, estold;
/* -- 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 */
--isave;
--isgn;
--x;
--v;
/* Function Body */
if (*kase == 0) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
x[i__] = 1. / (doublereal) (*n);
/* L10: */
}
*kase = 1;
isave[1] = 1;
return 0;
}
switch (isave[1]) {
case 1: goto L20;
case 2: goto L40;
case 3: goto L70;
case 4: goto L110;
case 5: goto L140;
}
/* ................ ENTRY (ISAVE( 1 ) = 1)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */
L20:
if (*n == 1) {
v[1] = x[1];
*est = abs(v[1]);
/* ... QUIT */
goto L150;
}
*est = igraphdasum_(n, &x[1], &c__1);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
x[i__] = d_sign(&c_b11, &x[i__]);
isgn[i__] = i_dnnt(&x[i__]);
/* L30: */
}
*kase = 2;
isave[1] = 2;
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 2)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L40:
isave[2] = igraphidamax_(n, &x[1], &c__1);
isave[3] = 2;
/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */
L50:
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
x[i__] = 0.;
/* L60: */
}
x[isave[2]] = 1.;
*kase = 1;
isave[1] = 3;
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 3)
X HAS BEEN OVERWRITTEN BY A*X. */
L70:
igraphdcopy_(n, &x[1], &c__1, &v[1], &c__1);
estold = *est;
*est = igraphdasum_(n, &v[1], &c__1);
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
d__1 = d_sign(&c_b11, &x[i__]);
if (i_dnnt(&d__1) != isgn[i__]) {
goto L90;
}
/* L80: */
}
/* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */
goto L120;
L90:
/* TEST FOR CYCLING. */
if (*est <= estold) {
goto L120;
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
x[i__] = d_sign(&c_b11, &x[i__]);
isgn[i__] = i_dnnt(&x[i__]);
/* L100: */
}
*kase = 2;
isave[1] = 4;
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 4)
X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L110:
jlast = isave[2];
isave[2] = igraphidamax_(n, &x[1], &c__1);
if (x[jlast] != (d__1 = x[isave[2]], abs(d__1)) && isave[3] < 5) {
++isave[3];
goto L50;
}
/* ITERATION COMPLETE. FINAL STAGE. */
L120:
altsgn = 1.;
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
x[i__] = altsgn * ((doublereal) (i__ - 1) / (doublereal) (*n - 1) +
1.);
altsgn = -altsgn;
/* L130: */
}
*kase = 1;
isave[1] = 5;
return 0;
/* ................ ENTRY (ISAVE( 1 ) = 5)
X HAS BEEN OVERWRITTEN BY A*X. */
L140:
temp = igraphdasum_(n, &x[1], &c__1) / (doublereal) (*n * 3) * 2.;
if (temp > *est) {
igraphdcopy_(n, &x[1], &c__1, &v[1], &c__1);
*est = temp;
}
L150:
*kase = 0;
return 0;
/* End of DLACN2 */
} /* igraphdlacn2_ */