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/*
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
*
*/
/*
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)
All rights reserved.
The source code is distributed under BSD license, see the file License.txt
*/
/*
Copyright (c) 1997 by Xerox Corporation. All rights reserved.
THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
Permission is hereby granted to use or copy this program for any
purpose, provided the above notices are retained on all copies.
Permission to modify the code and to distribute modified code is
granted, provided the above notices are retained, and a notice that
the code was modified is included with the above copyright notice.
*/
#include <math.h>
#include "slu_Cnames.h"
#include "slu_scomplex.h"
extern void ccopy_();
int
clacon_(int *n, complex *v, complex *x, float *est, int *kase)
{
/*
Purpose
=======
CLACON estimates the 1-norm of a square matrix A.
Reverse communication is used for evaluating matrix-vector products.
Arguments
=========
N (input) INT
The order of the matrix. N >= 1.
V (workspace) COMPLEX PRECISION array, dimension (N)
On the final return, V = A*W, where EST = norm(V)/norm(W)
(W is not returned).
X (input/output) COMPLEX PRECISION array, dimension (N)
On an intermediate return, X should be overwritten by
A * X, if KASE=1,
A' * X, if KASE=2,
where A' is the conjugate transpose of A,
and CLACON must be re-called with all the other parameters
unchanged.
EST (output) FLOAT PRECISION
An estimate (a lower bound) for norm(A).
KASE (input/output) INT
On the initial call to CLACON, 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' * X.
On the final return from CLACON, KASE will again be 0.
Further Details
======= =======
Contributed by Nick Higham, University of Manchester.
Originally named CONEST, dated March 16, 1988.
Reference: 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.
=====================================================================
*/
/* Table of constant values */
int c__1 = 1;
complex zero = {0.0, 0.0};
complex one = {1.0, 0.0};
/* System generated locals */
float d__1;
/* Local variables */
static int iter;
static int jump, jlast;
static float altsgn, estold;
static int i, j;
float temp;
float safmin;
extern double slamch_(char *);
extern int icmax1_(int *, complex *, int *);
extern double scsum1_(int *, complex *, int *);
safmin = slamch_("Safe minimum");
if ( *kase == 0 ) {
for (i = 0; i < *n; ++i) {
x[i].r = 1. / (float) (*n);
x[i].i = 0.;
}
*kase = 1;
jump = 1;
return 0;
}
switch (jump) {
case 1: goto L20;
case 2: goto L40;
case 3: goto L70;
case 4: goto L110;
case 5: goto L140;
}
/* ................ ENTRY (JUMP = 1)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */
L20:
if (*n == 1) {
v[0] = x[0];
*est = c_abs(&v[0]);
/* ... QUIT */
goto L150;
}
*est = scsum1_(n, x, &c__1);
for (i = 0; i < *n; ++i) {
d__1 = c_abs(&x[i]);
if (d__1 > safmin) {
d__1 = 1 / d__1;
x[i].r *= d__1;
x[i].i *= d__1;
} else {
x[i] = one;
}
}
*kase = 2;
jump = 2;
return 0;
/* ................ ENTRY (JUMP = 2)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L40:
j = icmax1_(n, &x[0], &c__1);
--j;
iter = 2;
/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */
L50:
for (i = 0; i < *n; ++i) x[i] = zero;
x[j] = one;
*kase = 1;
jump = 3;
return 0;
/* ................ ENTRY (JUMP = 3)
X HAS BEEN OVERWRITTEN BY A*X. */
L70:
#ifdef _CRAY
CCOPY(n, x, &c__1, v, &c__1);
#else
ccopy_(n, x, &c__1, v, &c__1);
#endif
estold = *est;
*est = scsum1_(n, v, &c__1);
L90:
/* TEST FOR CYCLING. */
if (*est <= estold) goto L120;
for (i = 0; i < *n; ++i) {
d__1 = c_abs(&x[i]);
if (d__1 > safmin) {
d__1 = 1 / d__1;
x[i].r *= d__1;
x[i].i *= d__1;
} else {
x[i] = one;
}
}
*kase = 2;
jump = 4;
return 0;
/* ................ ENTRY (JUMP = 4)
X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X. */
L110:
jlast = j;
j = icmax1_(n, &x[0], &c__1);
--j;
if (x[jlast].r != (d__1 = x[j].r, fabs(d__1)) && iter < 5) {
++iter;
goto L50;
}
/* ITERATION COMPLETE. FINAL STAGE. */
L120:
altsgn = 1.;
for (i = 1; i <= *n; ++i) {
x[i-1].r = altsgn * ((float)(i - 1) / (float)(*n - 1) + 1.);
x[i-1].i = 0.;
altsgn = -altsgn;
}
*kase = 1;
jump = 5;
return 0;
/* ................ ENTRY (JUMP = 5)
X HAS BEEN OVERWRITTEN BY A*X. */
L140:
temp = scsum1_(n, x, &c__1) / (float)(*n * 3) * 2.;
if (temp > *est) {
#ifdef _CRAY
CCOPY(n, &x[0], &c__1, &v[0], &c__1);
#else
ccopy_(n, &x[0], &c__1, &v[0], &c__1);
#endif
*est = temp;
}
L150:
*kase = 0;
return 0;
} /* clacon_ */
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