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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
*
*/
#include <math.h>
#include "Cnames.h"
#include "scomplex.h"
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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