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/*! @file dlacon.c
* \brief Estimates the 1-norm
*
* <pre>
* -- SuperLU routine (version 2.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* November 15, 1997
* </pre>
*/
#include <math.h>
#include "slu_Cnames.h"
/*! \brief
*
* <pre>
* Purpose
* =======
*
* DLACON 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) DOUBLE PRECISION array, dimension (N)
* On the final return, V = A*W, where EST = norm(V)/norm(W)
* (W is not returned).
*
* X (input/output) DOUBLE PRECISION array, dimension (N)
* On an intermediate return, X should be overwritten by
* A * X, if KASE=1,
* A' * X, if KASE=2,
* and DLACON must be re-called with all the other parameters
* unchanged.
*
* ISGN (workspace) INT array, dimension (N)
*
* EST (output) DOUBLE PRECISION
* An estimate (a lower bound) for norm(A).
*
* KASE (input/output) INT
* On the initial call to DLACON, 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 DLACON, 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.
* =====================================================================
* </pre>
*/
int
dlacon_(int *n, double *v, double *x, int *isgn, double *est, int *kase)
{
/* Table of constant values */
int c__1 = 1;
double zero = 0.0;
double one = 1.0;
/* Local variables */
static int iter;
static int jump, jlast;
static double altsgn, estold;
static int i, j;
double temp;
#ifdef _CRAY
extern int ISAMAX(int *, double *, int *);
extern double SASUM(int *, double *, int *);
extern int SCOPY(int *, double *, int *, double *, int *);
#else
extern int idamax_(int *, double *, int *);
extern double dasum_(int *, double *, int *);
extern int dcopy_(int *, double *, int *, double *, int *);
#endif
#define d_sign(a, b) (b >= 0 ? fabs(a) : -fabs(a)) /* Copy sign */
#define i_dnnt(a) \
( a>=0 ? floor(a+.5) : -floor(.5-a) ) /* Round to nearest integer */
if ( *kase == 0 ) {
for (i = 0; i < *n; ++i) {
x[i] = 1. / (double) (*n);
}
*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 = fabs(v[0]);
/* ... QUIT */
goto L150;
}
#ifdef _CRAY
*est = SASUM(n, x, &c__1);
#else
*est = dasum_(n, x, &c__1);
#endif
for (i = 0; i < *n; ++i) {
x[i] = d_sign(one, x[i]);
isgn[i] = i_dnnt(x[i]);
}
*kase = 2;
jump = 2;
return 0;
/* ................ ENTRY (JUMP = 2)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L40:
#ifdef _CRAY
j = ISAMAX(n, &x[0], &c__1);
#else
j = idamax_(n, &x[0], &c__1);
#endif
--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
SCOPY(n, x, &c__1, v, &c__1);
#else
dcopy_(n, x, &c__1, v, &c__1);
#endif
estold = *est;
#ifdef _CRAY
*est = SASUM(n, v, &c__1);
#else
*est = dasum_(n, v, &c__1);
#endif
for (i = 0; i < *n; ++i)
if (i_dnnt(d_sign(one, x[i])) != isgn[i])
goto L90;
/* REPEATED SIGN VECTOR DETECTED, HENCE ALGORITHM HAS CONVERGED. */
goto L120;
L90:
/* TEST FOR CYCLING. */
if (*est <= estold) goto L120;
for (i = 0; i < *n; ++i) {
x[i] = d_sign(one, x[i]);
isgn[i] = i_dnnt(x[i]);
}
*kase = 2;
jump = 4;
return 0;
/* ................ ENTRY (JUMP = 4)
X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X. */
L110:
jlast = j;
#ifdef _CRAY
j = ISAMAX(n, &x[0], &c__1);
#else
j = idamax_(n, &x[0], &c__1);
#endif
--j;
if (x[jlast] != fabs(x[j]) && iter < 5) {
++iter;
goto L50;
}
/* ITERATION COMPLETE. FINAL STAGE. */
L120:
altsgn = 1.;
for (i = 1; i <= *n; ++i) {
x[i-1] = altsgn * ((double)(i - 1) / (double)(*n - 1) + 1.);
altsgn = -altsgn;
}
*kase = 1;
jump = 5;
return 0;
/* ................ ENTRY (JUMP = 5)
X HAS BEEN OVERWRITTEN BY A*X. */
L140:
#ifdef _CRAY
temp = SASUM(n, x, &c__1) / (double)(*n * 3) * 2.;
#else
temp = dasum_(n, x, &c__1) / (double)(*n * 3) * 2.;
#endif
if (temp > *est) {
#ifdef _CRAY
SCOPY(n, &x[0], &c__1, &v[0], &c__1);
#else
dcopy_(n, &x[0], &c__1, &v[0], &c__1);
#endif
*est = temp;
}
L150:
*kase = 0;
return 0;
} /* dlacon_ */
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