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/*! \file
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
at the top-level directory.
*/
/*! @file zlacon2.c
* \brief Estimates the 1-norm
*
* <pre>
* -- SuperLU routine (version 5.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* July 25, 2015
* </pre>
*/
#include <math.h>
#include "slu_Cnames.h"
#include "slu_dcomplex.h"
/*! \brief
*
* <pre>
* Purpose
* =======
*
* ZLACON2 estimates the 1-norm of a square matrix A.
* Reverse communication is used for evaluating matrix-vector products.
*
* This is a thread safe version of ZLACON, which uses the array ISAVE
* in place of a STATIC variables, as follows:
*
* ZLACON ZLACON2
* jump isave[0]
* j isave[1]
* iter isave[2]
*
*
* Arguments
* =========
*
* N (input) INT
* The order of the matrix. N >= 1.
*
* V (workspace) DOUBLE 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) DOUBLE 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 ZLACON must be re-called with all the other parameters
* unchanged.
*
*
* EST (output) DOUBLE PRECISION
* An estimate (a lower bound) for norm(A).
*
* KASE (input/output) INT
* On the initial call to ZLACON, 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 ZLACON, KASE will again be 0.
*
* isave (input/output) int [3]
* ISAVE is INTEGER array, dimension (3)
* ISAVE is used to save variables between calls to ZLACON2
*
* 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
zlacon2_(int *n, doublecomplex *v, doublecomplex *x, double *est, int *kase, int isave[3])
{
/* Table of constant values */
int c__1 = 1;
doublecomplex zero = {0.0, 0.0};
doublecomplex one = {1.0, 0.0};
/* System generated locals */
double d__1;
/* Local variables */
int jlast;
double altsgn, estold;
int i;
double temp;
double safmin;
extern double dmach(char *);
extern int izmax1_slu(int *, doublecomplex *, int *);
extern double dzsum1_slu(int *, doublecomplex *, int *);
safmin = dmach("Safe minimum"); /* lamch_("Safe minimum"); */
if ( *kase == 0 ) {
for (i = 0; i < *n; ++i) {
x[i].r = 1. / (double) (*n);
x[i].i = 0.;
}
*kase = 1;
isave[0] = 1; /* jump = 1; */
return 0;
}
switch (isave[0]) {
case 1: goto L20;
case 2: goto L40;
case 3: goto L70;
case 4: goto L110;
case 5: goto L140;
}
/* ................ ENTRY (isave[0] = 1)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY A*X. */
L20:
if (*n == 1) {
v[0] = x[0];
*est = z_abs(&v[0]);
/* ... QUIT */
goto L150;
}
*est = dzsum1_slu(n, x, &c__1);
for (i = 0; i < *n; ++i) {
d__1 = z_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;
isave[0] = 2; /* jump = 2; */
return 0;
/* ................ ENTRY (isave[0] = 2)
FIRST ITERATION. X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L40:
isave[1] = izmax1_slu(n, &x[0], &c__1); /* j */
--isave[1]; /* --j; */
isave[2] = 2; /* iter = 2; */
/* MAIN LOOP - ITERATIONS 2,3,...,ITMAX. */
L50:
for (i = 0; i < *n; ++i) x[i] = zero;
x[isave[1]] = one;
*kase = 1;
isave[0] = 3; /* jump = 3; */
return 0;
/* ................ ENTRY (isave[0] = 3)
X HAS BEEN OVERWRITTEN BY A*X. */
L70:
#ifdef _CRAY
CCOPY(n, x, &c__1, v, &c__1);
#else
zcopy_(n, x, &c__1, v, &c__1);
#endif
estold = *est;
*est = dzsum1_slu(n, v, &c__1);
L90:
/* TEST FOR CYCLING. */
if (*est <= estold) goto L120;
for (i = 0; i < *n; ++i) {
d__1 = z_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;
isave[0] = 4; /* jump = 4; */
return 0;
/* ................ ENTRY (isave[0] = 4)
X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X. */
L110:
jlast = isave[1]; /* j; */
isave[1] = izmax1_slu(n, &x[0], &c__1); /* j */
isave[1] = isave[1] - 1; /* --j; */
if (x[jlast].r != (d__1 = x[isave[1]].r, fabs(d__1)) && isave[2] < 5) {
isave[2] = isave[2] + 1; /* ++iter; */
goto L50;
}
/* ITERATION COMPLETE. FINAL STAGE. */
L120:
altsgn = 1.;
for (i = 1; i <= *n; ++i) {
x[i-1].r = altsgn * ((double)(i - 1) / (double)(*n - 1) + 1.);
x[i-1].i = 0.;
altsgn = -altsgn;
}
*kase = 1;
isave[0] = 5; /* jump = 5; */
return 0;
/* ................ ENTRY (isave[0] = 5)
X HAS BEEN OVERWRITTEN BY A*X. */
L140:
temp = dzsum1_slu(n, x, &c__1) / (double)(*n * 3) * 2.;
if (temp > *est) {
#ifdef _CRAY
CCOPY(n, &x[0], &c__1, &v[0], &c__1);
#else
zcopy_(n, &x[0], &c__1, &v[0], &c__1);
#endif
*est = temp;
}
L150:
*kase = 0;
return 0;
} /* zlacon_ */
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