#include "slu_Cnames.h"
#include "slu_dcomplex.h"
/*! \brief
*
*
* 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.
* =====================================================================
*
*/
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_ */