/*! @file zlacon.c

 * \brief Estimates the 1-norm

 *

 * 

 * -- 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></math.h>

#include "slu_Cnames.h"

#include "slu_dcomplex.h"

/*! \brief

 *

 * 

 *   Purpose   

 *   =======   

 *

 *   ZLACON 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 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.   

 *

 *   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

zlacon_(int *n, doublecomplex *v, doublecomplex *x, double *est, int *kase)

{

    /* 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 */

    static int iter;

    static int jump, jlast;

    static double altsgn, estold;

    static int i, j;

    double temp;

    double safmin;

    extern double dlamch_(char *);

    extern int izmax1_(int *, doublecomplex *, int *);

    extern double dzsum1_(int *, doublecomplex *, int *);

    safmin = dlamch_("Safe minimum");

    if ( *kase == 0 ) {

	for (i = 0; i < *n; ++i) {

	    x[i].r = 1. / (double) (*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 = z_abs(&v[0]);

	/*        ... QUIT */

	goto L150;

    }

    *est = dzsum1_(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;

    jump = 2;

    return 0;

    /*     ................ ENTRY   (JUMP = 2)   

	   FIRST ITERATION.  X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */

L40:

    j = izmax1_(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

    zcopy_(n, x, &c__1, v, &c__1);

#endif

    estold = *est;

    *est = dzsum1_(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;

    jump = 4;

    return 0;

    /*     ................ ENTRY   (JUMP = 4)   

	   X HAS BEEN OVERWRITTEN BY TRANDPOSE(A)*X. */

L110:

    jlast = j;

    j = izmax1_(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 * ((double)(i - 1) / (double)(*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 = dzsum1_(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_ */