/*! \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 clacon2.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 24, 2022
 * </pre>
 */
#include <math.h>
#include "slu_Cnames.h"
#include "slu_scomplex.h"

/*! \brief
 *
 * <pre>
 *   Purpose   
 *   =======   
 *
 *   CLACON2 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 CLACON, which uses the array ISAVE
 *   in place of a STATIC variables, as follows:
 *
 *     CLACON     CLACON2
 *      jump     isave[0]
 *      j        isave[1]
 *      iter     isave[2]
 *
 *
 *   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.   
 *
 *   isave  (input/output) int [3]
 *          ISAVE is INTEGER array, dimension (3)
 *          ISAVE is used to save variables between calls to CLACON2
 *
 *   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
clacon2_(int *n, complex *v, complex *x, float *est, int *kase, int isave[3])
{
    /* 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 */
    int jlast;
    float altsgn, estold;
    int i;
    float temp;
    float safmin;
    extern float smach(char *);
    extern int icmax1_slu(int *, complex *, int *);
    extern double scsum1_slu(int *, complex *, int *);
    extern int ccopy_(int *, complex *, int *, complex *, int *);

    safmin = smach("Safe minimum");
    if ( *kase == 0 ) {
	for (i = 0; i < *n; ++i) {
	    x[i].r = 1. / (float) (*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 = c_abs(&v[0]);
	/*        ... QUIT */
	goto L150;
    }
    *est = scsum1_slu(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;
    isave[0] = 2;  /* jump = 2; */
    return 0;

    /*     ................ ENTRY   (isave[0] == 2)   
	   FIRST ITERATION.  X HAS BEEN OVERWRITTEN BY TRANSPOSE(A)*X. */
L40:
    isave[1] = icmax1_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
    ccopy_(n, x, &c__1, v, &c__1);
#endif
    estold = *est;
    *est = scsum1_slu(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;
    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] = icmax1_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 * ((float)(i - 1) / (float)(*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 = scsum1_slu(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;

} /* clacon2_ */
