/*! @file cgscon.c

 * \brief Estimates reciprocal of the condition number of a general matrix

 * 

 * 

 * -- SuperLU routine (version 3.0) --

 * Univ. of California Berkeley, Xerox Palo Alto Research Center,

 * and Lawrence Berkeley National Lab.

 * October 15, 2003

 *

 * Modified from lapack routines CGECON.

 *  

 */

/*

 * File name:	cgscon.c

 * History:     Modified from lapack routines CGECON.

 */

#include <math.h></math.h>

#include "slu_cdefs.h"

/*! \brief

 *

 * 

 *   Purpose   

 *   =======   

 *

 *   CGSCON estimates the reciprocal of the condition number of a general 

 *   real matrix A, in either the 1-norm or the infinity-norm, using   

 *   the LU factorization computed by CGETRF.   *

 *

 *   An estimate is obtained for norm(inv(A)), and the reciprocal of the   

 *   condition number is computed as   

 *      RCOND = 1 / ( norm(A) * norm(inv(A)) ).   

 *

 *   See supermatrix.h for the definition of 'SuperMatrix' structure.

 * 

 *   Arguments   

 *   =========   

 *

 *    NORM    (input) char*

 *            Specifies whether the 1-norm condition number or the   

 *            infinity-norm condition number is required:   

 *            = '1' or 'O':  1-norm;   

 *            = 'I':         Infinity-norm.

 *	    

 *    L       (input) SuperMatrix*

 *            The factor L from the factorization Pr*A*Pc=L*U as computed by

 *            cgstrf(). Use compressed row subscripts storage for supernodes,

 *            i.e., L has types: Stype = SLU_SC, Dtype = SLU_C, Mtype = SLU_TRLU.

 * 

 *    U       (input) SuperMatrix*

 *            The factor U from the factorization Pr*A*Pc=L*U as computed by

 *            cgstrf(). Use column-wise storage scheme, i.e., U has types:

 *            Stype = SLU_NC, Dtype = SLU_C, Mtype = SLU_TRU.

 *	    

 *    ANORM   (input) float

 *            If NORM = '1' or 'O', the 1-norm of the original matrix A.   

 *            If NORM = 'I', the infinity-norm of the original matrix A.

 *	    

 *    RCOND   (output) float*

 *           The reciprocal of the condition number of the matrix A,   

 *           computed as RCOND = 1/(norm(A) * norm(inv(A))).

 *	    

 *    INFO    (output) int*

 *           = 0:  successful exit   

 *           < 0:  if INFO = -i, the i-th argument had an illegal value   

 *

 *    ===================================================================== 

 * 

 */

void

cgscon(char *norm, SuperMatrix *L, SuperMatrix *U,

       float anorm, float *rcond, SuperLUStat_t *stat, int *info)

{

    /* Local variables */

    int    kase, kase1, onenrm, i;

    float ainvnm;

    complex *work;

    extern int crscl_(int *, complex *, complex *, int *);

    extern int clacon_(int *, complex *, complex *, float *, int *);

    /* Test the input parameters. */

    *info = 0;

    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");

    if (! onenrm && ! lsame_(norm, "I")) *info = -1;

    else if (L->nrow < 0 || L->nrow != L->ncol ||

             L->Stype != SLU_SC || L->Dtype != SLU_C || L->Mtype != SLU_TRLU)

	 *info = -2;

    else if (U->nrow < 0 || U->nrow != U->ncol ||

             U->Stype != SLU_NC || U->Dtype != SLU_C || U->Mtype != SLU_TRU) 

	*info = -3;

    if (*info != 0) {

	i = -(*info);

	xerbla_("cgscon", &i);

	return;

    }

    /* Quick return if possible */

    *rcond = 0.;

    if ( L->nrow == 0 || U->nrow == 0) {

	*rcond = 1.;

	return;

    }

    work = complexCalloc( 3*L->nrow );

    if ( !work )

	ABORT("Malloc fails for work arrays in cgscon.");

    /* Estimate the norm of inv(A). */

    ainvnm = 0.;

    if ( onenrm ) kase1 = 1;

    else kase1 = 2;

    kase = 0;

    do {

	clacon_(&L->nrow, &work[L->nrow], &work[0], &ainvnm, &kase);

	if (kase == 0) break;

	if (kase == kase1) {

	    /* Multiply by inv(L). */

	    sp_ctrsv("L", "No trans", "Unit", L, U, &work[0], stat, info);

	    /* Multiply by inv(U). */

	    sp_ctrsv("U", "No trans", "Non-unit", L, U, &work[0], stat, info);

	} else {

	    /* Multiply by inv(U'). */

	    sp_ctrsv("U", "Transpose", "Non-unit", L, U, &work[0], stat, info);

	    /* Multiply by inv(L'). */

	    sp_ctrsv("L", "Transpose", "Unit", L, U, &work[0], stat, info);

	}

    } while ( kase != 0 );

    /* Compute the estimate of the reciprocal condition number. */

    if (ainvnm != 0.) *rcond = (1. / ainvnm) / anorm;

    SUPERLU_FREE (work);

    return;

} /* cgscon */