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/*! @file cgscon.c
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 * \brief Estimates reciprocal of the condition number of a general matrix
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 * 
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 * 
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 * -- SuperLU routine (version 3.0) --
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 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
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 * and Lawrence Berkeley National Lab.
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 * October 15, 2003
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 *
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 * Modified from lapack routines CGECON.
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 *  
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 */
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/*
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 * File name:	cgscon.c
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 * History:     Modified from lapack routines CGECON.
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 */
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#include <math.h></math.h>
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#include "slu_cdefs.h"
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/*! \brief
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 *
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 * 
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 *   Purpose   
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 *   =======   
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 *
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 *   CGSCON estimates the reciprocal of the condition number of a general 
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 *   real matrix A, in either the 1-norm or the infinity-norm, using   
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 *   the LU factorization computed by CGETRF.   *
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 *
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 *   An estimate is obtained for norm(inv(A)), and the reciprocal of the   
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 *   condition number is computed as   
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 *      RCOND = 1 / ( norm(A) * norm(inv(A)) ).   
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 *
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 *   See supermatrix.h for the definition of 'SuperMatrix' structure.
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 * 
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 *   Arguments   
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 *   =========   
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 *
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 *    NORM    (input) char*
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 *            Specifies whether the 1-norm condition number or the   
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 *            infinity-norm condition number is required:   
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 *            = '1' or 'O':  1-norm;   
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 *            = 'I':         Infinity-norm.
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 *	    
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 *    L       (input) SuperMatrix*
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 *            The factor L from the factorization Pr*A*Pc=L*U as computed by
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 *            cgstrf(). Use compressed row subscripts storage for supernodes,
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 *            i.e., L has types: Stype = SLU_SC, Dtype = SLU_C, Mtype = SLU_TRLU.
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 * 
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 *    U       (input) SuperMatrix*
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 *            The factor U from the factorization Pr*A*Pc=L*U as computed by
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 *            cgstrf(). Use column-wise storage scheme, i.e., U has types:
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 *            Stype = SLU_NC, Dtype = SLU_C, Mtype = SLU_TRU.
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 *	    
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 *    ANORM   (input) float
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 *            If NORM = '1' or 'O', the 1-norm of the original matrix A.   
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 *            If NORM = 'I', the infinity-norm of the original matrix A.
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 *	    
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 *    RCOND   (output) float*
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 *           The reciprocal of the condition number of the matrix A,   
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 *           computed as RCOND = 1/(norm(A) * norm(inv(A))).
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 *	    
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 *    INFO    (output) int*
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 *           = 0:  successful exit   
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 *           < 0:  if INFO = -i, the i-th argument had an illegal value   
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 *
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 *    ===================================================================== 
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 * 
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 */
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void
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cgscon(char *norm, SuperMatrix *L, SuperMatrix *U,
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       float anorm, float *rcond, SuperLUStat_t *stat, int *info)
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{
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    /* Local variables */
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    int    kase, kase1, onenrm, i;
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    float ainvnm;
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    complex *work;
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    extern int crscl_(int *, complex *, complex *, int *);
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    extern int clacon_(int *, complex *, complex *, float *, int *);
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    /* Test the input parameters. */
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    *info = 0;
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    onenrm = *(unsigned char *)norm == '1' || lsame_(norm, "O");
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    if (! onenrm && ! lsame_(norm, "I")) *info = -1;
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    else if (L->nrow < 0 || L->nrow != L->ncol ||
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             L->Stype != SLU_SC || L->Dtype != SLU_C || L->Mtype != SLU_TRLU)
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	 *info = -2;
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    else if (U->nrow < 0 || U->nrow != U->ncol ||
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             U->Stype != SLU_NC || U->Dtype != SLU_C || U->Mtype != SLU_TRU) 
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	*info = -3;
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    if (*info != 0) {
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	i = -(*info);
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	xerbla_("cgscon", &i);
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	return;
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    }
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    /* Quick return if possible */
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    *rcond = 0.;
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    if ( L->nrow == 0 || U->nrow == 0) {
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	*rcond = 1.;
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	return;
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    }
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    work = complexCalloc( 3*L->nrow );
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    if ( !work )
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	ABORT("Malloc fails for work arrays in cgscon.");
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    /* Estimate the norm of inv(A). */
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    ainvnm = 0.;
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    if ( onenrm ) kase1 = 1;
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    else kase1 = 2;
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    kase = 0;
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    do {
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	clacon_(&L->nrow, &work[L->nrow], &work[0], &ainvnm, &kase);
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	if (kase == 0) break;
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	if (kase == kase1) {
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	    /* Multiply by inv(L). */
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	    sp_ctrsv("L", "No trans", "Unit", L, U, &work[0], stat, info);
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	    /* Multiply by inv(U). */
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	    sp_ctrsv("U", "No trans", "Non-unit", L, U, &work[0], stat, info);
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	} else {
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	    /* Multiply by inv(U'). */
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	    sp_ctrsv("U", "Transpose", "Non-unit", L, U, &work[0], stat, info);
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	    /* Multiply by inv(L'). */
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	    sp_ctrsv("L", "Transpose", "Unit", L, U, &work[0], stat, info);
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	}
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    } while ( kase != 0 );
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    /* Compute the estimate of the reciprocal condition number. */
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    if (ainvnm != 0.) *rcond = (1. / ainvnm) / anorm;
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    SUPERLU_FREE (work);
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    return;
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} /* cgscon */
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