/*! @file dgsequ.c
 * \brief Computes row and column scalings
 *
 * <pre>
 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * November 15, 1997
 *
 * Modified from LAPACK routine DGEEQU
 * </pre>
 */
/*
 * File name:	dgsequ.c
 * History:     Modified from LAPACK routine DGEEQU
 */
#include <math.h>
#include "slu_ddefs.h"



/*! \brief
 *
 * <pre>
 * Purpose   
 *   =======   
 *
 *   DGSEQU computes row and column scalings intended to equilibrate an   
 *   M-by-N sparse matrix A and reduce its condition number. R returns the row
 *   scale factors and C the column scale factors, chosen to try to make   
 *   the largest element in each row and column of the matrix B with   
 *   elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.   
 *
 *   R(i) and C(j) are restricted to be between SMLNUM = smallest safe   
 *   number and BIGNUM = largest safe number.  Use of these scaling   
 *   factors is not guaranteed to reduce the condition number of A but   
 *   works well in practice.   
 *
 *   See supermatrix.h for the definition of 'SuperMatrix' structure.
 *
 *   Arguments   
 *   =========   
 *
 *   A       (input) SuperMatrix*
 *           The matrix of dimension (A->nrow, A->ncol) whose equilibration
 *           factors are to be computed. The type of A can be:
 *           Stype = SLU_NC; Dtype = SLU_D; Mtype = SLU_GE.
 *	    
 *   R       (output) double*, size A->nrow
 *           If INFO = 0 or INFO > M, R contains the row scale factors   
 *           for A.
 *	    
 *   C       (output) double*, size A->ncol
 *           If INFO = 0,  C contains the column scale factors for A.
 *	    
 *   ROWCND  (output) double*
 *           If INFO = 0 or INFO > M, ROWCND contains the ratio of the   
 *           smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and   
 *           AMAX is neither too large nor too small, it is not worth   
 *           scaling by R.
 *	    
 *   COLCND  (output) double*
 *           If INFO = 0, COLCND contains the ratio of the smallest   
 *           C(i) to the largest C(i).  If COLCND >= 0.1, it is not   
 *           worth scaling by C.
 *	    
 *   AMAX    (output) double*
 *           Absolute value of largest matrix element.  If AMAX is very   
 *           close to overflow or very close to underflow, the matrix   
 *           should be scaled.
 *	    
 *   INFO    (output) int*
 *           = 0:  successful exit   
 *           < 0:  if INFO = -i, the i-th argument had an illegal value   
 *           > 0:  if INFO = i,  and i is   
 *                 <= A->nrow:  the i-th row of A is exactly zero   
 *                 >  A->ncol:  the (i-M)-th column of A is exactly zero   
 *
 *   ===================================================================== 
 * </pre>
 */
void
dgsequ(SuperMatrix *A, double *r, double *c, double *rowcnd,
	double *colcnd, double *amax, int *info)
{


    /* Local variables */
    NCformat *Astore;
    double   *Aval;
    int i, j, irow;
    double rcmin, rcmax;
    double bignum, smlnum;
    extern double dlamch_(char *);
    
    /* Test the input parameters. */
    *info = 0;
    if ( A->nrow < 0 || A->ncol < 0 ||
	 A->Stype != SLU_NC || A->Dtype != SLU_D || A->Mtype != SLU_GE )
	*info = -1;
    if (*info != 0) {
	i = -(*info);
	xerbla_("dgsequ", &i);
	return;
    }

    /* Quick return if possible */
    if ( A->nrow == 0 || A->ncol == 0 ) {
	*rowcnd = 1.;
	*colcnd = 1.;
	*amax = 0.;
	return;
    }

    Astore = A->Store;
    Aval = Astore->nzval;
    
    /* Get machine constants. */
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;

    /* Compute row scale factors. */
    for (i = 0; i < A->nrow; ++i) r[i] = 0.;

    /* Find the maximum element in each row. */
    for (j = 0; j < A->ncol; ++j)
	for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
	    irow = Astore->rowind[i];
	    r[irow] = SUPERLU_MAX( r[irow], fabs(Aval[i]) );
	}

    /* Find the maximum and minimum scale factors. */
    rcmin = bignum;
    rcmax = 0.;
    for (i = 0; i < A->nrow; ++i) {
	rcmax = SUPERLU_MAX(rcmax, r[i]);
	rcmin = SUPERLU_MIN(rcmin, r[i]);
    }
    *amax = rcmax;

    if (rcmin == 0.) {
	/* Find the first zero scale factor and return an error code. */
	for (i = 0; i < A->nrow; ++i)
	    if (r[i] == 0.) {
		*info = i + 1;
		return;
	    }
    } else {
	/* Invert the scale factors. */
	for (i = 0; i < A->nrow; ++i)
	    r[i] = 1. / SUPERLU_MIN( SUPERLU_MAX( r[i], smlnum ), bignum );
	/* Compute ROWCND = min(R(I)) / max(R(I)) */
	*rowcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
    }

    /* Compute column scale factors */
    for (j = 0; j < A->ncol; ++j) c[j] = 0.;

    /* Find the maximum element in each column, assuming the row
       scalings computed above. */
    for (j = 0; j < A->ncol; ++j)
	for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
	    irow = Astore->rowind[i];
	    c[j] = SUPERLU_MAX( c[j], fabs(Aval[i]) * r[irow] );
	}

    /* Find the maximum and minimum scale factors. */
    rcmin = bignum;
    rcmax = 0.;
    for (j = 0; j < A->ncol; ++j) {
	rcmax = SUPERLU_MAX(rcmax, c[j]);
	rcmin = SUPERLU_MIN(rcmin, c[j]);
    }

    if (rcmin == 0.) {
	/* Find the first zero scale factor and return an error code. */
	for (j = 0; j < A->ncol; ++j)
	    if ( c[j] == 0. ) {
		*info = A->nrow + j + 1;
		return;
	    }
    } else {
	/* Invert the scale factors. */
	for (j = 0; j < A->ncol; ++j)
	    c[j] = 1. / SUPERLU_MIN( SUPERLU_MAX( c[j], smlnum ), bignum);
	/* Compute COLCND = min(C(J)) / max(C(J)) */
	*colcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
    }

    return;

} /* dgsequ */