/*! @file dgsequ.c

 * \brief Computes row and column scalings

 *

 * 

 * -- 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

 * 

 */

/*

 * File name:	dgsequ.c

 * History:     Modified from LAPACK routine DGEEQU

 */

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

#include "slu_ddefs.h"

/*! \brief

 *

 * 

 * 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   

 *

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

 * 

 */

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 */