/*! \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.
*/

/*
 * -- SuperLU MT routine (version 3.0) --
 * Lawrence Berkeley National Lab, Univ. of California Berkeley,
 * and Xerox Palo Alto Research Center.
 * September 10, 2007
 *
 * History:     Modified from LAPACK routine ZGEEQU
 */
#include <math.h>
#include "slu_mt_zdefs.h"

void zgsequ(SuperMatrix* A, double* r, double* c, double* rowcnd, double* colcnd, double* amax, int_t* info) {
    /*
        Purpose
        =======

        zgsequ() 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_Z; 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_t*
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  if INFO = i,  and i is
                      <= M:  the i-th row of A is exactly zero
                      >  M:  the (i-M)-th column of A is exactly zero

        =====================================================================
    */

    /* Local variables */
    NCformat* Astore;
    doublecomplex* Aval;
    int_t j, irow;
    int i;
    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_Z || A->Mtype != SLU_GE)
        *info = -1;
    if(*info != 0) {
        i = -(*info);
        xerbla_("zgsequ", &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], z_abs1(&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], z_abs1(&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;

} /* zgsequ */
