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/*************************************************************************
 *
 *  $RCSfile: gauss.hxx,v $
 *
 *  $Revision: 1.1 $
 *
 *  last change: $Author: thb $ $Date: 2003-03-06 18:57:49 $
 *
 *  The Contents of this file are made available subject to the terms of
 *  either of the following licenses
 *
 *         - GNU Lesser General Public License Version 2.1
 *         - Sun Industry Standards Source License Version 1.1
 *
 *  Sun Microsystems Inc., October, 2000
 *
 *  GNU Lesser General Public License Version 2.1
 *  =============================================
 *  Copyright 2000 by Sun Microsystems, Inc.
 *  901 San Antonio Road, Palo Alto, CA 94303, USA
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License version 2.1, as published by the Free Software Foundation.
 *
 *  This library is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public
 *  License along with this library; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston,
 *  MA  02111-1307  USA
 *
 *
 *  Sun Industry Standards Source License Version 1.1
 *  =================================================
 *  The contents of this file are subject to the Sun Industry Standards
 *  Source License Version 1.1 (the "License"); You may not use this file
 *  except in compliance with the License. You may obtain a copy of the
 *  License at http://www.openoffice.org/license.html.
 *
 *  Software provided under this License is provided on an "AS IS" basis,
 *  WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING,
 *  WITHOUT LIMITATION, WARRANTIES THAT THE SOFTWARE IS FREE OF DEFECTS,
 *  MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE, OR NON-INFRINGING.
 *  See the License for the specific provisions governing your rights and
 *  obligations concerning the Software.
 *
 *  The Initial Developer of the Original Code is: Sun Microsystems, Inc.
 *
 *  Copyright: 2000 by Sun Microsystems, Inc.
 *
 *  All Rights Reserved.
 *
 *  Contributor(s): _______________________________________
 *
 *
 ************************************************************************/

/** This method eliminates elements below main diagonal in the given
    matrix by gaussian elimination.

    @param matrix
    The matrix to operate on. Last column is the result vector (right
    hand side of the linear equation). After successful termination,
    the matrix is upper triangular. The matrix is expected to be in
    row major order.

    @param rows
    Number of rows in matrix

    @param cols
    Number of columns in matrix

    @param minPivot
    If the pivot element gets lesser than minPivot, this method fails,
    otherwise, elimination succeeds and true is returned.

    @return true, if elimination succeeded.
 */
template <class Matrix, typename BaseType>
bool eliminate(     Matrix&         matrix,
                    int             rows,
                    int             cols,
                    const BaseType& minPivot    )
{
    BaseType    temp;
    int         max, i, j, k;   /* *must* be signed, when looping like: j>=0 ! */

    /* eliminate below main diagonal */
    for(i=0; i<cols-1; ++i)
    {
        /* find best pivot */
        max = i;
        for(j=i+1; j<rows; ++j)
            if( fabs(matrix[ j*cols + i ]) > fabs(matrix[ max*cols + i ]) )
                max = j;

        /* check pivot value */
        if( fabs(matrix[ max*cols + i ]) < minPivot )
            return false;   /* pivot too small! */

        /* interchange rows 'max' and 'i' */
        for(k=0; k<cols; ++k)
        {
            temp = matrix[ i*cols + k ];
            matrix[ i*cols + k ] = matrix[ max*cols + k ];
            matrix[ max*cols + k ] = temp;
        }

        /* eliminate column */
        for(j=i+1; j<rows; ++j)
            for(k=cols-1; k>=i; --k)
                matrix[ j*cols + k ] -= matrix[ i*cols + k ] *
                    matrix[ j*cols + i ] / matrix[ i*cols + i ];
    }

    /* everything went well */
    return true;
}


/** Retrieve solution vector of linear system by substituting backwards.

    This operation _relies_ on the previous successful
    application of eliminate()!

    @param matrix
    Matrix in upper diagonal form, as e.g. generated by eliminate()

    @param rows
    Number of rows in matrix

    @param cols
    Number of columns in matrix

    @param result
    Result vector. Given matrix must have space for one column (rows entries).

    @return true, if back substitution was possible (i.e. no division
    by zero occured).
 */
template <class Matrix, class Vector, typename BaseType>
bool substitute(    const Matrix&   matrix,
                    int             rows,
                    int             cols,
                    Vector&         result  )
{
    BaseType    temp;
    int         j,k;    /* *must* be signed, when looping like: j>=0 ! */

    /* substitute backwards */
    for(j=rows-1; j>=0; --j)
    {
        temp = 0.0;
        for(k=j+1; k<cols-1; ++k)
            temp += matrix[ j*cols + k ] * result[k];

        if( matrix[ j*cols + j ] == 0.0 )
            return false;   /* imminent division by zero! */

        result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ];
    }

    /* everything went well */
    return true;
}


/** This method determines solution of given linear system, if any

    This is a wrapper for eliminate and substitute, given matrix must
    contain right side of equation as the last column.

    @param matrix
    The matrix to operate on. Last column is the result vector (right
    hand side of the linear equation). After successful termination,
    the matrix is upper triangular. The matrix is expected to be in
    row major order.

    @param rows
    Number of rows in matrix

    @param cols
    Number of columns in matrix

    @param minPivot
    If the pivot element gets lesser than minPivot, this method fails,
    otherwise, elimination succeeds and true is returned.

    @return true, if elimination succeeded.
 */
template <class Matrix, class Vector, typename BaseType>
bool solve( Matrix&     matrix,
            int         rows,
            int         cols,
            Vector&     result,
            BaseType    minPivot    )
{
    if( eliminate<Matrix,BaseType>(matrix, rows, cols, minPivot) )
        return substitute<Matrix,Vector,BaseType>(matrix, rows, cols, result);

    return false;
}