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/*************************************************************************
*
* $RCSfile: gauss.hxx,v $
*
* $Revision: 1.2 $
*
* last change: $Author: aw $ $Date: 2003-11-05 12:25:58 $
*
* 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 sal_True is returned.
@return sal_True, if elimination succeeded.
*/
template <class Matrix, typename BaseType>
sal_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 sal_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 sal_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 sal_True, if back substitution was possible (i.e. no division
by zero occured).
*/
template <class Matrix, class Vector, typename BaseType>
sal_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 sal_False; /* imminent division by zero! */
result[j] = (matrix[ j*cols + cols-1 ] - temp) / matrix[ j*cols + j ];
}
/* everything went well */
return sal_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 sal_True is returned.
@return sal_True, if elimination succeeded.
*/
template <class Matrix, class Vector, typename BaseType>
sal_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 sal_False;
}
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