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/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*************************************************************************
*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* Copyright 2000, 2010 Oracle and/or its affiliates.
*
* OpenOffice.org - a multi-platform office productivity suite
*
* This file is part of OpenOffice.org.
*
* OpenOffice.org is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License version 3
* only, as published by the Free Software Foundation.
*
* OpenOffice.org 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 version 3 for more details
* (a copy is included in the LICENSE file that accompanied this code).
*
* You should have received a copy of the GNU Lesser General Public License
* version 3 along with OpenOffice.org. If not, see
* <http://www.openoffice.org/license.html>
* for a copy of the LGPLv3 License.
*
************************************************************************/
/** 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 occurred).
*/
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;
}
/* vim:set shiftwidth=4 softtabstop=4 expandtab: */
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