gaussian_elimination.h

// -*- c++ -*-

// Copyright (C) 2008,2009 Ethan Eade, Tom Drummond (twd20@cam.ac.uk)
// and Ed Rosten (er258@cam.ac.uk)
//
// This file is part of the TooN Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 2, or (at your option)
// any later version.

// 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 General Public License for more details.

// You should have received a copy of the GNU General Public License along
// with this library; see the file COPYING.  If not, write to the Free
// Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
// USA.

// As a special exception, you may use this file as part of a free software
// library without restriction.  Specifically, if other files instantiate
// templates or use macros or inline functions from this file, or you compile
// this file and link it with other files to produce an executable, this
// file does not by itself cause the resulting executable to be covered by
// the GNU General Public License.  This exception does not however
// invalidate any other reasons why the executable file might be covered by
// the GNU General Public License.


#ifndef GAUSSIAN_ELIMINATION_H
#define GAUSSIAN_ELIMINATION_H

#include <utility>
#include <cmath>
#include <TooN/TooN.h>

namespace TooN {
    ///@ingroup gEquations
    ///Return the solution for \f$Ax = b\f$, given \f$A\f$ and \f$b\f$
    ///@param A \f$A\f$
    ///@param b \f$b\f$
    template<int N, typename Precision>
    inline Vector<N, Precision> gaussian_elimination (Matrix<N,N,Precision> A, Vector<N, Precision> b) {
        using std::swap;
        using std::abs;

        int size=b.size();

        for (int i=0; i<size; ++i) {
            int argmax = i;
            Precision maxval = abs(A[i][i]);
            
            for (int ii=i+1; ii<size; ++ii) {
                double v =  abs(A[ii][i]);
                if (v > maxval) {
                    maxval = v;
                    argmax = ii;
                }
            }
            Precision pivot = A[argmax][i];
            //assert(abs(pivot) > 1e-16);
            Precision inv_pivot = static_cast<Precision>(1)/pivot;
            if (argmax != i) {
                for (int j=i; j<size; ++j)
                    swap(A[i][j], A[argmax][j]);
                swap(b[i], b[argmax]);
            }
            //A[i][i] = 1;
            for (int j=i+1; j<size; ++j)
                A[i][j] *= inv_pivot;
            b[i] *= inv_pivot;
            
            for (int u=i+1; u<size; ++u) {
                double factor = A[u][i];
                //A[u][i] = 0;
                for (int j=i+1; j<size; ++j)
                    A[u][j] -= factor * A[i][j];
                b[u] -= factor * b[i];
            }
        }
        
        Vector<N,Precision> x(size);
        for (int i=size-1; i>=0; --i) {
            x[i] = b[i];
            for (int j=i+1; j<size; ++j)
                x[i] -= A[i][j] * x[j];
        }
        return x;
    }
    
    namespace Internal
    {
        template<int i, int j, int k> struct Size3
        {
            static const int s = !IsStatic<i>::is?i: (!IsStatic<j>::is?j:k);
        };

    };

    ///@ingroup gEquations
    ///Return the solution for \f$Ax = b\f$, given \f$A\f$ and \f$b\f$
    ///@param A \f$A\f$
    ///@param b \f$b\f$
    template<int R1, int C1, int R2, int C2, typename Precision>
    inline Matrix<Internal::Size3<R1, C1, R2>::s, C2, Precision> gaussian_elimination (Matrix<R1,C1,Precision> A, Matrix<R2, C2, Precision> b) {
        using std::swap;
        using std::abs;
        SizeMismatch<R1, C1>::test(A.num_rows(), A.num_cols());
        SizeMismatch<R1, R2>::test(A.num_rows(), b.num_rows());

        int size=A.num_rows();

        for (int i=0; i<size; ++i) {
            int argmax = i;
            Precision maxval = abs(A[i][i]);
            
            for (int ii=i+1; ii<size; ++ii) {
                Precision v =  abs(A[ii][i]);
                if (v > maxval) {
                    maxval = v;
                    argmax = ii;
                }
            }
            Precision pivot = A[argmax][i];
            //assert(abs(pivot) > 1e-16);
            Precision inv_pivot = static_cast<Precision>(1)/pivot;
            if (argmax != i) {
                for (int j=i; j<size; ++j)
                    swap(A[i][j], A[argmax][j]);

                for(int j=0; j < b.num_cols(); j++)
                    swap(b[i][j], b[argmax][j]);
            }
            //A[i][i] = 1;
            for (int j=i+1; j<size; ++j)
                A[i][j] *= inv_pivot;
            b[i] *= inv_pivot;
            
            for (int u=i+1; u<size; ++u) {
                Precision factor = A[u][i];
                //A[u][i] = 0;
                for (int j=i+1; j<size; ++j)
                    A[u][j] -= factor * A[i][j];
                b[u] -= factor * b[i];
            }
        }
        
        Matrix<Internal::Size3<R1, C1, R2>::s,C2,Precision> x(b.num_rows(), b.num_cols());
        for (int i=size-1; i>=0; --i) {
            for(int k=0; k <b.num_cols(); k++)
            {
                x[i][k] = b[i][k];
                for (int j=i+1; j<size; ++j)
                    x[i][k] -= A[i][j] * x[j][k];
            }
        }
        return x;
    }
}
#endif