gaussian_elimination.h

// -*- c++ -*-

// Copyright (C) 2008,2009 Ethan Eade, Tom Drummond (twd20@cam.ac.uk)
// and Ed Rosten (er258@cam.ac.uk)

//All rights reserved.
//
//Redistribution and use in source and binary forms, with or without
//modification, are permitted provided that the following conditions
//are met:
//1. Redistributions of source code must retain the above copyright
//    notice, this list of conditions and the following disclaimer.
//2. Redistributions in binary form must reproduce the above copyright
//   notice, this list of conditions and the following disclaimer in the
//   documentation and/or other materials provided with the distribution.
//
//THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND OTHER CONTRIBUTORS ``AS IS''
//AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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//ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR OTHER CONTRIBUTORS BE
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#ifndef GAUSSIAN_ELIMINATION_H
#define GAUSSIAN_ELIMINATION_H

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

namespace TooN {
    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);
        };

    };

    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