sl.h

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// -*- c++ -*-

// Copyright (C) 2005,2009 Tom Drummond (twd20@cam.ac.uk),
// Gerhard Reitmayr (gr281@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 TOON_INCLUDE_SL_H
#define TOON_INCLUDE_SL_H

#include "TooN.h"
#include "helpers.h"
#include "gaussian_elimination.h"
#include "determinant.h"
#include <cassert>

namespace TooN {

template <int N, typename P> class SL;
template <int N, typename P> std::istream & operator>>(std::istream &, SL<N, P> &);

template <int N, typename Precision = double>
class SL {
    friend std::istream & operator>> <N,Precision>(std::istream &, SL &);
public:
    static const int size = N;          
    static const int dim = N*N - 1;     

    SL() : my_matrix(Identity) {}

    template <int S, typename P, typename B>
    SL( const Vector<S,P,B> & v ) { *this = exp(v); }

    template <int R, int C, typename P, typename A>
    SL(const Matrix<R,C,P,A>& M) : my_matrix(M) { coerce(); }

    const Matrix<N,N,Precision> & get_matrix() const { return my_matrix; }
    SL inverse() const { return SL(*this, Invert()); }

    SL operator*( const SL & rhs) const { return SL(*this, rhs); }
    SL operator*=( const SL & rhs) { *this = *this*rhs; return *this; }

    template <int S, typename P, typename B>
    static inline SL exp( const Vector<S,P,B> &);

    static inline Matrix<N,N,Precision> generator(int);

private:
    struct Invert {};
    SL( const SL & from, struct Invert ) {
        Matrix<N> id = Identity;
        my_matrix = gaussian_elimination(from.my_matrix, id);
    }
    SL( const SL & a, const SL & b) : my_matrix(a.get_matrix() * b.get_matrix()) {}

    void coerce(){
        using std::abs;
        Precision det = determinant(my_matrix);
        assert(abs(det) > 0);
        using std::pow;
        my_matrix /= pow(det, 1.0/N);
    }

    static const int COUNT_DIAG = N - 1;
    static const int COUNT_SYMM = (dim - COUNT_DIAG)/2;
    static const int COUNT_ASYMM = COUNT_SYMM;
    static const int DIAG_LIMIT = COUNT_DIAG;
    static const int SYMM_LIMIT = COUNT_SYMM + DIAG_LIMIT;

    Matrix<N,N,Precision> my_matrix;
};

template <int N, typename Precision>
template <int S, typename P, typename B>
inline SL<N, Precision> SL<N, Precision>::exp( const Vector<S,P,B> & v){
    SizeMismatch<S,dim>::test(v.size(), dim);
    Matrix<N,N,Precision> t(Zeros);
    for(int i = 0; i < dim; ++i)
        t += generator(i) * v[i];
    SL<N, Precision> result;
    result.my_matrix = TooN::exp(t);
    return result;
}

template <int N, typename Precision>
inline Matrix<N,N,Precision> SL<N, Precision>::generator(int i){
    assert( i > -1 && i < dim );
    Matrix<N,N,Precision> result(Zeros);
    if(i < DIAG_LIMIT) {                // first ones are the diagonal ones
        result(i,i) = 1;
        result(i+1,i+1) = -1;
    } else if(i < SYMM_LIMIT){          // then the symmetric ones
        int row = 0, col = i - DIAG_LIMIT + 1;
        while(col > (N - row - 1)){
            col -= (N - row - 1); 
            ++row;
        }
        col += row;
        result(row, col) = result(col, row) = 1;
    } else {                            // finally the antisymmetric ones
        int row = 0, col = i - SYMM_LIMIT + 1;
        while(col > N - row - 1){
            col -= N - row - 1; 
            ++row;
        }
        col += row;
        result(row, col) = -1;
        result(col, row) = 1;
    }
    return result;
}

template <int S, typename PV, typename B, int N, typename P>
Vector<N, typename Internal::MultiplyType<P, PV>::type> operator*( const SL<N, P> & lhs, const Vector<S,PV,B> & rhs ){
    return lhs.get_matrix() * rhs;
}

template <int S, typename PV, typename B, int N, typename P>
Vector<N, typename Internal::MultiplyType<PV, P>::type> operator*( const Vector<S,PV,B> & lhs, const SL<N,P> & rhs ){
    return lhs * rhs.get_matrix();
}

template<int R, int C, typename PM, typename A, int N, typename P> inline
Matrix<N, C, typename Internal::MultiplyType<P, PM>::type> operator*(const SL<N,P>& lhs, const Matrix<R, C, PM, A>& rhs){
    return lhs.get_matrix() * rhs;
}

template<int R, int C, typename PM, typename A, int N, typename P> inline
Matrix<R, N, typename Internal::MultiplyType<PM, P>::type> operator*(const Matrix<R, C, PM, A>& lhs, const SL<N,P>& rhs){
    return lhs * rhs.get_matrix();
}

template <int N, typename P>
std::ostream & operator<<(std::ostream & out, const SL<N, P> & h){
    out << h.get_matrix();
    return out;
}

template <int N, typename P>
std::istream & operator>>(std::istream & in, SL<N, P> & h){
    in >> h.my_matrix;
    h.coerce();
    return in;
}

};

#endif