sl.h

// -*- c++ -*-

// Copyright (C) 2005,2009 Tom Drummond (twd20@cam.ac.uk),
// Gerhard Reitmayr (gr281@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
//IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
//ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR OTHER CONTRIBUTORS BE
//LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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#ifndef TOON_INCLUDE_SL_H
#define TOON_INCLUDE_SL_H

#include <TooN/TooN.h>
#include <TooN/helpers.h>
#include <TooN/gaussian_elimination.h>
#include <TooN/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 = DefaultPrecision>
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()); }

    template <typename P>
    SL<N,typename Internal::MultiplyType<Precision, P>::type> operator*( const SL<N,P> & rhs) const { return SL<N,typename Internal::MultiplyType<Precision, P>::type>(*this, rhs); }

    template <typename P>
    SL operator*=( const SL<N,P> & rhs) { *this = *this*rhs; return *this; }

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

    inline Vector<N*N-1, Precision> ln() const ;

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

private:
    struct Invert {};
    SL( const SL & from, struct Invert ) {
        const 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 Vector<N*N-1, Precision> SL<N, Precision>::ln() const {
    const Matrix<N> l = TooN::log(my_matrix);
    Vector<SL<N,Precision>::dim, Precision> v;
    Precision last = 0;
    for(int i = 0; i < DIAG_LIMIT; ++i){    // diagonal elements
        v[i] = l(i,i) + last;
        last = l(i,i);
    }
    for(int i = DIAG_LIMIT, row = 0, col = 1; i < SYMM_LIMIT; ++i) {    // calculate symmetric and antisymmetric in one go
        // do the right thing here to calculate the correct indices !
        v[i] = (l(row, col) + l(col, row))*0.5;
        v[i+COUNT_SYMM] = (-l(row, col) + l(col, row))*0.5;
        ++col;
        if( col == N ){
            ++row;
            col = row+1;
        }
    }
    return v;
}

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