examples/gram_schmidt.hpp

/*
 boost header: numeric/odeint/gram_schmitt.hpp

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011 Mario Mulansky

 Distributed under the Boost Software License, Version 1.0.
 (See accompanying file LICENSE_1_0.txt or
 copy at http://www.boost.org/LICENSE_1_0.txt)
 */

#ifndef BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED

#include <boost/throw_exception.hpp>
#include <iterator>
#include <algorithm>
#include <numeric>

namespace boost {
namespace numeric {
namespace odeint {

template< class Iterator , class T >
void normalize( Iterator first , Iterator last , T norm )
{
    while( first != last ) *first++ /= norm;
}

template< class Iterator , class T >
void substract_vector( Iterator first1 , Iterator last1 ,
        Iterator first2 , T val )
{
    while( first1 != last1 ) *first1++ -= val * ( *first2++ );
}

template< size_t num_of_lyap , class StateType , class LyapType >
void gram_schmidt( StateType &x , LyapType &lyap , size_t n )
{
    if( !num_of_lyap ) return;
    if( ptrdiff_t( ( num_of_lyap + 1 ) * n ) != std::distance( x.begin() , x.end() ) )
        BOOST_THROW_EXCEPTION( std::domain_error( "renormalization() : size of state does not match the number of lyapunov exponents." ) );

    typedef typename StateType::value_type value_type;
    typedef typename StateType::iterator iterator;

    value_type norm[num_of_lyap];
    value_type tmp[num_of_lyap];
    iterator first = x.begin() + n;
    iterator beg1 = first , end1 = first + n ;

    std::fill( norm , norm+num_of_lyap , 0.0 );

    // normalize first vector
    norm[0] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
    normalize( beg1 , end1 , norm[0] );

    beg1 += n;
    end1 += n;

    for( size_t j=1 ; j<num_of_lyap ; ++j , beg1+=n , end1+=n )
    {
        for( size_t k=0 ; k<j ; ++k )
        {
            tmp[k] = std::inner_product( beg1 , end1 , first + k*n , 0.0 );
            //  clog << j << " " << k << " " << tmp[k] << "\n";
        }



        for( size_t k=0 ; k<j ; ++k )
            substract_vector( beg1 , end1 , first + k*n , tmp[k] );

        // normalize j-th vector
        norm[j] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
        // clog << j << " " << norm[j] << "\n";
        normalize( beg1 , end1 , norm[j] );
    }

    for( size_t j=0 ; j<num_of_lyap ; j++ )
        lyap[j] += log( norm[j] );
}


} // namespace odeint
} // namespace numeric
} // namespace boost

#endif //BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED