Squashed 'third_party/boostorg/odeint/' content from commit 6ff2719
Change-Id: If4892e29c1a5e6cf3a7aa51486a2725c251b0c7d
git-subtree-dir: third_party/boostorg/odeint
git-subtree-split: 6ff2719b6907b86596c3d43e88c1bcfdf29df560
diff --git a/examples/gram_schmidt.hpp b/examples/gram_schmidt.hpp
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+++ b/examples/gram_schmidt.hpp
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+/*
+ 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