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-rw-r--r--libs/numeric/odeint/examples/mtl/Jamfile.v218
-rw-r--r--libs/numeric/odeint/examples/mtl/gauss_packet.cpp141
-rw-r--r--libs/numeric/odeint/examples/mtl/implicit_euler_mtl.cpp324
3 files changed, 483 insertions, 0 deletions
diff --git a/libs/numeric/odeint/examples/mtl/Jamfile.v2 b/libs/numeric/odeint/examples/mtl/Jamfile.v2
new file mode 100644
index 0000000000..bd2ec3caed
--- /dev/null
+++ b/libs/numeric/odeint/examples/mtl/Jamfile.v2
@@ -0,0 +1,18 @@
+# Copyright 2011-2013 Mario Mulansky
+# Copyright 2012 Karsten Ahnert
+# 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)
+
+# set your MTL4 directory here
+MTL4_INCLUDE = /home/mario/MTL4 ;
+
+project
+ : requirements
+ <include>../../../../..
+ <include>$(MTL4_INCLUDE)
+ <define>BOOST_ALL_NO_LIB=1
+ ;
+
+exe gauss_packet : gauss_packet.cpp ;
+exe implicit_euler_mtl : implicit_euler_mtl.cpp ; \ No newline at end of file
diff --git a/libs/numeric/odeint/examples/mtl/gauss_packet.cpp b/libs/numeric/odeint/examples/mtl/gauss_packet.cpp
new file mode 100644
index 0000000000..9579e5d45e
--- /dev/null
+++ b/libs/numeric/odeint/examples/mtl/gauss_packet.cpp
@@ -0,0 +1,141 @@
+/*
+ * gauss_packet.cpp
+ *
+ * Schroedinger equation with potential barrier and periodic boundary conditions
+ * Initial Gauss packet moving to the right
+ *
+ * pipe output into gnuplot to see animation
+ *
+ * Implementation of Hamilton operator via MTL library
+ *
+ * Copyright 2011-2013 Mario Mulansky
+ * Copyright 2011-2012 Karsten Ahnert
+ *
+ * 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)
+ */
+
+
+#include <iostream>
+#include <complex>
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/numeric/odeint/external/mtl4/mtl4.hpp>
+
+#include <boost/numeric/mtl/mtl.hpp>
+
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+typedef mtl::dense_vector< complex< double > > state_type;
+
+struct hamiltonian {
+
+ typedef mtl::compressed2D< complex< double > > matrix_type;
+ matrix_type m_H;
+
+ hamiltonian( const int N ) : m_H( N , N )
+ {
+ // constructor with zero potential
+ m_H = 0.0;
+ initialize_kinetic_term();
+ }
+
+ //template< mtl::compressed2D< double > >
+ hamiltonian( mtl::compressed2D< double > &V ) : m_H( num_rows( V ) , num_cols( V ) )
+ {
+ // use potential V in hamiltonian
+ m_H = complex<double>( 0.0 , -1.0 ) * V;
+ initialize_kinetic_term();
+ }
+
+ void initialize_kinetic_term( )
+ {
+ const int N = num_rows( m_H );
+ mtl::matrix::inserter< matrix_type , mtl::update_plus< complex<double> > > ins( m_H );
+ const double z = 1.0;
+ // fill diagonal and upper and lower diagonal
+ for( int i = 0 ; i<N ; ++i )
+ {
+ ins[ i ][ (i+1) % N ] << complex< double >( 0.0 , -z );
+ ins[ i ][ i ] << complex< double >( 0.0 , z );
+ ins[ (i+1) % N ][ i ] << complex< double >( 0.0 , -z );
+ }
+ }
+
+ void operator()( const state_type &psi , state_type &dpsidt , const double t )
+ {
+ dpsidt = m_H * psi;
+ }
+
+};
+
+struct write_for_gnuplot
+{
+ size_t m_every , m_count;
+
+ write_for_gnuplot( size_t every = 10 )
+ : m_every( every ) , m_count( 0 ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ if( ( m_count % m_every ) == 0 )
+ {
+ //clog << t << endl;
+ cout << "p [0:" << mtl::size(x) << "][0:0.02] '-'" << endl;
+ for( size_t i=0 ; i<mtl::size(x) ; ++i )
+ {
+ cout << i << "\t" << norm(x[i]) << "\n";
+ }
+ cout << "e" << endl;
+ }
+
+ ++m_count;
+ }
+};
+
+static const int N = 1024;
+static const int N0 = 256;
+static const double sigma0 = 20;
+static const double k0 = -1.0;
+
+int main( int argc , char** argv )
+{
+ state_type x( N , 0.0 );
+
+ // initialize gauss packet with nonzero velocity
+ for( int i=0 ; i<N ; ++i )
+ {
+ x[i] = exp( -(i-N0)*(i-N0) / ( 4.0*sigma0*sigma0 ) ) * exp( complex< double >( 0.0 , k0*i ) );
+ //x[i] += 2.0*exp( -(i+N0-N)*(i+N0-N) / ( 4.0*sigma0*sigma0 ) ) * exp( complex< double >( 0.0 , -k0*i ) );
+ }
+ x /= mtl::two_norm( x );
+
+ typedef runge_kutta4< state_type > stepper;
+
+ // create potential barrier
+ mtl::compressed2D< double > V( N , N );
+ V = 0.0;
+ {
+ mtl::matrix::inserter< mtl::compressed2D< double > > ins( V );
+ for( int i=0 ; i<N ; ++i )
+ {
+ //ins[i][i] << 1E-4*(i-N/2)*(i-N/2);
+
+ if( i < N/2 )
+ ins[ i ][ i ] << 0.0 ;
+ else
+ ins[ i ][ i ] << 1.0 ;
+
+ }
+ }
+
+ // perform integration, output can be piped to gnuplot
+ integrate_const( stepper() , hamiltonian( V ) , x , 0.0 , 1000.0 , 0.1 , write_for_gnuplot( 10 ) );
+
+ clog << "Norm: " << mtl::two_norm( x ) << endl;
+
+ return 0;
+}
diff --git a/libs/numeric/odeint/examples/mtl/implicit_euler_mtl.cpp b/libs/numeric/odeint/examples/mtl/implicit_euler_mtl.cpp
new file mode 100644
index 0000000000..6a1b8e7319
--- /dev/null
+++ b/libs/numeric/odeint/examples/mtl/implicit_euler_mtl.cpp
@@ -0,0 +1,324 @@
+/*
+ * Copyright 2012 Karsten Ahnert
+ * Copyright 2012 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)
+ */
+
+
+#include <iostream>
+#include <fstream>
+#include <utility>
+#include "time.h"
+
+#include <boost/numeric/odeint.hpp>
+#include <boost/phoenix/phoenix.hpp>
+#include <boost/numeric/mtl/mtl.hpp>
+
+#include <boost/numeric/odeint/external/mtl4/implicit_euler_mtl4.hpp>
+
+using namespace std;
+using namespace boost::numeric::odeint;
+
+namespace phoenix = boost::phoenix;
+
+
+
+typedef mtl::dense_vector< double > vec_mtl4;
+typedef mtl::compressed2D< double > mat_mtl4;
+
+typedef boost::numeric::ublas::vector< double > vec_ublas;
+typedef boost::numeric::ublas::matrix< double > mat_ublas;
+
+
+// two systems defined 1 & 2 both are mostly sparse with the number of element variable
+struct system1_mtl4
+{
+
+ void operator()( const vec_mtl4 &x , vec_mtl4 &dxdt , double t )
+ {
+ int size = mtl::size(x);
+
+ dxdt[ 0 ] = -0.06*x[0];
+
+ for (int i =1; i< size ; ++i){
+
+ dxdt[ i ] = 4.2*x[i-1]-2.2*x[i]*x[i];
+ }
+
+ }
+};
+
+struct jacobi1_mtl4
+{
+ void operator()( const vec_mtl4 &x , mat_mtl4 &J , const double &t )
+ {
+ int size = mtl::size(x);
+ mtl::matrix::inserter<mat_mtl4> ins(J);
+
+ ins[0][0]=-0.06;
+
+ for (int i =1; i< size ; ++i)
+ {
+ ins[i][i-1] = + 4.2;
+ ins[i][i] = -4.2*x[i];
+ }
+ }
+};
+
+
+
+struct system1_ublas
+{
+
+ void operator()( const vec_ublas &x , vec_ublas &dxdt , double t )
+ {
+ int size = x.size();
+
+ dxdt[ 0 ] = -0.06*x[0];
+
+ for (int i =1; i< size ; ++i){
+
+ dxdt[ i ] = 4.2*x[i-1]-2.2*x[i]*x[i];
+ }
+
+ }
+};
+
+struct jacobi1_ublas
+{
+ void operator()( const vec_ublas &x , mat_ublas &J , const double &t )
+ {
+ int size = x.size();
+// mtl::matrix::inserter<mat_mtl4> ins(J);
+
+ J(0,0)=-0.06;
+
+ for (int i =1; i< size ; ++i){
+//ins[i][0]=120.0*x[i];
+ J(i,i-1) = + 4.2;
+ J(i,i) = -4.2*x[i];
+
+ }
+ }
+};
+
+struct system2_mtl4
+{
+
+ void operator()( const vec_mtl4 &x , vec_mtl4 &dxdt , double t )
+ {
+ int size = mtl::size(x);
+
+
+ for (int i =0; i< size/5 ; i+=5){
+
+ dxdt[ i ] = -0.5*x[i];
+ dxdt[i+1]= +25*x[i+1]*x[i+2]-740*x[i+3]*x[i+3]+4.2e-2*x[i];
+ dxdt[i+2]= +25*x[i]*x[i]-740*x[i+3]*x[i+3];
+ dxdt[i+3]= -25*x[i+1]*x[i+2]+740*x[i+3]*x[i+3];
+ dxdt[i+4] = 0.250*x[i]*x[i+1]-44.5*x[i+3];
+
+ }
+
+ }
+};
+
+struct jacobi2_mtl4
+{
+ void operator()( const vec_mtl4 &x , mat_mtl4 &J , const double &t )
+ {
+ int size = mtl::size(x);
+ mtl::matrix::inserter<mat_mtl4> ins(J);
+
+ for (int i =0; i< size/5 ; i+=5){
+
+ ins[ i ][i] = -0.5;
+ ins[i+1][i+1]=25*x[i+2];
+ ins[i+1][i+2] = 25*x[i+1];
+ ins[i+1][i+3] = -740*2*x[i+3];
+ ins[i+1][i] =+4.2e-2;
+
+ ins[i+2][i]= 50*x[i];
+ ins[i+2][i+3]= -740*2*x[i+3];
+ ins[i+3][i+1] = -25*x[i+2];
+ ins[i+3][i+2] = -25*x[i+1];
+ ins[i+3][i+3] = +740*2*x[i+3];
+ ins[i+4][i] = 0.25*x[i+1];
+ ins[i+4][i+1] =0.25*x[i];
+ ins[i+4][i+3]=-44.5;
+
+
+
+ }
+ }
+};
+
+
+
+struct system2_ublas
+{
+
+ void operator()( const vec_ublas &x , vec_ublas &dxdt , double t )
+ {
+ int size = x.size();
+ for (int i =0; i< size/5 ; i+=5){
+
+ dxdt[ i ] = -4.2e-2*x[i];
+ dxdt[i+1]= +25*x[i+1]*x[i+2]-740*x[i+3]*x[i+3]+4.2e-2*x[i];
+ dxdt[i+2]= +25*x[i]*x[i]-740*x[i+3]*x[i+3];
+ dxdt[i+3]= -25*x[i+1]*x[i+2]+740*x[i+3]*x[i+3];
+ dxdt[i+4] = 0.250*x[i]*x[i+1]-44.5*x[i+3];
+
+ }
+
+ }
+};
+
+struct jacobi2_ublas
+{
+ void operator()( const vec_ublas &x , mat_ublas &J , const double &t )
+ {
+ int size = x.size();
+
+ for (int i =0; i< size/5 ; i+=5){
+
+ J(i ,i) = -4.2e-2;
+ J(i+1,i+1)=25*x[i+2];
+ J(i+1,i+2) = 25*x[i+1];
+ J(i+1,i+3) = -740*2*x[i+3];
+ J(i+1,i) =+4.2e-2;
+
+ J(i+2,i)= 50*x[i];
+ J(i+2,i+3)= -740*2*x[i+3];
+ J(i+3,i+1) = -25*x[i+2];
+ J(i+3,i+2) = -25*x[i+1];
+ J(i+3,i+3) = +740*2*x[i+3];
+ J(i+4,i) = 0.25*x[i+1];
+ J(i+4,i+1) =0.25*x[i];
+ J(i+4,i+3)=-44.5;
+
+
+
+ }
+
+
+ }
+};
+
+
+
+
+void testRidiculouslyMassiveArray( int size )
+{
+ typedef boost::numeric::odeint::implicit_euler_mtl4 < double > mtl4stepper;
+ typedef boost::numeric::odeint::implicit_euler< double > booststepper;
+
+ vec_mtl4 x(size , 0.0);
+ x[0]=1;
+
+
+ double dt = 0.02;
+ double endtime = 10.0;
+
+ clock_t tstart_mtl4 = clock();
+ size_t num_of_steps_mtl4 = integrate_const(
+ mtl4stepper() ,
+ make_pair( system1_mtl4() , jacobi1_mtl4() ) ,
+ x , 0.0 , endtime , dt );
+ clock_t tend_mtl4 = clock() ;
+
+ clog << x[0] << endl;
+ clog << num_of_steps_mtl4 << " time elapsed: " << (double)(tend_mtl4-tstart_mtl4 )/CLOCKS_PER_SEC << endl;
+
+ vec_ublas x_ublas(size , 0.0);
+ x_ublas[0]=1;
+
+ clock_t tstart_boost = clock();
+ size_t num_of_steps_ublas = integrate_const(
+ booststepper() ,
+ make_pair( system1_ublas() , jacobi1_ublas() ) ,
+ x_ublas , 0.0 , endtime , dt );
+ clock_t tend_boost = clock() ;
+
+ clog << x_ublas[0] << endl;
+ clog << num_of_steps_ublas << " time elapsed: " << (double)(tend_boost-tstart_boost)/CLOCKS_PER_SEC<< endl;
+
+ clog << "dt_ublas/dt_mtl4 = " << (double)( tend_boost-tstart_boost )/( tend_mtl4-tstart_mtl4 ) << endl << endl;
+ return ;
+}
+
+
+
+void testRidiculouslyMassiveArray2( int size )
+{
+ typedef boost::numeric::odeint::implicit_euler_mtl4 < double > mtl4stepper;
+ typedef boost::numeric::odeint::implicit_euler< double > booststepper;
+
+
+ vec_mtl4 x(size , 0.0);
+ x[0]=100;
+
+
+ double dt = 0.01;
+ double endtime = 10.0;
+
+ clock_t tstart_mtl4 = clock();
+ size_t num_of_steps_mtl4 = integrate_const(
+ mtl4stepper() ,
+ make_pair( system1_mtl4() , jacobi1_mtl4() ) ,
+ x , 0.0 , endtime , dt );
+
+
+ clock_t tend_mtl4 = clock() ;
+
+ clog << x[0] << endl;
+ clog << num_of_steps_mtl4 << " time elapsed: " << (double)(tend_mtl4-tstart_mtl4 )/CLOCKS_PER_SEC << endl;
+
+ vec_ublas x_ublas(size , 0.0);
+ x_ublas[0]=100;
+
+ clock_t tstart_boost = clock();
+ size_t num_of_steps_ublas = integrate_const(
+ booststepper() ,
+ make_pair( system1_ublas() , jacobi1_ublas() ) ,
+ x_ublas , 0.0 , endtime , dt );
+
+
+ clock_t tend_boost = clock() ;
+
+ clog << x_ublas[0] << endl;
+ clog << num_of_steps_ublas << " time elapsed: " << (double)(tend_boost-tstart_boost)/CLOCKS_PER_SEC<< endl;
+
+ clog << "dt_ublas/dt_mtl4 = " << (double)( tend_boost-tstart_boost )/( tend_mtl4-tstart_mtl4 ) << endl << endl;
+ return ;
+}
+
+
+
+
+int main( int argc , char **argv )
+{
+ std::vector< size_t > length;
+ length.push_back( 8 );
+ length.push_back( 16 );
+ length.push_back( 32 );
+ length.push_back( 64 );
+ length.push_back( 128 );
+ length.push_back( 256 );
+
+ for( size_t i=0 ; i<length.size() ; ++i )
+ {
+ clog << "Testing with size " << length[i] << endl;
+ testRidiculouslyMassiveArray( length[i] );
+ }
+ clog << endl << endl;
+
+ for( size_t i=0 ; i<length.size() ; ++i )
+ {
+ clog << "Testing with size " << length[i] << endl;
+ testRidiculouslyMassiveArray2( length[i] );
+ }
+}
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