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/mtl/implicit_euler_mtl.cpp b/examples/mtl/implicit_euler_mtl.cpp
new file mode 100644
index 0000000..6a1b8e7
--- /dev/null
+++ b/examples/mtl/implicit_euler_mtl.cpp
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+/*
+ * 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] );
+ }
+}