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bulirsch stoer with dense output can now be used - tested on nontrivial example (elliptic functions), everything looks fine.

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This commit is contained in:
Mario Mulansky
2011-08-12 01:10:07 +02:00
parent 69f12a025e
commit 21f76a784d
5 changed files with 148 additions and 102 deletions
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28
libs/numeric/odeint/examples/bulirsch_stoer.cpp
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@@ -10,6 +10,7 @@
#include <cmath>
#include <boost/array.hpp>
#include <boost/ref.hpp>
#include <boost/numeric/odeint/config.hpp>
@@ -50,36 +51,39 @@ void write_out( const state_type &x , const double t )
int main()
{
bulirsch_stoer_dense_out< state_type > stepper( 1E-10 , 0.0 , 0.0 , 0.0 );
bulirsch_stoer_dense_out< state_type > stepper( 1E-8 , 0.0 , 0.0 , 0.0 );
state_type x = {{ 0.0 }};
state_type x = {{ 2.0 / sqrt(3.0) }};
//double t = M_PI/6.0;
double t = 0.0;
double t = M_PI/6.0;
//double t = 0.0;
double dt = 0.01;
//double t_end = M_PI/2.0 - 0.1;
double t_end = 100.0;
double t_end = M_PI/2.0 - 0.1;
//double t_end = 100.0;
out.open( "bs.dat" );
integrate_const( stepper , rhs2 , x , t , t_end , dt , write_out );
out.precision(16);
integrate_const( stepper , rhs , x , t , t_end , dt , write_out );
out.close();
x[0] = 0.0;
x[0] = 2.0 / sqrt(3.0);
out.open( "bs2.dat" );
integrate_adaptive( stepper , rhs2 , x , t , t_end , dt , write_out );
out.precision(16);
integrate_adaptive( stepper , rhs , x , t , t_end , dt , write_out );
out.close();
typedef runge_kutta_dopri5< state_type > dopri5_type;
typedef controlled_error_stepper< dopri5_type > controlled_dopri5_type;
typedef dense_output_controlled_explicit_fsal< controlled_dopri5_type > dense_output_dopri5_type;
dense_output_dopri5_type dopri5( controlled_dopri5_type( dopri5_type() , default_error_checker< double >( 1E-10 , 0.0 , 0.0 , 0.0 ) ) );
dense_output_dopri5_type dopri5( controlled_dopri5_type( dopri5_type() , default_error_checker< double >( 1E-2 , 0.0 , 0.0 , 0.0 ) ) );
x[0] = 0.0;
x[0] = 2.0 / sqrt(3.0);
out.open( "bs3.dat" );
integrate_adaptive( dopri5 , rhs2 , x , t , t_end , dt , write_out );
out.precision(16);
integrate_adaptive( dopri5 , rhs , x , t , t_end , dt , write_out );
out.close();
}

19
libs/numeric/odeint/examples/elliptic.py Normal file
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@@ -0,0 +1,19 @@
from pylab import *
from scipy import special
data1 = loadtxt("elliptic1.dat")
data2 = loadtxt("elliptic2.dat")
data3 = loadtxt("elliptic3.dat")
sn1,cn1,dn1,phi1 = special.ellipj( data1[:,0] , 0.51 )
sn2,cn2,dn2,phi2 = special.ellipj( data2[:,0] , 0.51 )
sn3,cn3,dn3,phi3 = special.ellipj( data3[:,0] , 0.51 )
semilogy( data1[:,0] , abs(data1[:,1]-sn1) )
semilogy( data2[:,0] , abs(data2[:,1]-sn2) , 'ro' )
semilogy( data3[:,0] , abs(data3[:,1]-sn3) , '--' )
show()

21
libs/numeric/odeint/examples/elliptic_functions.cpp
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@@ -27,14 +27,16 @@ typedef boost::array< double , 3 > state_type;
/*
* x1' = x2*x3
* x2' = -x1*x3
* x3' = -0.51*x1*x2
* x3' = -m*x1*x2
*/
void rhs( const state_type &x , state_type &dxdt , const double t )
{
static const double m = 0.51;
dxdt[0] = x[1]*x[2];
dxdt[1] = -x[0]*x[2];
dxdt[2] = -0.51*x[0]*x[1];
dxdt[2] = -m*x[0]*x[1];
}
ofstream out;
@@ -46,32 +48,35 @@ void write_out( const state_type &x , const double t )
int main()
{
bulirsch_stoer_dense_out< state_type > stepper( 1E-10 , 1E-10 , 1.0 , 0.0 );
bulirsch_stoer_dense_out< state_type > stepper( 1E-9 , 1E-9 , 1.0 , 0.0 );
state_type x1 = {{ 0.0 , 1.0 , 1.0 }};
double t = 0.0;
double dt = 0.1;
double dt = 0.01;
out.open( "elliptic1.dat" );
integrate_const( stepper , rhs , x1 , t , 10.0 , dt , write_out );
out.precision(16);
integrate_const( stepper , rhs , x1 , t , 100.0 , dt , write_out );
out.close();
state_type x2 = {{ 0.0 , 1.0 , 1.0 }};
out.open( "elliptic2.dat" );
integrate_adaptive( stepper , rhs , x2 , t , 10.0 , dt , write_out );
out.precision(16);
integrate_adaptive( stepper , rhs , x2 , t , 100.0 , dt , write_out );
out.close();
typedef runge_kutta_dopri5< state_type > dopri5_type;
typedef controlled_error_stepper< dopri5_type > controlled_dopri5_type;
typedef dense_output_controlled_explicit_fsal< controlled_dopri5_type > dense_output_dopri5_type;
dense_output_dopri5_type dopri5( controlled_dopri5_type( dopri5_type() , default_error_checker< double >( 1E-10 , 0.0 , 0.0 , 0.0 ) ) );
dense_output_dopri5_type dopri5( controlled_dopri5_type( dopri5_type() , default_error_checker< double >( 1E-9 , 0.0 , 0.0 , 0.0 ) ) );
state_type x3 = {{ 0.0 , 1.0 , 1.0 }};
out.open( "elliptic3.dat" );
integrate_adaptive( dopri5 , rhs , x3 , t , 10.0 , dt , write_out );
out.precision(16);
integrate_adaptive( dopri5 , rhs , x3 , t , 100.0 , dt , write_out );
out.close();
}