odeint streaming observer and related questions - numerical-methods

Question

I have a system of 4 coupled equations to solve and a parameter Gamma[i] to iterate over. Since I am quite new to C++, my code is a very rudimentary. If it looks sophisticated and elegant in certain parts, it is only because I have adapted code from the author of odeint. :)
This question is related to (http://stackoverflow.com/questions/12060111/using-odeint-function-definition/12066958#comment16253600_12066958) but not exactly the same. Please do not delete this. :(
Questions have been inserted between the lines of code.
#include <iostream>
#include <iterator>
#include <algorithm>
#include <boost/numeric/odeint.hpp>
#include <cmath>
#include <vector>
#include <fstream>
#include <iomanip>
using namespace std;
using namespace boost::numeric::odeint;
class NLI_class {
private:
double gamma;
public:
NLI_class (double r) : gamma(r) {}
void operator()( vector<double> &u , vector<double> &du , double z ) {
du[0] = u[0]*u[1]*cos(u[3]); //u1
du[1] = -u[0]*u[0]*cos(u[3]); //u2
du[2] = gamma * (2/(u[0]*u[0]) - 1/(u[1]*u[1])); //theta
du[3] = gamma * (1.0/(u[0]*u[0])); //phi1
du[4] = gamma * (1.0/(u[1]*u[1])); //phi2;
}
};
Question #1:
In my original program, I had something like this to pipe the output to a csv file:
inline void save(vector<double>& v, string filename)
{
ofstream output(filename);
for(int i=0;i<v.size();++i){
output << setprecision(64) << v[i] << endl;
}
}
How do I adapt streaming_observer to do what my save() does? Basically, I want to generate .csv files for each iteration i. At this point, I am doing it the ugly way, i.e compiling everything, opening a windows command prompt and then piping the exe output to a text file. This generates one big file with all iterations thrown in there.
This becomes very painful to analyze for a large number of iterations.
struct streaming_observer {
std::ostream &m_out;
streaming_observer( std::ostream &out ) : m_out( out ) {}
void operator()( const vector<double> &x , double t ) const
{
m_out << t;
for( size_t i=0 ; i < x.size() ; ++i )
m_out << "\t" << x[i];
m_out << "\n";
}
};
int main(){
vector<double> x( 5 );
vector<double> Gamma;
vector<double>delta;
const double pi=acos(-1.0);
short delta_n=5;
const double delta_step=(2*pi)/delta_n;
const double dz = 0.01;
const double zeta = 3.0;
const double theta_initial=0.0;
const double u20=tanh(zeta);
const double u10=sqrt(1.0-(u20*u20));
double d=0.0;
double G=0.0;
for(int i=0;i<=delta_n;i++){
//When i=0, the d=0.0 and G=0.0 are pushed into the vector.
delta.push_back(d);
Gamma.push_back(G);
// Compute delta and Gamma
d=d+delta_step;
G=-u10*u10*u20*sin(theta_initial+d);
}
save(delta,"delta.csv");
save(Gamma,"Gamma.csv");
Question#2:
The results I get here do not agree with what I get with what I get using a simple explicit Euler method. Hence, I would like to see the RK4 coefficients (preferably dump them to a file) or the intermediate steps. How can I get this information?
//Numeric Integration
for (unsigned i = 0; i < Gamma.size(); ++i) {
x[0] = u10;
x[1] = u20;
x[2] = 0.0;
x[3] = 0.0;
x[4] = 0.0;
NLI_class nli_obj(Gamma[i]);
integrate_const( runge_kutta4< vector<double > >(), nli_obj, x , 0.0 , 3.0 , dz,streaming_observer( std::cout ) );
}
}
Thank you for all those who helped!
Edit:
Is there some way to get a running error estimate? Note that u[0]*u[0]+u[1]*u[1]=1 at all times.

Answer 1

Question #1 :
I do not understand exactly what kind of output you need. But if you want to write the result after each iteration you can implement an output observer like this:
struct output_observer
{
string filename_;
size_t count_;
output_observer( const string &filename ) : filename_( filename ) , count_( 0 ) { }
void operator()( const state_type &x , time_type dt )
{
char fn[512] = "";
sprintf( fn , "%s_%04lu.csv" , filename_.c_str() , count_ );
ofstream fout( fn );
for( size_t i=0 ; i<x.size() ; ++i ) fout << x[i] << "\n";
++count_;
}
};
You can apply this observer simply by
integrate_const( runge_kutta4< vector<double > >() , nli_obj , x ,
0.0 , 3.0 , dz , output_observer( "filename" ) );
Is this the desired functionality?
Question #2 :
It is not possible to see the intermediate e steps of runge_kutta4. The coefficients are the standard ones for the classical Runge-Kutta method: http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
Question #3 :
odeint has several error steppers, which estimate the error made during one step. You can use for example the Runge_Kutta Cash Karp algorithm;
runge_kutta_cash_karp54< state_type > rk;
state_type xerr;
rk.do_step( nli_obj , x , t , xerr );
which makes ONE step and estimates the error and writes the error result in xerr.