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/*
[auto_generated]
libs/numeric/odeint/test/step_size_limitation.cpp
[begin_description]
Tests the step size limitation functionality
[end_description]
Copyright 2015 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)
*/
#define BOOST_TEST_MODULE odeint_integrate_times
#include <boost/test/unit_test.hpp>
#include <utility>
#include <iostream>
#include <vector>
#include <boost/numeric/odeint.hpp>
using namespace boost::unit_test;
using namespace boost::numeric::odeint;
typedef double value_type;
typedef std::vector< value_type > state_type;
/***********************************************
* first part of the tests: explicit methods
***********************************************
*/
void damped_osc( const state_type &x , state_type &dxdt , const value_type t )
{
const value_type gam( 0.1);
dxdt[0] = x[1];
dxdt[1] = -x[0] - gam*x[1];
}
struct push_back_time
{
std::vector< double >& m_times;
push_back_time( std::vector< double > × )
: m_times( times ) { }
template<typename State>
void operator()( const State &x , double t )
{
m_times.push_back( t );
}
};
BOOST_AUTO_TEST_SUITE( step_size_limitation_test )
BOOST_AUTO_TEST_CASE( test_step_adjuster )
{
// first use adjuster without step size limitation
default_step_adjuster<double, double> step_adjuster;
const double dt = 0.1;
double dt_new = step_adjuster.decrease_step(dt, 1.5, 2);
BOOST_CHECK(dt_new < dt*2.0/3.0);
dt_new = step_adjuster.increase_step(dt, 0.8, 1);
// for errors > 0.5 no increase is performed
BOOST_CHECK(dt_new == dt);
dt_new = step_adjuster.increase_step(dt, 0.4, 1);
// smaller errors should lead to step size increase
std::cout << dt_new << std::endl;
BOOST_CHECK(dt_new > dt);
// now test with step size limitation max_dt = 0.1
default_step_adjuster<double, double>
limited_adjuster(dt);
dt_new = limited_adjuster.decrease_step(dt, 1.5, 2);
// decreasing works as before
BOOST_CHECK(dt_new < dt*2.0/3.0);
dt_new = limited_adjuster.decrease_step(2*dt, 1.1, 2);
// decreasing a large step size should give max_dt
BOOST_CHECK(dt_new == dt);
dt_new = limited_adjuster.increase_step(dt, 0.8, 1);
// for errors > 0.5 no increase is performed, still valid
BOOST_CHECK(dt_new == dt);
dt_new = limited_adjuster.increase_step(dt, 0.4, 1);
// but even for smaller errors, we should at most get 0.1
BOOST_CHECK_EQUAL(dt_new, dt);
dt_new = limited_adjuster.increase_step(0.9*dt, 0.1, 1);
std::cout << dt_new << std::endl;
// check that we don't increase beyond max_dt
BOOST_CHECK(dt_new == dt);
}
template<class Stepper>
void test_explicit_stepper(Stepper stepper, const double max_dt)
{
state_type x( 2 );
x[0] = x[1] = 10.0;
const size_t steps = 100;
std::vector<double> times;
integrate_adaptive(stepper, damped_osc, x, 0.0, steps*max_dt, max_dt, push_back_time(times));
BOOST_CHECK_EQUAL(times.size(), steps+1);
// check that dt remains at exactly max_dt
for( size_t i=0 ; i<times.size() ; ++i )
// check if observer was called at times 0,1,2,...
BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
times.clear();
// this should also work when we provide some bigger initial dt
integrate_adaptive(stepper, damped_osc, x, 0.0, steps*max_dt, 10*max_dt, push_back_time(times));
BOOST_CHECK_EQUAL(times.size(), steps+1);
// check that dt remains at exactly max_dt
for( size_t i=0 ; i<times.size() ; ++i )
// check if observer was called at times 0,1,2,...
BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
times.clear();
}
BOOST_AUTO_TEST_CASE( test_controlled )
{
const double max_dt = 0.01;
test_explicit_stepper(make_controlled(1E-2, 1E-2, max_dt,
runge_kutta_dopri5<state_type>()),
max_dt);
test_explicit_stepper(make_controlled(1E-2, 1E-2, -max_dt,
runge_kutta_dopri5<state_type>()),
-max_dt);
test_explicit_stepper(make_controlled(1E-2, 1E-2, max_dt,
runge_kutta_cash_karp54<state_type>()),
max_dt);
test_explicit_stepper(make_controlled(1E-2, 1E-2, -max_dt,
runge_kutta_cash_karp54<state_type>()),
-max_dt);
test_explicit_stepper(bulirsch_stoer<state_type>(1E-2, 1E-2, 1.0, 1.0, max_dt),
max_dt);
test_explicit_stepper(bulirsch_stoer<state_type>(1E-2, 1E-2, 1.0, 1.0, -max_dt),
-max_dt);
}
BOOST_AUTO_TEST_CASE( test_dense_out )
{
const double max_dt = 0.01;
test_explicit_stepper(make_dense_output(1E-2, 1E-2, max_dt,
runge_kutta_dopri5<state_type>()),
max_dt);
test_explicit_stepper(make_dense_output(1E-2, 1E-2, -max_dt,
runge_kutta_dopri5<state_type>()),
-max_dt);
test_explicit_stepper(bulirsch_stoer_dense_out<state_type>(1E-2, 1E-2, 1, 1, max_dt),
max_dt);
test_explicit_stepper(bulirsch_stoer_dense_out<state_type>(1E-2, 1E-2, 1, 1, -max_dt),
-max_dt);
}
/***********************************************
* second part of the tests: implicit Rosenbrock
***********************************************
*/
typedef boost::numeric::ublas::vector< value_type > vector_type;
typedef boost::numeric::ublas::matrix< value_type > matrix_type;
// harmonic oscillator, analytic solution x[0] = sin( t )
struct osc_rhs
{
void operator()( const vector_type &x , vector_type &dxdt , const value_type &t ) const
{
dxdt( 0 ) = x( 1 );
dxdt( 1 ) = -x( 0 );
}
};
struct osc_jacobi
{
void operator()( const vector_type &x , matrix_type &jacobi , const value_type &t , vector_type &dfdt ) const
{
jacobi( 0 , 0 ) = 0;
jacobi( 0 , 1 ) = 1;
jacobi( 1 , 0 ) = -1;
jacobi( 1 , 1 ) = 0;
dfdt( 0 ) = 0.0;
dfdt( 1 ) = 0.0;
}
};
template<class Stepper>
void test_rosenbrock_stepper(Stepper stepper, const double max_dt)
{
vector_type x( 2 );
x(0) = x(1) = 10.0;
const size_t steps = 100;
std::vector<double> times;
integrate_adaptive(stepper,
std::make_pair(osc_rhs(), osc_jacobi()),
x, 0.0, steps*max_dt, max_dt, push_back_time(times));
BOOST_CHECK_EQUAL(times.size(), steps+1);
// check that dt remains at exactly max_dt
for( size_t i=0 ; i<times.size() ; ++i )
// check if observer was called at times 0,1,2,...
BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
times.clear();
// this should also work when we provide some bigger initial dt
integrate_adaptive(stepper,
std::make_pair(osc_rhs(), osc_jacobi()),
x, 0.0, steps*max_dt, 10*max_dt, push_back_time(times));
BOOST_CHECK_EQUAL(times.size(), steps+1);
// check that dt remains at exactly max_dt
for( size_t i=0 ; i<times.size() ; ++i )
// check if observer was called at times 0,1,2,...
BOOST_CHECK_SMALL( times[i] - static_cast<double>(i)*max_dt , 1E-15);
times.clear();
}
BOOST_AUTO_TEST_CASE( test_controlled_rosenbrock )
{
const double max_dt = 0.01;
test_rosenbrock_stepper(make_controlled(1E-2, 1E-2, max_dt, rosenbrock4<value_type>()),
max_dt);
test_rosenbrock_stepper(make_controlled(1E-2, 1E-2, -max_dt, rosenbrock4<value_type>()),
-max_dt);
}
BOOST_AUTO_TEST_CASE( test_dense_out_rosenbrock )
{
const double max_dt = 0.01;
test_rosenbrock_stepper(make_dense_output(1E-2, 1E-2, max_dt, rosenbrock4<value_type>()),
max_dt);
test_rosenbrock_stepper(make_dense_output(1E-2, 1E-2, -max_dt, rosenbrock4<value_type>()),
-max_dt);
}
BOOST_AUTO_TEST_SUITE_END()
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