1 | /* Boost numeric test of the adams-bashforth steppers test file |
2 | |
3 | Copyright 2013 Karsten Ahnert |
4 | Copyright 2013-2015 Mario Mulansky |
5 | |
6 | Distributed under the Boost Software License, Version 1.0. |
7 | (See accompanying file LICENSE_1_0.txt or |
8 | copy at http://www.boost.org/LICENSE_1_0.txt) |
9 | */ |
10 | |
11 | // disable checked iterator warning for msvc |
12 | #include <boost/config.hpp> |
13 | #ifdef BOOST_MSVC |
14 | #pragma warning(disable:4996) |
15 | #endif |
16 | |
17 | #define BOOST_TEST_MODULE numeric_adams_bashforth |
18 | |
19 | #include <iostream> |
20 | #include <cmath> |
21 | |
22 | #include <array> |
23 | |
24 | #include <boost/test/unit_test.hpp> |
25 | |
26 | #include <boost/mpl/vector.hpp> |
27 | |
28 | #include <boost/numeric/odeint.hpp> |
29 | |
30 | using namespace boost::unit_test; |
31 | using namespace boost::numeric::odeint; |
32 | namespace mpl = boost::mpl; |
33 | |
34 | typedef double value_type; |
35 | |
36 | typedef std::array< double , 2 > state_type; |
37 | |
38 | // harmonic oscillator, analytic solution x[0] = sin( t ) |
39 | struct osc |
40 | { |
41 | void operator()( const state_type &x , state_type &dxdt , const double t ) const |
42 | { |
43 | dxdt[0] = x[1]; |
44 | dxdt[1] = -x[0]; |
45 | } |
46 | }; |
47 | |
48 | BOOST_AUTO_TEST_SUITE( numeric_adams_bashforth_test ) |
49 | |
50 | |
51 | /* generic test for all adams bashforth steppers */ |
52 | template< class Stepper > |
53 | struct perform_adams_bashforth_test |
54 | { |
55 | void operator()( void ) |
56 | { |
57 | Stepper stepper; |
58 | const int o = stepper.order()+1; //order of the error is order of approximation + 1 |
59 | |
60 | const state_type x0 = {._M_elems: { 0.0 , 1.0 }}; |
61 | state_type x1 = x0; |
62 | double t = 0.0; |
63 | double dt = 0.2; |
64 | // initialization, does a number of steps already to fill internal buffer, t is increased |
65 | stepper.initialize( osc() , x1 , t , dt ); |
66 | double A = std::sqrt( x: x1[0]*x1[0] + x1[1]*x1[1] ); |
67 | double phi = std::asin(x: x1[0]/A) - t; |
68 | // do a number of steps to fill the buffer with results from adams bashforth |
69 | for( size_t n=0 ; n < stepper.steps ; ++n ) |
70 | { |
71 | stepper.do_step( osc() , x1 , t , dt ); |
72 | t += dt; |
73 | } |
74 | // now we do the actual step |
75 | stepper.do_step( osc() , x1 , t , dt ); |
76 | // only examine the error of the adams-bashforth step, not the initialization |
77 | const double f = 2.0 * std::abs( x: A*sin(x: t+dt+phi) - x1[0] ) / std::pow( x: dt , y: o ); // upper bound |
78 | |
79 | std::cout << o << " , " |
80 | << Stepper::initializing_stepper_type::order_value+1 << " , " |
81 | << f << std::endl; |
82 | |
83 | /* as long as we have errors above machine precision */ |
84 | while( f*std::pow( x: dt , y: o ) > 1E-16 ) |
85 | { |
86 | x1 = x0; |
87 | t = 0.0; |
88 | stepper.initialize( osc() , x1 , t , dt ); |
89 | A = std::sqrt( x: x1[0]*x1[0] + x1[1]*x1[1] ); |
90 | phi = std::asin(x: x1[0]/A) - t; |
91 | // now we do the actual step |
92 | stepper.do_step( osc() , x1 , t , dt ); |
93 | // only examine the error of the adams-bashforth step, not the initialization |
94 | std::cout << "Testing dt=" << dt << " , " << std::abs( x: A*sin(x: t+dt+phi) - x1[0] ) << std::endl; |
95 | BOOST_CHECK_LT( std::abs( A*sin(t+dt+phi) - x1[0] ) , f*std::pow( dt , o ) ); |
96 | dt *= 0.5; |
97 | } |
98 | } |
99 | }; |
100 | |
101 | typedef mpl::vector< |
102 | adams_bashforth< 2 , state_type > , |
103 | adams_bashforth< 3 , state_type > , |
104 | adams_bashforth< 4 , state_type > , |
105 | adams_bashforth< 5 , state_type > , |
106 | adams_bashforth< 6 , state_type > , |
107 | adams_bashforth< 7 , state_type > , |
108 | adams_bashforth< 8 , state_type > |
109 | > adams_bashforth_steppers; |
110 | |
111 | BOOST_AUTO_TEST_CASE_TEMPLATE( adams_bashforth_test , Stepper, adams_bashforth_steppers ) |
112 | { |
113 | perform_adams_bashforth_test< Stepper > tester; |
114 | tester(); |
115 | } |
116 | |
117 | BOOST_AUTO_TEST_SUITE_END() |
118 | |