1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
|
/*
* fpu.cpp
*
* This example demonstrates how one can use odeint to solve the Fermi-Pasta-Ulam system.
* Created on: July 13, 2011
*
* Copyright 2011-2012 Karsten Ahnert
* Copyright 2011 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 <numeric>
#include <cmath>
#include <vector>
#include <boost/numeric/odeint.hpp>
#ifndef M_PI //not there on windows
#define M_PI 3.1415927 //...
#endif
using namespace std;
using namespace boost::numeric::odeint;
//[ fpu_system_function
typedef vector< double > container_type;
struct fpu
{
const double m_beta;
fpu( const double beta = 1.0 ) : m_beta( beta ) { }
// system function defining the ODE
void operator()( const container_type &q , container_type &dpdt ) const
{
size_t n = q.size();
double tmp = q[0] - 0.0;
double tmp2 = tmp + m_beta * tmp * tmp * tmp;
dpdt[0] = -tmp2;
for( size_t i=0 ; i<n-1 ; ++i )
{
tmp = q[i+1] - q[i];
tmp2 = tmp + m_beta * tmp * tmp * tmp;
dpdt[i] += tmp2;
dpdt[i+1] = -tmp2;
}
tmp = - q[n-1];
tmp2 = tmp + m_beta * tmp * tmp * tmp;
dpdt[n-1] += tmp2;
}
// calculates the energy of the system
double energy( const container_type &q , const container_type &p ) const
{
// ...
//<-
double energy = 0.0;
size_t n = q.size();
double tmp = q[0];
energy += 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
for( size_t i=0 ; i<n-1 ; ++i )
{
tmp = q[i+1] - q[i];
energy += 0.5 * ( p[i] * p[i] + tmp * tmp ) + 0.25 * m_beta * tmp * tmp * tmp * tmp;
}
energy += 0.5 * p[n-1] * p[n-1];
tmp = q[n-1];
energy += 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
return energy;
//->
}
// calculates the local energy of the system
void local_energy( const container_type &q , const container_type &p , container_type &e ) const
{
// ...
//<-
size_t n = q.size();
double tmp = q[0];
double tmp2 = 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
e[0] = tmp2;
for( size_t i=0 ; i<n-1 ; ++i )
{
tmp = q[i+1] - q[i];
tmp2 = 0.25 * tmp * tmp + 0.125 * m_beta * tmp * tmp * tmp * tmp;
e[i] += 0.5 * p[i] * p[i] + tmp2 ;
e[i+1] = tmp2;
}
tmp = q[n-1];
tmp2 = 0.5 * tmp * tmp + 0.25 * m_beta * tmp * tmp * tmp * tmp;
e[n-1] += 0.5 * p[n-1] * p[n-1] + tmp2;
//->
}
};
//]
//[ fpu_observer
struct streaming_observer
{
std::ostream& m_out;
const fpu &m_fpu;
size_t m_write_every;
size_t m_count;
streaming_observer( std::ostream &out , const fpu &f , size_t write_every = 100 )
: m_out( out ) , m_fpu( f ) , m_write_every( write_every ) , m_count( 0 ) { }
template< class State >
void operator()( const State &x , double t )
{
if( ( m_count % m_write_every ) == 0 )
{
container_type &q = x.first;
container_type &p = x.second;
container_type energy( q.size() );
m_fpu.local_energy( q , p , energy );
for( size_t i=0 ; i<q.size() ; ++i )
{
m_out << t << "\t" << i << "\t" << q[i] << "\t" << p[i] << "\t" << energy[i] << "\n";
}
m_out << "\n";
clog << t << "\t" << accumulate( energy.begin() , energy.end() , 0.0 ) << "\n";
}
++m_count;
}
};
//]
int main( int argc , char **argv )
{
//[ fpu_integration
const size_t n = 64;
container_type q( n , 0.0 ) , p( n , 0.0 );
for( size_t i=0 ; i<n ; ++i )
{
p[i] = 0.0;
q[i] = 32.0 * sin( double( i + 1 ) / double( n + 1 ) * M_PI );
}
const double dt = 0.1;
typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
fpu fpu_instance( 8.0 );
integrate_const( stepper_type() , fpu_instance ,
make_pair( boost::ref( q ) , boost::ref( p ) ) ,
0.0 , 1000.0 , dt , streaming_observer( cout , fpu_instance , 10 ) );
//]
return 0;
}
|
