1 /*
2  [auto_generated]
3  boost/numeric/odeint/stepper/rosenbrock4.hpp
4 
5  [begin_description]
6  Implementation of the Rosenbrock 4 method for solving stiff ODEs. Note, that a
7  controller and a dense-output stepper exist for this method,
8  [end_description]
9 
10  Copyright 2011-2013 Karsten Ahnert
11  Copyright 2011-2012 Mario Mulansky
12  Copyright 2012 Christoph Koke
13 
14  Distributed under the Boost Software License, Version 1.0.
15  (See accompanying file LICENSE_1_0.txt or
16  copy at http://www.boost.org/LICENSE_1_0.txt)
17  */
18 
19 
20 #ifndef BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
21 #define BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
22 
23 
24 #include <boost/numeric/odeint/util/bind.hpp>
25 #include <boost/numeric/odeint/util/unwrap_reference.hpp>
26 #include <boost/numeric/ublas/vector.hpp>
27 #include <boost/numeric/ublas/matrix.hpp>
28 #include <boost/numeric/ublas/lu.hpp>
29 
30 #include <boost/numeric/odeint/stepper/stepper_categories.hpp>
31 
32 #include <boost/numeric/odeint/util/ublas_wrapper.hpp>
33 #include <boost/numeric/odeint/util/is_resizeable.hpp>
34 #include <boost/numeric/odeint/util/resizer.hpp>
35 
36 #include <boost/numeric/ublas/vector.hpp>
37 #include <boost/numeric/ublas/matrix.hpp>
38 #include <boost/numeric/ublas/lu.hpp>
39 
40 
41 namespace boost {
42 namespace numeric {
43 namespace odeint {
44 
45 
46 /*
47  * ToDo:
48  *
49  * 2. Interfacing for odeint, check if controlled_error_stepper can be used
50  * 3. dense output
51  */
52 
53 
54 
55 template< class Value >
56 struct default_rosenbrock_coefficients
57 {
58     typedef Value value_type;
59     typedef unsigned short order_type;
60 
default_rosenbrock_coefficientsboost::numeric::odeint::default_rosenbrock_coefficients61     default_rosenbrock_coefficients( void )
62     : gamma ( static_cast< value_type >( 0.25 ) ) ,
63       d1 ( static_cast< value_type >( 0.25 ) ) ,
64       d2 ( static_cast< value_type >( -0.1043 ) ) ,
65       d3 ( static_cast< value_type >( 0.1035 ) ) ,
66       d4 ( static_cast< value_type >( 0.3620000000000023e-01 ) ) ,
67       c2 ( static_cast< value_type >( 0.386 ) ) ,
68       c3 ( static_cast< value_type >( 0.21 ) ) ,
69       c4 ( static_cast< value_type >( 0.63 ) ) ,
70       c21 ( static_cast< value_type >( -0.5668800000000000e+01 ) ) ,
71       a21 ( static_cast< value_type >( 0.1544000000000000e+01 ) ) ,
72       c31 ( static_cast< value_type >( -0.2430093356833875e+01 ) ) ,
73       c32 ( static_cast< value_type >( -0.2063599157091915e+00 ) ) ,
74       a31 ( static_cast< value_type >( 0.9466785280815826e+00 ) ) ,
75       a32 ( static_cast< value_type >( 0.2557011698983284e+00 ) ) ,
76       c41 ( static_cast< value_type >( -0.1073529058151375e+00 ) ) ,
77       c42 ( static_cast< value_type >( -0.9594562251023355e+01 ) ) ,
78       c43 ( static_cast< value_type >( -0.2047028614809616e+02 ) ) ,
79       a41 ( static_cast< value_type >( 0.3314825187068521e+01 ) ) ,
80       a42 ( static_cast< value_type >( 0.2896124015972201e+01 ) ) ,
81       a43 ( static_cast< value_type >( 0.9986419139977817e+00 ) ) ,
82       c51 ( static_cast< value_type >( 0.7496443313967647e+01 ) ) ,
83       c52 ( static_cast< value_type >( -0.1024680431464352e+02 ) ) ,
84       c53 ( static_cast< value_type >( -0.3399990352819905e+02 ) ) ,
85       c54 ( static_cast< value_type >(  0.1170890893206160e+02 ) ) ,
86       a51 ( static_cast< value_type >( 0.1221224509226641e+01 ) ) ,
87       a52 ( static_cast< value_type >( 0.6019134481288629e+01 ) ) ,
88       a53 ( static_cast< value_type >( 0.1253708332932087e+02 ) ) ,
89       a54 ( static_cast< value_type >( -0.6878860361058950e+00 ) ) ,
90       c61 ( static_cast< value_type >( 0.8083246795921522e+01 ) ) ,
91       c62 ( static_cast< value_type >( -0.7981132988064893e+01 ) ) ,
92       c63 ( static_cast< value_type >( -0.3152159432874371e+02 ) ) ,
93       c64 ( static_cast< value_type >( 0.1631930543123136e+02 ) ) ,
94       c65 ( static_cast< value_type >( -0.6058818238834054e+01 ) ) ,
95       d21 ( static_cast< value_type >( 0.1012623508344586e+02 ) ) ,
96       d22 ( static_cast< value_type >( -0.7487995877610167e+01 ) ) ,
97       d23 ( static_cast< value_type >( -0.3480091861555747e+02 ) ) ,
98       d24 ( static_cast< value_type >( -0.7992771707568823e+01 ) ) ,
99       d25 ( static_cast< value_type >( 0.1025137723295662e+01 ) ) ,
100       d31 ( static_cast< value_type >( -0.6762803392801253e+00 ) ) ,
101       d32 ( static_cast< value_type >( 0.6087714651680015e+01 ) ) ,
102       d33 ( static_cast< value_type >( 0.1643084320892478e+02 ) ) ,
103       d34 ( static_cast< value_type >( 0.2476722511418386e+02 ) ) ,
104       d35 ( static_cast< value_type >( -0.6594389125716872e+01 ) )
105     {}
106 
107     const value_type gamma;
108     const value_type d1 , d2 , d3 , d4;
109     const value_type c2 , c3 , c4;
110     const value_type c21 ;
111     const value_type a21;
112     const value_type c31 , c32;
113     const value_type a31 , a32;
114     const value_type c41 , c42 , c43;
115     const value_type a41 , a42 , a43;
116     const value_type c51 , c52 , c53 , c54;
117     const value_type a51 , a52 , a53 , a54;
118     const value_type c61 , c62 , c63 , c64 , c65;
119     const value_type d21 , d22 , d23 , d24 , d25;
120     const value_type d31 , d32 , d33 , d34 , d35;
121 
122     static const order_type stepper_order = 4;
123     static const order_type error_order = 3;
124 };
125 
126 
127 
128 template< class Value , class Coefficients = default_rosenbrock_coefficients< Value > , class Resizer = initially_resizer >
129 class rosenbrock4
130 {
131 private:
132 
133 public:
134 
135     typedef Value value_type;
136     typedef boost::numeric::ublas::vector< value_type > state_type;
137     typedef state_type deriv_type;
138     typedef value_type time_type;
139     typedef boost::numeric::ublas::matrix< value_type > matrix_type;
140     typedef boost::numeric::ublas::permutation_matrix< size_t > pmatrix_type;
141     typedef Resizer resizer_type;
142     typedef Coefficients rosenbrock_coefficients;
143     typedef stepper_tag stepper_category;
144     typedef unsigned short order_type;
145 
146     typedef state_wrapper< state_type > wrapped_state_type;
147     typedef state_wrapper< deriv_type > wrapped_deriv_type;
148     typedef state_wrapper< matrix_type > wrapped_matrix_type;
149     typedef state_wrapper< pmatrix_type > wrapped_pmatrix_type;
150 
151     typedef rosenbrock4< Value , Coefficients , Resizer > stepper_type;
152 
153     const static order_type stepper_order = rosenbrock_coefficients::stepper_order;
154     const static order_type error_order = rosenbrock_coefficients::error_order;
155 
rosenbrock4(void)156     rosenbrock4( void )
157     : m_resizer() , m_x_err_resizer() ,
158       m_jac() , m_pm() ,
159       m_dfdt() , m_dxdt() , m_dxdtnew() ,
160       m_g1() , m_g2() , m_g3() , m_g4() , m_g5() ,
161       m_cont3() , m_cont4() , m_xtmp() , m_x_err() ,
162       m_coef()
163     { }
164 
165 
order() const166     order_type order() const { return stepper_order; }
167 
168     template< class System >
do_step(System system,const state_type & x,time_type t,state_type & xout,time_type dt,state_type & xerr)169     void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt , state_type &xerr )
170     {
171         // get the system and jacobi function
172         typedef typename odeint::unwrap_reference< System >::type system_type;
173         typedef typename odeint::unwrap_reference< typename system_type::first_type >::type deriv_func_type;
174         typedef typename odeint::unwrap_reference< typename system_type::second_type >::type jacobi_func_type;
175         system_type &sys = system;
176         deriv_func_type &deriv_func = sys.first;
177         jacobi_func_type &jacobi_func = sys.second;
178 
179         const size_t n = x.size();
180 
181         m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<state_type> , detail::ref( *this ) , detail::_1 ) );
182 
183         for( size_t i=0 ; i<n ; ++i )
184             m_pm.m_v( i ) = i;
185 
186         deriv_func( x , m_dxdt.m_v , t );
187         jacobi_func( x , m_jac.m_v , t , m_dfdt.m_v );
188 
189         m_jac.m_v *= -1.0;
190         m_jac.m_v += 1.0 / m_coef.gamma / dt * boost::numeric::ublas::identity_matrix< value_type >( n );
191         boost::numeric::ublas::lu_factorize( m_jac.m_v , m_pm.m_v );
192 
193         for( size_t i=0 ; i<n ; ++i )
194             m_g1.m_v[i] = m_dxdt.m_v[i] + dt * m_coef.d1 * m_dfdt.m_v[i];
195         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g1.m_v );
196 
197 
198         for( size_t i=0 ; i<n ; ++i )
199             m_xtmp.m_v[i] = x[i] + m_coef.a21 * m_g1.m_v[i];
200         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c2 * dt );
201         for( size_t i=0 ; i<n ; ++i )
202             m_g2.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d2 * m_dfdt.m_v[i] + m_coef.c21 * m_g1.m_v[i] / dt;
203         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g2.m_v );
204 
205 
206         for( size_t i=0 ; i<n ; ++i )
207             m_xtmp.m_v[i] = x[i] + m_coef.a31 * m_g1.m_v[i] + m_coef.a32 * m_g2.m_v[i];
208         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c3 * dt );
209         for( size_t i=0 ; i<n ; ++i )
210             m_g3.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d3 * m_dfdt.m_v[i] + ( m_coef.c31 * m_g1.m_v[i] + m_coef.c32 * m_g2.m_v[i] ) / dt;
211         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g3.m_v );
212 
213 
214         for( size_t i=0 ; i<n ; ++i )
215             m_xtmp.m_v[i] = x[i] + m_coef.a41 * m_g1.m_v[i] + m_coef.a42 * m_g2.m_v[i] + m_coef.a43 * m_g3.m_v[i];
216         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + m_coef.c4 * dt );
217         for( size_t i=0 ; i<n ; ++i )
218             m_g4.m_v[i] = m_dxdtnew.m_v[i] + dt * m_coef.d4 * m_dfdt.m_v[i] + ( m_coef.c41 * m_g1.m_v[i] + m_coef.c42 * m_g2.m_v[i] + m_coef.c43 * m_g3.m_v[i] ) / dt;
219         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g4.m_v );
220 
221 
222         for( size_t i=0 ; i<n ; ++i )
223             m_xtmp.m_v[i] = x[i] + m_coef.a51 * m_g1.m_v[i] + m_coef.a52 * m_g2.m_v[i] + m_coef.a53 * m_g3.m_v[i] + m_coef.a54 * m_g4.m_v[i];
224         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt );
225         for( size_t i=0 ; i<n ; ++i )
226             m_g5.m_v[i] = m_dxdtnew.m_v[i] + ( m_coef.c51 * m_g1.m_v[i] + m_coef.c52 * m_g2.m_v[i] + m_coef.c53 * m_g3.m_v[i] + m_coef.c54 * m_g4.m_v[i] ) / dt;
227         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , m_g5.m_v );
228 
229         for( size_t i=0 ; i<n ; ++i )
230             m_xtmp.m_v[i] += m_g5.m_v[i];
231         deriv_func( m_xtmp.m_v , m_dxdtnew.m_v , t + dt );
232         for( size_t i=0 ; i<n ; ++i )
233             xerr[i] = m_dxdtnew.m_v[i] + ( m_coef.c61 * m_g1.m_v[i] + m_coef.c62 * m_g2.m_v[i] + m_coef.c63 * m_g3.m_v[i] + m_coef.c64 * m_g4.m_v[i] + m_coef.c65 * m_g5.m_v[i] ) / dt;
234         boost::numeric::ublas::lu_substitute( m_jac.m_v , m_pm.m_v , xerr );
235 
236         for( size_t i=0 ; i<n ; ++i )
237             xout[i] = m_xtmp.m_v[i] + xerr[i];
238     }
239 
240     template< class System >
do_step(System system,state_type & x,time_type t,time_type dt,state_type & xerr)241     void do_step( System system , state_type &x , time_type t , time_type dt , state_type &xerr )
242     {
243         do_step( system , x , t , x , dt , xerr );
244     }
245 
246     /*
247      * do_step without error output - just calls above functions with and neglects the error estimate
248      */
249     template< class System >
do_step(System system,const state_type & x,time_type t,state_type & xout,time_type dt)250     void do_step( System system , const state_type &x , time_type t , state_type &xout , time_type dt )
251     {
252         m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) );
253         do_step( system , x , t , xout , dt , m_x_err.m_v );
254     }
255 
256     template< class System >
do_step(System system,state_type & x,time_type t,time_type dt)257     void do_step( System system , state_type &x , time_type t , time_type dt )
258     {
259         m_x_err_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_x_err<state_type> , detail::ref( *this ) , detail::_1 ) );
260         do_step( system , x , t , dt , m_x_err.m_v );
261     }
262 
prepare_dense_output()263     void prepare_dense_output()
264     {
265         const size_t n = m_g1.m_v.size();
266         for( size_t i=0 ; i<n ; ++i )
267         {
268             m_cont3.m_v[i] = m_coef.d21 * m_g1.m_v[i] + m_coef.d22 * m_g2.m_v[i] + m_coef.d23 * m_g3.m_v[i] + m_coef.d24 * m_g4.m_v[i] + m_coef.d25 * m_g5.m_v[i];
269             m_cont4.m_v[i] = m_coef.d31 * m_g1.m_v[i] + m_coef.d32 * m_g2.m_v[i] + m_coef.d33 * m_g3.m_v[i] + m_coef.d34 * m_g4.m_v[i] + m_coef.d35 * m_g5.m_v[i];
270         }
271     }
272 
273 
calc_state(time_type t,state_type & x,const state_type & x_old,time_type t_old,const state_type & x_new,time_type t_new)274     void calc_state( time_type t , state_type &x ,
275             const state_type &x_old , time_type t_old ,
276             const state_type &x_new , time_type t_new )
277     {
278         const size_t n = m_g1.m_v.size();
279         time_type dt = t_new - t_old;
280         time_type s = ( t - t_old ) / dt;
281         time_type s1 = 1.0 - s;
282         for( size_t i=0 ; i<n ; ++i )
283             x[i] = x_old[i] * s1 + s * ( x_new[i] + s1 * ( m_cont3.m_v[i] + s * m_cont4.m_v[i] ) );
284     }
285 
286 
287 
288     template< class StateType >
adjust_size(const StateType & x)289     void adjust_size( const StateType &x )
290     {
291         resize_impl( x );
292         resize_x_err( x );
293     }
294 
295 
296 protected:
297 
298     template< class StateIn >
resize_impl(const StateIn & x)299     bool resize_impl( const StateIn &x )
300     {
301         bool resized = false;
302         resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
303         resized |= adjust_size_by_resizeability( m_dfdt , x , typename is_resizeable<deriv_type>::type() );
304         resized |= adjust_size_by_resizeability( m_dxdtnew , x , typename is_resizeable<deriv_type>::type() );
305         resized |= adjust_size_by_resizeability( m_xtmp , x , typename is_resizeable<state_type>::type() );
306         resized |= adjust_size_by_resizeability( m_g1 , x , typename is_resizeable<state_type>::type() );
307         resized |= adjust_size_by_resizeability( m_g2 , x , typename is_resizeable<state_type>::type() );
308         resized |= adjust_size_by_resizeability( m_g3 , x , typename is_resizeable<state_type>::type() );
309         resized |= adjust_size_by_resizeability( m_g4 , x , typename is_resizeable<state_type>::type() );
310         resized |= adjust_size_by_resizeability( m_g5 , x , typename is_resizeable<state_type>::type() );
311         resized |= adjust_size_by_resizeability( m_cont3 , x , typename is_resizeable<state_type>::type() );
312         resized |= adjust_size_by_resizeability( m_cont4 , x , typename is_resizeable<state_type>::type() );
313         resized |= adjust_size_by_resizeability( m_jac , x , typename is_resizeable<matrix_type>::type() );
314         resized |= adjust_size_by_resizeability( m_pm , x , typename is_resizeable<pmatrix_type>::type() );
315         return resized;
316     }
317 
318     template< class StateIn >
resize_x_err(const StateIn & x)319     bool resize_x_err( const StateIn &x )
320     {
321         return adjust_size_by_resizeability( m_x_err , x , typename is_resizeable<state_type>::type() );
322     }
323 
324 private:
325 
326 
327     resizer_type m_resizer;
328     resizer_type m_x_err_resizer;
329 
330     wrapped_matrix_type m_jac;
331     wrapped_pmatrix_type m_pm;
332     wrapped_deriv_type m_dfdt , m_dxdt , m_dxdtnew;
333     wrapped_state_type m_g1 , m_g2 , m_g3 , m_g4 , m_g5;
334     wrapped_state_type m_cont3 , m_cont4;
335     wrapped_state_type m_xtmp;
336     wrapped_state_type m_x_err;
337 
338     const rosenbrock_coefficients m_coef;
339 };
340 
341 
342 } // namespace odeint
343 } // namespace numeric
344 } // namespace boost
345 
346 #endif // BOOST_NUMERIC_ODEINT_STEPPER_ROSENBROCK4_HPP_INCLUDED
347