Convenience
+
diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/state_types__algebras_and_operations.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/state_types__algebras_and_operations.html
index de6957c2..c3871cc3 100644
--- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/state_types__algebras_and_operations.html
+++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/state_types__algebras_and_operations.html
@@ -399,7 +399,6 @@
as resizeable as it is a dynamically sized array:
-
class my_vector : public std::vector< double >
{
@@ -534,7 +533,6 @@
specializations:
-
typedef std::list< double > state_type;
@@ -547,7 +545,7 @@
const static bool value = type::value;
};
-template< >
+template< >
struct same_size_impl< state_type , state_type >
{
static bool same_size( const state_type &v1 ,
@@ -567,7 +565,7 @@
}
};
-} } }
+} } }
@@ -627,7 +625,6 @@
instances of state types:
-
template<>
struct state_wrapper< gsl_vector* >
@@ -664,7 +661,7 @@
This state_wrapper
specialization tells odeint how gsl_vectors are created, copied and
destroyed. Next we need resizing, this is required because gsl_vectors
- are dynamically sized objects:
+ are dynamically sized objects:
template<>
struct is_resizeable< gsl_vector* >
@@ -699,13 +696,12 @@
support iterators, so we first implement a gsl iterator:
-
-class gsl_vector_iterator
- : public boost::iterator_facade< gsl_vector_iterator , double ,
+class gsl_vector_iterator
+ : public boost::iterator_facade< gsl_vector_iterator , double ,
boost::random_access_traversal_tag >
{
public :
@@ -734,7 +730,7 @@
A similar class exists for the const
version of the iterator. Then we have a function returning the end
iterator (similarily for const
- again):
+ again):
gsl_vector_iterator end_iterator( gsl_vector *x )
{
@@ -747,7 +743,7 @@
Finally, the bindings for Boost.Range
- are added:
+ are added:
inline gsl_vector_iterator range_begin( gsl_vector *x )
@@ -1061,7 +1057,6 @@
function so all that has to be done in this case is to declare resizability:
-
typedef boost::numeric::ublas::vector< double > state_type;
@@ -1085,7 +1080,6 @@
code shows the corresponding definitions:
-
int main()
{
@@ -1118,9 +1112,8 @@
type looks as follows:
-
-class point3D :
+class point3D :
boost::additive1< point3D ,
boost::additive2< point3D , double ,
boost::multiplicative2< point3D , double > > >
@@ -1132,7 +1125,7 @@
point3D()
: x( 0.0 ) , y( 0.0 ) , z( 0.0 )
{ }
-
+
point3D( const double val )
: x( val ) , y( val ) , z( val )
{ }
@@ -1173,7 +1166,6 @@
type:
-
point3D operator/( const point3D &p1 , const point3D &p2 )
@@ -1193,7 +1185,6 @@
implementing a reduction over the state type:
-
namespace boost { namespace numeric { namespace odeint {
@@ -1209,7 +1200,7 @@
return init;
}
};
-} } }
+} } }
@@ -1221,7 +1212,6 @@
easily perform the integration on a lorenz system by using the vector_space_algebra again:
-
const double sigma = 10.0;
const double R = 28.0;
@@ -1242,9 +1232,9 @@
point3D x( 10.0 , 5.0 , 5.0 );
- typedef runge_kutta_dopri5< point3D , double , point3D ,
+ typedef runge_kutta_dopri5< point3D , double , point3D ,
double , vector_space_algebra > stepper;
- integrate_adaptive( make_controlled<stepper>( 1E-8 , 1E-8 ) , lorenz , x ,
+ integrate_adaptive( make_controlled<stepper>( 1E-8 , 1E-8 ) , lorenz , x ,
0.0 , 10.0 , 0.1 );
std::cout << x << std::endl;
}
diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html
index 9f92349a..951f5431 100644
--- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html
+++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html
@@ -132,7 +132,6 @@
is the Runge Kutta stepper of fourth order:
-
runge_kutta4< state_type > rk;
rk.do_step( sys1 , inout , t , dt );
@@ -177,7 +176,6 @@
how the FSAL steppers can be used is
-
runge_kutta_dopri5< state_type > rk;
rk.do_step( sys1 , in , t , out , dt );
@@ -243,7 +241,6 @@
again simple C-functions of functors. An example is the harmonic oscillator:
-
typedef boost::array< double , 1 > vector_type;
@@ -272,7 +269,6 @@
example for the harmonic oscillator is now:
-
pair< vector_type , vector_type > x;
x.first[0] = 1.0; x.second[0] = 0.0;
@@ -286,7 +282,6 @@
two public method:
-
struct harm_osc
{
@@ -304,7 +299,6 @@
-
harm_osc h;
rkn.do_step( make_pair( boost::bind( &harm_osc::f1 , h , _1 , _2 ) , boost::bind( &harm_osc::f2 , h , _1 , _2 ) ) ,
@@ -324,7 +318,6 @@
can be written as
-
pair< vector_type , vector_type > x;
x.first[0] = 1.0; x.second[0] = 0.0;
@@ -348,7 +341,6 @@
takes q and p without combining them into a pair:
-
rkn.do_step( harm_osc_f1() , make_pair( boost::ref( q ) , boost::ref( p ) ) , t , dt );
rkn.do_step( harm_osc_f1() , q , p , t , dt );
@@ -414,7 +406,6 @@
steps is instantiated and initialized;
-
adams_bashforth_moulton< 5 , state_type > abm;
abm.initialize( sys , inout , t , dt );
@@ -432,7 +423,6 @@
state of the Adams-Bashforth-Stepper:
-
abm.initialize( runge_kutta_fehlberg78< state_type >() , sys , inout , t , dt );
@@ -695,7 +685,6 @@
An example is
-
dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > > dense;
dense.initialize( in , t , dt );
@@ -721,7 +710,6 @@
exist:
-
boost::numeric::odeint::result_of::make_dense_output< runge_kutta_dopri5< state_type > >::type dense2 = make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() );
@@ -739,7 +727,6 @@
for easy use with the integrate functions:
-
integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() ) , sys , inout , t_start , t_end , dt );
@@ -808,7 +795,6 @@
4 internal derivatives of the solution at times (t-dt,t-2dt,t-3dt,t-4dt).
-
adams_bashforth_moulton< 4 , state_type > stepper;
stepper.do_step( sys , x , t , dt );
@@ -1939,39 +1925,89 @@
x(t+Δ t) = x(t) + Δ t f(x(t)) + Δ t1/2 g(x) ξ(t)
- where ξ(t) is a independent and identically distributed normal random variable.
+ where ξ(t) is an independent normal distributed random variable.
- Now we will implement this method. We will call the stepper stochastic_euler. Its class definition
- looks like
+ Now we will implement this method. We will call the stepper stochastic_euler. It models the __stepper_concept.
+ The class definition looks like
-
-class stochastic_euler
+template< size_t N > class stochastic_euler
{
public:
- typedef std::vector< double > state_type;
- typedef std::vector< double > deriv_type;
+ typedef std::array< double , N > state_type;
+ typedef std::array< double , N > deriv_type;
typedef double value_type;
typedef double time_type;
typedef unsigned short order_type;
-
typedef boost::numeric::odeint::stepper_tag stepper_category;
+
+ static order_type order( void ) { return 1; }
+
+
};
- System function
+ The types are needed in order to fulfill the stepper concept. As internal
+ state and deriv type we use simple arrays in the stochastic euler, they
+ are needed for the temporaries. The stepper has the order one which is
+ returned from the order() function.
- steppers body
+ The system functions needs to calculate the deterministic and the stochastic
+ part of our stochastic differential equation. So it might be suitable that
+ the system function itself is a pair of functions, one for computing the
+ deterministic and one for the stochastic part. The first element of the
+ pair simply computes the deterministic part while the second the stochastic
+ one. Then, the second part also needs to calculate the random numbers in
+ order to simulate the stochastic process. We can now implement the do_step
+ method
- do_step method
+
+template< size_t N > class stochastic_euler
+{
+public:
+
+
+
+ template< class System >
+ void do_step( System system , state_type &x , time_type t , time_type dt ) const
+ {
+ deriv_type det , stoch ;
+ system.first( x , det );
+ system.second( x , stoch );
+ for( size_t i=0 ; i<x.size() ; ++i )
+ x[i] += dt * det[i] + sqrt( dt ) * stoch[i];
+ }
+};
+
+
+
+ This is all. It is quite simple and the stochastic euler stepper implement
+ here is quite general. Of course it can be enhanced, for example
+
+
+-
+ use of operations and algebras as well as the resizing mechanism for
+ maximal flexibility and portability
+
+-
+ use of
boost::ref for the system functions
+
+-
+ use of
boost::range for the state type in the
+ do_step method
+
+-
+ ...
+
+
examples, with integrate function
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html b/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html
index f576b099..566791b9 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html
@@ -61,7 +61,6 @@
The implementation of the Lorenz system is
-
const double sigma = 10.0;
const double R = 28.0;
@@ -84,7 +83,6 @@
the perturbation could look like:
-
const size_t n = 3;
const size_t num_of_lyap = 3;
@@ -116,7 +114,6 @@
inside a functor with templatized arguments:
-
struct lorenz
{
@@ -138,7 +135,7 @@
This works fine and lorenz_with_lyap
- can be used for example via
+ can be used for example via
state_type x;
@@ -154,7 +151,6 @@
current state lies on the attractor, hence it would look like
-
state_type x;
@@ -170,7 +166,6 @@
by pointer to the state and an appropriate length, something similar to
-
void lorenz( double* x , double *dxdt , double t, void* params )
{
@@ -188,7 +183,6 @@
the system has to by changed:
-
struct lorenz
{
@@ -211,7 +205,6 @@
with an suited range:
-
integrate_n_steps( rk4 , lorenz() , std::make_pair( x.begin() , x.begin() + n ) , 0.0 , dt , 10000 );
@@ -242,7 +235,6 @@
-
fill( x.begin()+n , x.end() , 0.0 );
for( size_t i=0 ; i<num_of_lyap ; ++i ) x[n+n*i+i] = 1.0;
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html b/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html
index 0836da63..5332e1bd 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html
@@ -52,7 +52,6 @@
to just define a function, e.g:
-
typedef std::vector< double > state_type;
@@ -79,7 +78,6 @@
parameter structure as above:
-
class harm_osc {
@@ -1138,7 +1136,6 @@
) function from odeint:
-
runge_kutta4< state_type > stepper;
integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
@@ -1155,7 +1152,6 @@
method which can used directly. So, you write down the above example as
-
const double dt = 0.01;
for( double t=0.0 ; t<10.0 ; t+= dt )
@@ -1179,7 +1175,6 @@
with 4th order error estimation and coefficients introduced by Cash-Karp.
-
typedef runge_kutta_cash_karp54< state_type > error_stepper_type;
@@ -1192,7 +1187,6 @@
stepper exists which can be used via
-
typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type;
controlled_stepper_type controlled_stepper;
@@ -1219,7 +1213,6 @@
by using make_controlled:
-
integrate_adaptive( make_controlled< error_stepper_type >( 1.0e-10 , 1.0e-6 ) , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
@@ -1235,7 +1228,6 @@
is
-
integrate_adaptive( make_controlled( 1.0e-10 , 1.0e-6 , error_stepper_type() ) , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
@@ -1251,7 +1243,6 @@
with all parameters is therefore
-
double abs_err = 1.0e-10 , rel_err = 1.0e-6 , a_x = 1.0 , a_dxdt = 1.0;
controlled_stepper_type controlled_stepper( default_error_checker< double >( abs_err , rel_err , a_x , a_dxdt ) );
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html b/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html
index 05d75810..927dddd0 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/solar_system.html
@@ -98,7 +98,6 @@
space as well as the velocity. Therefore, we use the operators from Boost.Operators:
-
template< class T , size_t Dim >
@@ -136,7 +135,6 @@
type we use std::tr1::array
-
const size_t n = 6;
@@ -159,7 +157,6 @@
As system function we have to provide f(p) and f(q):
-
const double gravitational_constant = 2.95912208286e-4;
@@ -179,7 +176,6 @@
-
struct solar_system_momentum
{
@@ -221,7 +217,6 @@
apply here:
-
typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
const double dt = 100.0;
@@ -246,7 +241,6 @@
The reference wrapper is also passed, but this is not a problem at all:
-
struct streaming_observer
{
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html b/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html
index 774b2d1a..310cecac 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/special_topics.html
@@ -63,7 +63,6 @@
code is very simple
-
typedef boost::array< complex< double > , 1 > state_type;
@@ -89,7 +88,6 @@
function. In this cast the Stuart-Landau oscillator looks like
-
double eta = 1.0;
double alpha = 1.0;
@@ -111,7 +109,6 @@
Integration is also very easy:
-
state_type x = {{ complex< double >( 1.0 , 0.0 ) }};
@@ -156,7 +153,6 @@
components. Here, is how this function looks like
-
typedef vector< double > container_type;
@@ -208,7 +204,6 @@
All this can be easily done with the following piece of code:
-
const size_t n = 64;
container_type q( n , 0.0 ) , p( n , 0.0 );
@@ -235,7 +230,6 @@
The observer is more or less trivial
-
struct streaming_observer
{
@@ -304,7 +298,6 @@
also need to store the individual frequencies of each oscillator.
-
typedef vector< double > container_type;
@@ -367,7 +360,6 @@
and we record Z for different values of ε.
-
struct statistics_observer
{
@@ -400,7 +392,6 @@
2.
-
const size_t n = 16384;
const double dt = 0.1;
@@ -458,7 +449,6 @@
all quantities
-
#define BOOST_FUSION_INVOKE_MAX_ARITY 15
@@ -500,7 +490,6 @@
equivalent to the example in the first section of this tutorial
-
struct oscillator
{
@@ -524,7 +513,6 @@
Furthermore, the basic calculations are now performed by the fusion_algebra which must also be given.
-
typedef runge_kutta_dopri5< state_type , double , deriv_type , time_type , fusion_algebra > stepper_type;
@@ -539,7 +527,6 @@
the observer is defined a bit different
-
struct streaming_observer
{
@@ -611,7 +598,6 @@
The definition of the system is
-
typedef boost::numeric::ublas::matrix< double > state_type;
@@ -705,7 +691,6 @@
Here is a simple example:
-
typedef mpf_class value_type;
typedef boost::array< value_type , 3 > state_type;
@@ -730,7 +715,6 @@
which can be used
-
const int precision = 1024;
mpf_set_default_prec( precision );
@@ -792,7 +776,6 @@
is kept which should be changed whenever the states' size change.
-
typedef vector< double > coord_type;
typedef pair< coord_type , coord_type > state_type;
@@ -878,7 +861,6 @@
of 60.
-
const int N_start = 60;
@@ -914,7 +896,6 @@
the start index of the potential changes in this case.
-
double t = 0.0;
const double dt = 0.1;
@@ -947,7 +928,6 @@
, p and distr.
-
void do_resize( coord_type &q , coord_type &p , coord_type &distr , const int N )
{
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html b/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html
index 0d0fd902..a874b455 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/stiff_systems.html
@@ -45,7 +45,6 @@
is needed. Here is the definition of the above example
-
typedef boost::numeric::ublas::vector< double > vector_type;
typedef boost::numeric::ublas::matrix< double > matrix_type;
@@ -82,7 +81,6 @@
just templatize the operator():
-
typedef boost::numeric::ublas::vector< double > vector_type;
typedef boost::numeric::ublas::matrix< double > matrix_type;
@@ -118,7 +116,6 @@
all the other stepper:
-
vector_type x( 3 , 1.0 );
@@ -135,7 +132,6 @@
5 method with step size control and dense output yields 1531 steps.
-
vector_type x2( 3 , 1.0 );
diff --git a/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html b/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html
index 7e40ed7d..ba716c69 100644
--- a/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html
+++ b/doc/boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html
@@ -87,7 +87,6 @@
website.
-
typedef double value_type;
@@ -103,7 +102,7 @@
a calculation on the GPU you usually have to call a global function like
thrust::for_each, thrust::reduce,
... with an appropriate local functor which performs the basic operation.
- An example is
+ An example is
struct add_two
{
@@ -138,7 +137,6 @@
The mean field is calculated in a class mean_field_calculator
-
struct mean_field_calculator
{
@@ -192,7 +190,6 @@
GPU as well as on the CPU. The line
-
value_type sin_sum = thrust::reduce(
thrust::make_transform_iterator( x.begin() , sin_functor() ) ,
@@ -208,7 +205,6 @@
The system function is defined via
-
class phase_oscillator_ensemble
{
@@ -264,7 +260,6 @@
thrust algebra:
-
typedef runge_kutta4< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
@@ -274,7 +269,6 @@
Of course, you can also use a controlled or dense output stepper, e.g.
-
typedef runge_kutta_dopri5< state_type , value_type , state_type , value_type , thrust_algebra , thrust_operations > stepper_type;
@@ -285,14 +279,12 @@
an instance of the rhs class and using an integration function:
-
phase_oscillator_ensemble ensemble( N , 1.0 );
-
size_t steps1 = integrate_const( make_controlled( 1.0e-6 , 1.0e-6 , stepper_type() ) , boost::ref( ensemble ) , x , 0.0 , t_transients , dt );
@@ -334,7 +326,6 @@
in front. The full system class is:
-
typedef thrust::device_vector< value_type > state_type;
@@ -423,7 +414,6 @@
current state, hence the phase of each oscillator.
-
vector< value_type > x_host( N );
@@ -486,7 +476,6 @@
>.
-
vector< value_type > beta_host( N );
const value_type beta_min = 0.0 , beta_max = 56.0;
@@ -504,7 +493,6 @@
calculates one particular realization of the Lorenz ensemble
-
struct lorenz_system
{
@@ -586,7 +574,6 @@
which is used within this observer is defined
-
struct lyap_functor
{
@@ -626,7 +613,6 @@
and written to stdout.
-
state_type x( 6 * N );
diff --git a/doc/index.html b/doc/index.html
index c83312c4..1a88e146 100644
--- a/doc/index.html
+++ b/doc/index.html
@@ -24,7 +24,7 @@
Copyright © 2009-2011 Karsten Ahnert
and Mario Mulansky