From 83c55a46326ab268cca3de8a3bf1c482de8ffd78 Mon Sep 17 00:00:00 2001 From: Karsten Ahnert Date: Mon, 2 Apr 2012 20:27:51 +0200 Subject: [PATCH] documentation: steppers and boost_ref --- .../odeint_in_detail/steppers.html | 69 +++++++++++++++++-- .../odeint_in_detail/using_boost__range.html | 20 +++++- .../odeint_in_detail/using_boost__ref.html | 39 ++++++++++- doc/index.html | 2 +- .../odeint/doc/details_boost_range.qbk | 8 +++ libs/numeric/odeint/doc/details_boost_ref.qbk | 17 +++++ libs/numeric/odeint/doc/details_steppers.qbk | 11 ++- .../odeint/examples/stochastic_euler.cpp | 7 +- 8 files changed, 157 insertions(+), 16 deletions(-) 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 951f5431..e58d3df5 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html @@ -1912,9 +1912,9 @@

where ξ is Gaussian white noise with zero mean and - a standard deviation σ. f(x) is - said to be the deterministic part while g(x) ξ is the - noisy part. In case g(x) is independent of x + a standard deviation σ(t). f(x) + is said to be the deterministic part while g(x) ξ is + the noisy part. In case g(x) is independent of x the SDE is said to have additive noise. It is not possible to solve SDE with the classical solvers for ODEs since the noisy part of the SDE has to be scaled differently then the deterministic part with respect to the @@ -1964,8 +1964,7 @@ 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 + order to simulate the stochastic process. We can now implement the do_step method

@@ -2009,7 +2008,65 @@

- examples, with integrate function + Now, lets look how we use the new stepper. A nice example is the Ornstein-Uhlenbeck + process. It consists of a simple Brownian motion overlapped with an relaxation + process. Its SDE reads +

+

+ dx/dt = - x + ξ +

+

+ where ξ is Gaussian white noise with standard deviation σ. + Implementing the Ornstein-Uhlenbeck process is quite simple. We need two + functions or funtors - one for the deterministic and one for the stochastic + part: +

+

+

+
const static size_t N = 1;
+typedef std::array< double , N > state_type;
+
+struct ornstein_det
+{
+    void operator()( const state_type &x , state_type &dxdt ) const
+    {
+        dxdt[0] = -x[0];
+    }
+};
+
+struct ornstein_stoch
+{
+    std::mt19937 m_rng;
+    std::normal_distribution<> m_dist;
+
+    ornstein_stoch( double sigma ) : m_rng() , m_dist( 0.0 , sigma ) { }
+
+    void operator()( const state_type &x , state_type &dxdt )
+    {
+        dxdt[0] = m_dist( m_rng );
+    }
+};
+
+

+

+

+ In the stochastic part we have used the Mersenne twister for the random + number generation and a Gaussian white noise generator normal_distribution + with standard deviation σ. Now, we can use the stochastic + Euler stepper with the integrate functions: +

+

+

+
double dt = 0.1;
+state_type x = {{ 1.0 }};
+integrate_const( stochastic_euler< N >() , make_pair( ornstein_det() , ornstein_stoch( 1.0 ) ) ,
+        x , 0.0 , 10.0 , dt , streaming_observer() );
+
+

+

+

+ Note, how we have used the make_pair + function for the generation of the system function.

diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html index dcae81ab..b66d42d5 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html @@ -15,10 +15,26 @@
PrevUpHomeNext
-

+
+
+

+

+ Most steppers in odeint also accept the state give as a range. A range is + sequence of values modelled by a range concept, see Boost.Range + for an overview over existing concepts and examples of ranges. +

+

+ state type mus not necessary be used in the steppers +

+

+ example +

+

+ table which steppers support boost::range and with which algebra +

+
Copyright © 2009-2011 Karsten Ahnert diff --git a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html index 966dbccc..ad5d647e 100644 --- a/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html +++ b/doc/boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html @@ -15,10 +15,45 @@
PrevUpHomeNext
-
+

+ In odeint all system functions and observers are passed by value. For example, + if you call a do_step method + of a particular stepper or the integration functions your system and your + stepper will be passed by value: +

+

+

+
rk4.do_step( sys , x , t , dt );   // pass sys by value
+
+

+

+

+ This behaviour is suitable for most systems, especially if your system only + does not contain any data or only a few parameters. However, in some cases + you might pass some large amount of data with you system function and passing + them by value is not desired since the data will be copied. +

+

+ In such cases you can easily use boost::ref (and + its relative boost::cref) which passes its argument by reference + (or const reference). odeint will unpack the arguments and no copying at + all of you system will take place: +

+

+

+
rk4.do_step( boost::ref( sys ) , x , t , dt );   // pass sys as references
+
+

+

+

+ The same mechanism can for the observers in the integrate functions. +

+
Copyright © 2009-2011 Karsten Ahnert diff --git a/doc/index.html b/doc/index.html index 1a88e146..802efb15 100644 --- a/doc/index.html +++ b/doc/index.html @@ -125,7 +125,7 @@
- +

Last revised: April 02, 2012 at 06:51:21 GMT

Last revised: April 02, 2012 at 16:04:40 GMT
diff --git a/libs/numeric/odeint/doc/details_boost_range.qbk b/libs/numeric/odeint/doc/details_boost_range.qbk index a3ece168..e70f1207 100644 --- a/libs/numeric/odeint/doc/details_boost_range.qbk +++ b/libs/numeric/odeint/doc/details_boost_range.qbk @@ -1,3 +1,11 @@ [section Using boost::range] +Most steppers in odeint also accept the state give as a range. A range is sequence of values modelled by a range concept, see __boost_range for an overview over existing concepts and examples of ranges. + +state type mus not necessary be used in the steppers + +example + +table which steppers support boost::range and with which algebra + [endsect] diff --git a/libs/numeric/odeint/doc/details_boost_ref.qbk b/libs/numeric/odeint/doc/details_boost_ref.qbk index 007ffc7b..331ce0f6 100644 --- a/libs/numeric/odeint/doc/details_boost_ref.qbk +++ b/libs/numeric/odeint/doc/details_boost_ref.qbk @@ -1,3 +1,20 @@ [section Using boost::ref] +In odeint all system functions and observers are passed by value. For example, if you call a `do_step` method of a particular stepper or the integration functions your system and your stepper will be passed by value: + +[c++] +`` +rk4.do_step( sys , x , t , dt ); // pass sys by value +`` + +This behaviour is suitable for most systems, especially if your system only does not contain any data or only a few parameters. However, in some cases you might pass some large amount of data with you system function and passing them by value is not desired since the data will be copied. + +In such cases you can easily use `boost::ref` (and its relative `boost::cref`) which passes its argument by reference (or const reference). odeint will unpack the arguments and no copying at all of you system will take place: + +`` +rk4.do_step( boost::ref( sys ) , x , t , dt ); // pass sys as references +`` + +The same mechanism can for the observers in the integrate functions. + [endsect] diff --git a/libs/numeric/odeint/doc/details_steppers.qbk b/libs/numeric/odeint/doc/details_steppers.qbk index 8e37cd07..9016ca65 100644 --- a/libs/numeric/odeint/doc/details_steppers.qbk +++ b/libs/numeric/odeint/doc/details_steppers.qbk @@ -248,11 +248,16 @@ Now, lets look how we use the new stepper. A nice example is the Ornstein-Uhlenb ['dx/dt = - x + __xi] -where __xi is Gaussian white noise with standard deviation ['__sigma]. +where __xi is Gaussian white noise with standard deviation ['__sigma]. Implementing the Ornstein-Uhlenbeck process is quite simple. We need two functions or funtors - one for the deterministic and one for the stochastic part: -[stochastic_euler_ornstein_uhlenbeck_det] +[stochastic_euler_ornstein_uhlenbeck_def] + +In the stochastic part we have used the Mersenne twister for the random number generation and a Gaussian white noise generator `normal_distribution` with standard deviation ['__sigma]. Now, we can use the stochastic Euler stepper with the integrate functions: + +[ornstein_uhlenbeck_main] + +Note, how we have used the `make_pair` function for the generation of the system function. -examples, with integrate function diff --git a/libs/numeric/odeint/examples/stochastic_euler.cpp b/libs/numeric/odeint/examples/stochastic_euler.cpp index 8f995b5e..5bf6b6f4 100644 --- a/libs/numeric/odeint/examples/stochastic_euler.cpp +++ b/libs/numeric/odeint/examples/stochastic_euler.cpp @@ -116,14 +116,17 @@ struct streaming_observer } }; + int main( int argc , char **argv ) { using namespace std; using namespace boost::numeric::odeint; + //[ ornstein_uhlenbeck_main double dt = 0.1; state_type x = {{ 1.0 }}; - integrate_const( stochastic_euler< N >() , make_pair( ornstein_det() , ornstein_stoch( 1.0 ) ) , x , 0.0 , 10.0 , dt , streaming_observer() ); - + integrate_const( stochastic_euler< N >() , make_pair( ornstein_det() , ornstein_stoch( 1.0 ) ) , + x , 0.0 , 10.0 , dt , streaming_observer() ); + //] return 0; }