dysii Dynamical Systems Library: StochasticNumericalSolver Class Reference

StochasticNumericalSolver	(	const unsigned int	dimensions,
		const unsigned int	noises
	)

Constructor.

Parameters:

	dimensions	Dimensionality of the state space.
	noises	Dimensionality of the noise space.

The time is initialised to zero, but the state is uninitialised and should be set with setVariable() or setState().

Definition at line 7 of file StochasticNumericalSolver.cpp.

StochasticNumericalSolver	(	const indii::ml::aux::vector &	y0,
		const unsigned int	noises
	)

Constructor.

Parameters:

	y0	Initial state.
	noises	Dimensionality of the noise space.

The time is initialised to zero and the state to that given.

Definition at line 13 of file StochasticNumericalSolver.cpp.

~StochasticNumericalSolver ( ) [virtual]

Destructor.

Definition at line 18 of file StochasticNumericalSolver.cpp.

bool sampleNoise ( double * ts ) [protected]

Sample Wiener process noise.

This conditions on previous samples of the Wiener trajectory at future times resulting from time steps rejected by the adaptive step size control. This ensures that steps are rejected only due to error bounds being exceeded and not due to an improbable but perfectly valid Wiener trajectory.

Parameters:

ts

; the time at which to sample the noise. If this is greater than the earliest time in the future path, will be adjusted to this earliest time on return.

Returns:: True if a new Wiener increment was sampled, false if an existing increment has been used.

Let

be the current time and $t_s$

the time at which to sample the noise.

Of the stored Wiener increments at times $t_1,t_2,\ldots > t$ , let $t_l$ be the greatest time less than or equal to $t_s$ , and $t_u$ the least time greater than $t_s$ . $\Delta\mathbf{W}(t_l)$ and $\Delta\mathbf{W}(t_u)$ are the corresponding Wiener increments.

If $t_l$ does not exist, set $t_l \leftarrow t$ .

Then, if $t_s \neq t_l$ , draw $\mathbf{\delta} \sim \mathcal{N}(0,\sqrt{t_s-t_l})$ . If $t_u$ does not exist, set $\Delta\mathbf{W}(t_s) \leftarrow \mathbf{\delta}$ . Otherwise, set:

$\begin{eqnarray*} \Delta\mathbf{W}(t_s) &\leftarrow& \frac{t_s - t_l}{t_u - t_l}\Delta\mathbf{W}(t_u) + \mathbf{\delta} \\ \Delta\mathbf{W}(t_u) &\leftarrow& \frac{t_u - t_s}{t_u - t_l}\Delta\mathbf{W}(t_u) - \mathbf{\delta} \\ \end{eqnarray*}$

and store.

Definition at line 22 of file StochasticNumericalSolver.cpp.

void reset ( ) [protected, virtual]

Reset the model.

This is used internally to reset GSL structures when the next step will not be a continuation of the last, usually when the time or state is changed with a call to setTime(), setVariable() or setState().

Reimplemented from NumericalSolver.

Definition at line 56 of file StochasticNumericalSolver.cpp.

indii::ml::aux::WienerProcess<double> W [protected]

Wiener process system noise.

Definition at line 54 of file StochasticNumericalSolver.hpp.

std::stack<double> tf [protected]

$t_1,t_2,\ldots > t$ ; future times.

Definition at line 59 of file StochasticNumericalSolver.hpp.

std::stack<indii::ml::aux::vector> dWf [protected]

$\Delta\mathbf{W}(t_1),\Delta\mathbf{W}(t_2),\ldots$ ; Wiener process increments at future times.

Definition at line 65 of file StochasticNumericalSolver.hpp.

StochasticNumericalSolver Class Reference

Detailed Description

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation


Public Member Functions
	StochasticNumericalSolver (const unsigned int dimensions, const unsigned int noises)
	Constructor.
	StochasticNumericalSolver (const indii::ml::aux::vector &y0, const unsigned int noises)
	Constructor.
virtual	~StochasticNumericalSolver ()
	Destructor.
Protected Member Functions
bool	sampleNoise (double *ts)
	Sample Wiener process noise.
virtual void	reset ()
	Reset the model.
Protected Attributes
indii::ml::aux::WienerProcess < double >	W
	Wiener process system noise.
std::stack< double >	tf
	$t_1,t_2,\ldots > t$ ; future times.
std::stack < indii::ml::aux::vector >	dWf
	$\Delta\mathbf{W}(t_1),\Delta\mathbf{W}(t_2),\ldots$ ; Wiener process increments at future times.