Module: stateVecStochasticIntegrator

class StateVecStochasticIntegrator : public StateVecIntegrator

#include <stateVecStochasticIntegrator.h>

state vector integrator class for stochastic dynamics

Subclassed by svIntegratorWeakStochasticRungeKutta< numberStages >

Public Functions

std::vector<StateIdToIndexMap> getStateIdToNoiseIndexMaps()

Returns a vector with length equal to the total number of noise sources in the system. Each index contains a map that indicates how that noise source maps to individual noise indices for each relevant StateData.

For example, consider the following SDE:

\[ dx_0 = f_0(t,x)\,dt + g_{00}(t,x)\,dW_0 + g_{01}(t,x)\,dW_1 \]

\[ dx_1 = f_1(t,x)\,dt + g_{11}(t,x)\,dW_1 \]

In this case, state ‘x_0’ is affected by 2 sources of noise and ‘x_1’ by 1 source of noise. The source ‘W_1’ is shared between ‘x_0’ and ‘x_1’.

This function would return (pseudo-code):

[ {(0, “x_0”) -> 0}, {(0, “x_0”) -> 1, (0, “x_1”) -> 0}, ]

because there are 2 unique sources of noise, the first of which affects the first noise index of ‘x_0’ and the second of which affects the second noise index of ‘x_0’ and the first noise index of “x_1”.

void propagateState(double timeStep, const Eigen::VectorXd &pseudoTimeSteps, const std::vector<StateIdToIndexMap> &stateIdToNoiseIndexMaps)

This method calls propagateStateVector on every state of the dynamic objects handled by this integrator.

The length of pseudoTimeSteps must match the size of stateIdToNoiseIndexMaps. The stateIdToNoiseIndexMaps are used to map each pseudoTimeStep to a noise index for each state.

Consider the following SDE:

\[ dx_0 = f_0(t,x)\,dt + g_{00}(t,x)\,dW_0 + g_{01}(t,x)\,dW_1 \]

\[ dx_1 = f_1(t,x)\,dt + g_{11}(t,x)\,dW_1 \]

Assume that the values of the drift and diffusion have been computed and are stored in the state objects. If this method is called with:

• timeStep: h

• pseudoTimeSteps: [W_0, W_1]

• stateIdToNoiseIndexMaps: [ {(0, “x_0”) -> 0}, {(0, “x_0”) -> 1, (0, “x_1”) -> 0}, ]

Then the states will be changed by:

\[ x_0 \mathrel{+}= f_0(t,x)\,h + g_{00}(t,x)\,W_0 + g_{01}(t,x)\,W_1 \]

\[ x_1 \mathrel{+}= f_1(t,x)\,h + g_{11}(t,x)\,W_1 \]

StateVecIntegrator(DynamicObject *dynIn)

Constructor.