Utility functions

solver(ds::ContinuousTimeDynamicalSystem) -> Any

Returns the SDE solver specified in the diffeq settings of the CoupledSDEs.

drift(
    sys::Union{CoupledODEs{IIP}, CoupledSDEs{IIP}},
    x;
    t
) -> Any

Returns the deterministic drift $f(x)$ of the CoupledSDEs sys at state x. For time-dependent systems, the time can be specified as a keyword argument t (by default t=0).

div_drift(sys::ContinuousTimeDynamicalSystem, x) -> Any
div_drift(sys::ContinuousTimeDynamicalSystem, x, t) -> Any

Computes the divergence of the drift field $f(x)$ at state x. For time- dependent systems, the time can be specified as a keyword argument t (by default t=0).

covariance_matrix(ds::CoupledSDEs)

Returns the covariance matrix of the stochastic term of the CoupledSDEs ds, provided that the diffusion function g can be expressed as a constant invertible matrix. If this is not the case, returns nothing.

See also diffusion_matrix.

diffusion_matrix(ds::CoupledSDEs)

Returns the diffusion matrix of the stochastic term of the CoupledSDEs ds, provided that the diffusion function g can be expressed as a constant invertible matrix. If this is not the case, returns nothing.

Note: The diffusion matrix $Σ$ is the square root of the noise covariance matrix $Q$ (see covariance_matrix), defined via the Cholesky decomposition $Q = Σ Σ^\top$.

noise_process(sys::CoupledSDEs) -> Any

Fetches the stochastic process $\mathcal{N}$ specified in the intergrator of sys. Returns the type DiffEqNoiseProcess.NoiseProcess.

intervals_to_box(bmin::Vector, bmax::Vector) -> Any

Generates a box from specifying the interval limits in each dimension.

• bmin (Vector): lower limit of the box in each dimension
• bmax (Vector): upper limit

Example

intervals_to_box([-2,-1,0], [2,1,1]) returns a 3D box of dimensions [-2,2] × [-1,1] × [0,1].