dynamo.vf.Ao_pot_map

dynamo.vf.Ao_pot_map(vecFunc, X, fjac=None, D=None, **kwargs)[source]

Mapping potential landscape with the algorithm developed by Ao method. References: Potential in stochastic differential equations: novel construction. Journal of physics A: mathematical and

general, Ao Ping, 2004

Parameters:

vecFunc (Callable) – The vector field function.
X (ndarray) – A (n_cell x n_dim) matrix of coordinates where the potential function is evaluated.
fjac (Optional[Callable]) – function that returns the Jacobian of the vector field function evaluated at a particular point.
D (Optional[ndarray]) – Diffusion matrix. It must be a square matrix with size corresponds to the number of columns (features) in the X matrix.

Returns:

A matrix storing the x-coordinates on the two-dimesional grid. U: A matrix storing the potential value at each position. P: Steady state distribution or the Boltzmann-Gibbs distribution for the state variable. vecMat: List velocity vector at each position from X. S: List of constant symmetric and semi-positive matrix or friction (dissipative) matrix, corresponding to the divergence part,

at each position from X.

A: List of constant antisymmetric matrix or transverse (non-dissipative) matrix, corresponding to the curl part, at each position: from X.

Return type:

X