dynamo.vf.Ao_pot_map

dynamo.vf.Ao_pot_map(vecFunc, X, 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 (function) – The vector field function
X (ndarray) – A n_cell x n_dim matrix of coordinates where the potential function is evaluated.
D (None or ndarray) – Diffusion matrix. It must be a square matrix with size corresponds to the number of columns (features) in the X matrix.

Returns:

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