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

  • 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.


A matrix storing the x-coordinates on the two-dimensional 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: