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.