dynamo.vf.Ao_pot_map

dynamo.vf.Ao_pot_map(vecFunc, X, D=None)[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 (numpy.ndarray) – A matrix of coordinates to calculate potential values for. Rows are observations (cells), columns are features (genes)

  • D (None or numpy.ndarray) – Diffusion matrix. It must be a square matrix with size corresponds to the number of columns (features) in the X matrix.

Returns

  • X (numpy.ndarray) – A matrix storing the x-coordinates on the two-dimesional grid.

  • U (numpy.ndarray) – A matrix storing the potential value at each position.

  • P (numpy.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.