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.