dynamo.vf.path_integral¶
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dynamo.vf.
path_integral
(VecFnc, x_lim, y_lim, xyGridSpacing, dt=0.01, tol=0.01, numTimeSteps=1400)[source]¶ A deterministic map of Waddington’s epigenetic landscape for cell fate specification Sudin Bhattacharya, Qiang Zhang and Melvin E. Andersen
- Parameters
VecFnc –
x_lim (list) – Lower or upper limit of x-axis.
y_lim (list) – Lower or upper limit of y-axis
xyGridSpacing (float) – Grid spacing for “starting points” for each “path” on the pot. surface
dt (float) – Time step for the path integral.
tol (float (default: 1.0e-2)) – Tolerance to test for convergence.
numTimeSteps (int) – A high-enough number for convergence with given dt.
- Returns
numAttractors (int) – Number of attractors identified by the path integral approach.
attractors_num_X_Y (numpy.ndarray) – Attractor number and the corresponding x, y coordinates.
sepx_old_new_pathNum (numpy.ndarray) – The IDs of the two attractors for each separaxis per row.
numPaths_att numpy.ndarray – Number of paths per attractor
numPaths (int) – Total Number of paths for defined grid spacing.
numTimeSteps (int) – A high-enough number for convergence with given dt.
pot_path (numpy.ndarray (dimension: numPaths x numTimeSteps)) – Potential along the path.
path_tag (numpy.ndarray (dimension: numPaths x 1)) – Tag for given path (to denote basin of attraction).
attractors_pot (numpy.ndarray) – Potential value of each identified attractors by the path integral approach.
x_path (numpy.ndarray) – x-coord. along path.
y_path (numpy.ndarray) – y-coord. along path.