2.3. ECT on Graphs
- class ect.ect_graph.ECT(directions=None, num_dirs=None, num_thresh=None, bound_radius=None, thresholds=None, dtype=<class 'numpy.int32'>)[source]
A class to calculate the Euler Characteristic Transform (ECT) from an input
EmbeddedGraphorEmbeddedCW.The result is a matrix where entry
M[i,j]is \(\chi(K_{a_i})\) for the direction \(\omega_j\) where \(a_i\) is the ith entry inself.thresholds, and \(\omega_j\) is the ith entry inself.thetas.- Attributes
- num_dirs (int):
The number of directions to consider in the matrix.
- num_thresh (int):
The number of thresholds to consider in the matrix.
- directions (Directions):
The directions to consider for projection.
- bound_radius (float):
Either
None, or a positive radius of the bounding circle.
- __init__(directions=None, num_dirs=None, num_thresh=None, bound_radius=None, thresholds=None, dtype=<class 'numpy.int32'>)[source]
Initialize ECT calculator with either a Directions object or sampling parameters
- Parameters:
directions – Optional pre-configured Directions object
num_dirs – Number of directions to sample (ignored if directions provided)
num_thresh – Number of threshold values (required if directions not provided)
bound_radius – Optional radius for bounding circle
thresholds – Optional array of thresholds
dtype – Data type for output array
- calculate(graph, theta=None, override_bound_radius=None)[source]
Calculate Euler Characteristic Transform (ECT) for a given graph and direction theta
- Parameters:
graph (EmbeddedGraph/EmbeddedCW) – The input graph to calculate the ECT for.
theta (float) – The angle in \([0,2\pi]\) for the direction to calculate the ECT.
override_bound_radius (float) – If None, uses the following in order: (i) the bounding radius stored in the class; or if not available (ii) the bounding radius of the given graph. Otherwise, should be a positive float \(R\) where the ECC will be computed at thresholds in \([-R,R]\). Default is None.