pytspl.decomposition.hodge_decomposition

Module for calculating the Hodge decomposition of a edge flow defined over a network.

The following components can be extracted: - Total variance - Divergence - Curl - Gradient component - Curl component - Harmonic component

Functions

get_gradient_flow(→ numpy.ndarray)	Calculate the gradient flow of a flow on a graph.
get_curl_flow(→ numpy.ndarray)	Calculate the curl flow of a flow on a graph.
get_harmonic_flow(→ numpy.ndarray)	Calculate the harmonic flow of a flow on a graph.

Module Contents

pytspl.decomposition.hodge_decomposition.get_gradient_flow(B1: scipy.sparse.csr_matrix, flow: numpy.ndarray, round_fig: bool = True, round_sig_fig: int = 2) → numpy.ndarray

Calculate the gradient flow of a flow on a graph.

Args:

B1 (csr_matrix): The incidence matrix of the graph, nodes to edges (B1). flow (np.ndarray): The flow on the graph. round_sig_fig (int, optional): Round to significant figure. Defaults to 2.

Returns:

np.ndarray: The gradient flow.

pytspl.decomposition.hodge_decomposition.get_curl_flow(B2: scipy.sparse.csr_matrix, flow: numpy.ndarray, round_fig: bool = True, round_sig_fig: int = 2) → numpy.ndarray

Calculate the curl flow of a flow on a graph.

Args:

B2 (csr_matrix): The incidence matrix of the graph, edges to triangles (B2). flow (np.ndarray): The flow on the graph. round_sig_fig (int, optional): Round to significant figure. Defaults to 2.

Returns:

np.ndarray: The curl flow.

pytspl.decomposition.hodge_decomposition.get_harmonic_flow(B1: scipy.sparse.csr_matrix, B2: scipy.sparse.csr_matrix, flow: numpy.ndarray, round_fig: bool = True, round_sig_fig: int = 2) → numpy.ndarray

Calculate the harmonic flow of a flow on a graph.

Args:

B1 (csr_matrix): The incidence matrix of the graph, nodes to edges (B1). B2 (csr_matrix): The incidence matrix of the graph, flow (np.ndarray): The flow on the graph. round_sig_fig (int, optional): Round to significant figure. Defaults to 2.

Returns:

np.ndarray: The harmonic flow.