steenroder.rips_barcodes

steenroder.rips_barcodes(X, max_edge_length=inf, distance_matrix=False, k=1, max_simplex_dimension=2, absolute=False, n_jobs=1, verbose=False)[source]

Construct a Rips filtration and compute ordinary persistent (relative or absolute) cohomology barcodes and relative Steenrod barcodes.

Parameters

  • X (ndarray of shape (n_samples, n_features) or (n_samples, n_samples)) – Input point cloud (if distance_matrix is False) or distance matrix (if distance_matrix is True).

  • max_edge_length (float, optional, default: np.inf) – Vietoris–Rips filtration threshold.

  • distance_matrix (bool, optional, default: False) – Whether the input X is a distance matrix or a point cloud.

  • k (int) – Positive integer defining the cohomology operation Sq^k to be performed.

  • max_simplex_dimension (int, optional, default: 2) – Maximum simplex dimension to be included in the Rips filtration.

  • absolute (bool, optional, default: False) – If True, return the ordinary persistent absolute homology barcode, and move inessential relative Steenrod bars to one degree lower while keeping essential bars in their degree. If False, return the ordinary persistent relative cohomology barcode and relative Steenrod barcode.

  • n_jobs (int, optional, default: 1) – [Experimental] Controls the number of threads to be used during parallel computation of the Steenrod squares. -1 means using all available physical cores.

  • verbose (bool, optional, default: False) – Whether to print information about the intermediate steps in the computation.

Returns

  • barcode (list of ndarray) – For each dimension d, a 2D int or float array of shape (n_bars, 2) containing the births and deaths of persistent relative cohomology classes in degree d. If absolute is False, the birth of a bar is in entry 1 and the death in entry 0; otherwise, the positions are reversed. Births and death are expressed either as global filtration indices or as filtration values depending on filtration_values and return_filtration_values. If they are expressed as indices, essential bars have death equal to -1; otherwise, essential bars have death equal to numpy.inf.

  • steenrod_barcode (list of ndarray) – The (relative) Sq^k-barcode. For each dimension d, a 2D int or float array of shape (n_bars, 2) containing the birth (entry 1) and death (entry 0) indices of Steenrod bars. The same conventions as for barcode are used for birth and death values.