ripser.Rips

class ripser.Rips(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm=None, verbose=True)[source]

sklearn style class interface for ripser with fit and transform methods..

Parameters:
  • maxdim (int, optional, default 1) – Maximum homology dimension computed. Will compute all dimensions lower than and equal to this value. For 1, H_0 and H_1 will be computed.
  • thresh (float, default infinity) – Maximum distances considered when constructing filtration. If infinity, compute the entire filtration.
  • coeff (int prime, default 2) – Compute homology with coefficients in the prime field Z/pZ for p=coeff.
  • do_cocycles (bool) – Indicator of whether to compute cocycles, if so, we compute and store cocycles in the cocycles_ dictionary Rips member variable
  • n_perm (int) – The number of points to subsample in a “greedy permutation,” or a furthest point sampling of the points. These points will be used in lieu of the full point cloud for a faster computation, at the expense of some accuracy, which can be bounded as a maximum bottleneck distance to all diagrams on the original point set
  • verbose (boolean) – Whether to print out information about this object as it is constructed
`dgm_`

After transform, dgm_ contains computed persistence diagrams in each dimension

Type:list of ndarray, each shape (n_pairs, 2)
cocycles_

A list of representative cocycles in each dimension. The list in each dimension is parallel to the diagram in that dimension; that is, each entry of the list is a representative cocycle of the corresponding point expressed as an ndarray(K, d+1), where K is the number of nonzero values of the cocycle and d is the dimension of the cocycle. The first d columns of each array index into the simplices of the (subsampled) point cloud, and the last column is the value of the cocycle at that simplex

Type:list (size maxdim) of list of ndarray
dperm2all_

The distance matrix used in the computation if n_perm is none. Otherwise, the distance from all points in the permutation to all points in the dataset

Type:ndarray(n_samples, n_samples) or ndarray (n_perm, n_samples) if n_perm
metric_

The metric to use when calculating distance between instances in a feature array. If metric is a string, it must be one of the options specified in pairwise_distances, including “euclidean”, “manhattan”, or “cosine”. Alternatively, if metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays from X as input and return a value indicating the distance between them.

Type:string or callable
num_edges

The number of edges added during the computation

Type:int
idx_perm

Index into the original point cloud of the points used as a subsample in the greedy permutation

Type:ndarray(n_perm) if n_perm > 0
r_cover

Covering radius of the subsampled points. If n_perm <= 0, then the full point cloud was used and this is 0

Type:float

Examples

from ripser import Rips
import tadasets

data = tadasets.dsphere(n=110, d=2)[0]
rips = Rips()
rips.transform(data)
rips.plot()
__init__(maxdim=1, thresh=inf, coeff=2, do_cocycles=False, n_perm=None, verbose=True)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__([maxdim, thresh, coeff, …]) Initialize self.
fit_transform(X[, distance_matrix, metric]) Compute persistence diagrams for X data array and return the diagrams.
plot([diagrams]) A helper function to plot persistence diagrams.
transform(X[, distance_matrix, metric])
fit_transform(X, distance_matrix=False, metric='euclidean')[source]

Compute persistence diagrams for X data array and return the diagrams.

Parameters:
  • X (ndarray (n_samples, n_features)) – A numpy array of either data or distance matrix.
  • distance_matrix (bool) – Indicator that X is a distance matrix, if not we compute a distance matrix from X using the chosen metric.
  • metric (string or callable) – The metric to use when calculating distance between instances in a feature array. If metric is a string, it must be one of the options specified in pairwise_distances, including “euclidean”, “manhattan”, or “cosine”. Alternatively, if metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays from X as input and return a value indicating the distance between them.
Returns:

dgms (list (size maxdim) of ndarray (n_pairs, 2)) – A list of persistence diagrams, one for each dimension less than maxdim. Each diagram is an ndarray of size (n_pairs, 2) with the first column representing the birth time and the second column representing the death time of each pair.

plot(diagrams=None, *args, **kwargs)[source]

A helper function to plot persistence diagrams.

Parameters:
  • diagrams (ndarray (n_pairs, 2) or list of diagrams) – A diagram or list of diagrams as returned from self.fit. If diagram is None, we use self.dgm_ for plotting. If diagram is a list of diagrams, then plot all on the same plot using different colors.
  • plot_only (list of numeric) – If specified, an array of only the diagrams that should be plotted.
  • title (string, default is None) – If title is defined, add it as title of the plot.
  • xy_range (list of numeric [xmin, xmax, ymin, ymax]) – User provided range of axes. This is useful for comparing multiple persistence diagrams.
  • labels (string or list of strings) – Legend labels for each diagram. If none are specified, we use H_0, H_1, H_2,… by default.
  • colormap (string, default is 'default') –

    Any of matplotlib color palettes. Some options are ‘default’, ‘seaborn’, ‘sequential’. See all available styles with

    import matplotlib as mpl
    print(mpl.styles.available)
    
  • size (numeric, default is 20) – Pixel size of each point plotted.
  • ax_color (any valid matplitlib color type.) – See [https://matplotlib.org/api/colors_api.html](https://matplotlib.org/api/colors_api.html) for complete API.
  • diagonal (bool, default is True) – Plot the diagonal x=y line.
  • lifetime (bool, default is False. If True, diagonal is turned to False.) – Plot life time of each point instead of birth and death. Essentially, visualize (x, y-x).
  • legend (bool, default is True) – If true, show the legend.
  • show (bool, default is True) – Call plt.show() after plotting. If you are using self.plot() as part of a subplot, set show=False and call plt.show() only once at the end.