All Modules, Classes, and Methods¶
An alphabetical list of everything.
homology |
This module defines the the basic objects for persistence diagrams: |
homology.PersDiag(birth_index, death_index, …) |
Persistence Diagrams and related merge-tree information. |
homology.PersDiag.bin(width[, underflow, …]) |
Count bins on the transformed persistence diagram. |
homology.PersDiag.bin_bot(width[, …]) |
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homology.PersDiag.bin_diag(width[, …]) |
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homology.PersDiag.bin_len(width[, …]) |
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homology.PersDiag.bin_top(width[, …]) |
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homology.PersDiag.clip(beta) |
clip the barcode below beta. |
homology.PersDiag.grab(n) |
clip the barcode, using only the top n entries. |
homology.PersDiag.plot(canvas[, transform, …]) |
Plot the persistence diagram using matplotlib or bokeh. |
homology.PersDiag.syzygy(powers) |
compute the syzygy coordinate of my barcode. |
homology.PersDiag.transform([transform, points]) |
Produce an array of points, obtained by transforming the persistence diagram. |
homology.dim0 |
This Cython module contains the core algorithms for 0-dimension topological algorithms. |
homology.dim0.all_roots |
Reference each vertex directly to its representative root, from MergeTree. |
homology.dim0.mkforestDBL |
Make inclusion tree and parentage linked lists by walking across This method is for np.float64 arrays (for indexing speed). |
homology.dim0.unionfind |
Apply the UnionFind algorithm to compute zero-dimensional persistence diagram. |
homology.dim1 |
This Cython module contains the core algorithms for 1-dimensional topological algorithms. |
multidim |
The multidim class provides user-facing tools for topological data analysis of multi-dimensional data. |
multidim.PointCloud(data_array[, …]) |
PointCloud is a class for embedded, weighted simplicial complexes. |
multidim.PointCloud.cache_usage() |
Compute the size of the distance cache. |
multidim.PointCloud.cells(dim) |
iterate over all Simplex objects of dimension dim. |
multidim.PointCloud.check() |
Run consistency checks on all simplices in all dimensions. |
multidim.PointCloud.cover_ball([point_index]) |
Find a ball that covers the entire PointCloud. |
multidim.PointCloud.dists(indices0, indices1) |
Compute distances points indices0 and indices1. |
multidim.PointCloud.from_distances(*args, …) |
This method is not available for PointCloud, because actual coordinates are needed. |
multidim.PointCloud.from_multisample_multilabel(…) |
Produce a single labeled and weighted pointcloud from a list of samples and labels of those samples. |
multidim.PointCloud.gaussian_fit([center]) |
Fit a normalized Gaussian to this cloud (using SVD). |
multidim.PointCloud.make_pers0([cutoff]) |
Run the UnionFind algorithm to mark connected components of the SimplicialComplex. |
multidim.PointCloud.make_pers1_rca1([cutoff]) |
Run RCA1 and make a 1-dimensional homology.PersDiag for the edge-pairings for cycle generators. |
multidim.PointCloud.nearest_neighbors(k) |
Compute k nearest-neighbors of the PointCloud, using a clever CoverTree algorithm. |
multidim.PointCloud.plot(canvas[, cutoff, …]) |
Plot a PointCloud, decorated by various proeprties. |
multidim.PointCloud.reset() |
delete persistence diagrams, and forget all representative and positivity information. |
multidim.PointCloud.sever() |
Subdivide a SimplicialComplex or PointCloud into several smaller partitions, using the known 0-dimensional persistence diagram. |
multidim.PointCloud.unique_with_multiplicity() |
Look for duplicate points, and mark their multiplicity. |
multidim.PointCloud.witnessed_barycenters(k) |
Build the PointCloud of k-witnessed barycenters, weighted by distance-to-measure. |
multidim.SimplicialComplex([stratum]) |
A class for abstract weighted simplicial complexes. |
multidim.SimplicialComplex.cells(dim) |
iterate over all Simplex objects of dimension dim. |
multidim.SimplicialComplex.check() |
Run consistency checks on all simplices in all dimensions. |
multidim.SimplicialComplex.from_distances(dists) |
Construct a SimplicialComplex from a symmetric matrix of distances. |
multidim.SimplicialComplex.make_pers0([cutoff]) |
Run the UnionFind algorithm to mark connected components of the SimplicialComplex. |
multidim.SimplicialComplex.make_pers1_rca1([…]) |
Run RCA1 and make a 1-dimensional homology.PersDiag for the edge-pairings for cycle generators. |
multidim.SimplicialComplex.reset() |
delete persistence diagrams, and forget all representative and positivity information. |
multidim.covertree |
This module contains the essential classes for the “Cover-tree with friends” algorithm, namely: |
multidim.covertree.CoverLevel(covertree, …) |
A thin class to represent one level of the filtration in a CoverTree. |
multidim.covertree.CoverTree(pointcloud[, …]) |
An efficient and convenient implementation of the “Cover Tree with Friends” algorithm. |
multidim.fast_algorithms |
This Cython module contains core algorithms for multidimensional data. |
multidim.models |
This module contains classifiers based on the SciKitLearn framework. |
multidim.models.CDER([stop_level]) |
The CDER (Cover-Tree Differencing for Entropy Reduction) algorithm for supervised machine-learning of labelled cloud collections. |
multidim.models.GaussianMixtureClassifier([…]) |
A scikit-learn classification estimator, for any sort of Gaussian mixture model. |
timeseries |
This module defines tools for geometric analysis of one-dimensional (time-series) data sets. |
timeseries.jagged(persdiag, index) |
Produce a piecewise-linear function that matches the given persistence diagram. |
timeseries.Signal(values[, times]) |
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timeseries.Signal.feature([index]) |
return the region of a feature, with vertical displacement threshold tau. |
timeseries.Signal.feature_match(other[, …]) |
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timeseries.Signal.from_pointcloud(points, …) |
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timeseries.Signal.gap() |
Return the largest homology. |
timeseries.Signal.height_measure([sigma, …]) |
Use a simulation to estimate the height-measure of an interval. |
timeseries.Signal.interval_height(interval) |
the indicator-persistence function for intervals, called h_U(A) in the notes. |
timeseries.Signal.iter_features([min_pers, …]) |
walk the feature tree. |
timeseries.Signal.iter_intervals() |
return the itertools combinations iterator over all sub-intervals. |
timeseries.Signal.iter_windows_by_index(window) |
Produce equal-length Signals using a sliding-window on self. |
timeseries.Signal.jagged([beta]) |
call timeseries.jagged() on this Signal’s own persistence diagram. |
timeseries.Signal.normalize() |
change this Signal object to have mean = 0 and max-min = 1 |
timeseries.Signal.plot(canvas[, title]) |
Plot the Signal. |
timeseries.Signal.profile(arch[, normalize, …]) |
produce profile by dragging an archetype across self, looking for matches. |
timeseries.Signal.sample_near([sigma]) |
return a Signal object that is L2-near self in the normal distribution. |
timeseries.Signal.self_similarity(window[, …]) |
Compare sliding windows of this Signal using a distance function. |
timeseries.SpaceCurve(tn[, px, py, pz, …]) |
SpaceCurve is a Python class for studying curves in \(\mathbb{R}^2\) or \(\mathbb{R}^3\). |
timeseries.SpaceCurve.accel(rate) |
Change time parametrization, to represent a constant tangential acceleration (or deceleration). |
timeseries.SpaceCurve.arclength_param() |
Change time parametrization to the universal speed=1 arclength parametrization. |
timeseries.SpaceCurve.auto_bin([num_bins, …]) |
Count bins on the transformed persistence diagrams of -Speed/7 (so it is expected to be between 0 and 100) -Climb/3 (so it is expected to be between 0 and 100) -Curvature*10000 (so it is expected to be between 0 and 100) -Torsion*10000 (so it is expected to be between 0 and 100) -Bank*100/(pi/4) (==grade, between 0 and 100) |
timeseries.SpaceCurve.clean_copy([cleanup_func]) |
Make copy in which a cleanup function performed on the data. |
timeseries.SpaceCurve.compute() |
Compute some nice invariants and store them to self.info. |
timeseries.SpaceCurve.copy() |
make an identical copy of self. |
timeseries.SpaceCurve.duration() |
return string of duraction of SpaceCurve, converting integer nanoseconds to string seconds. |
timeseries.SpaceCurve.featurize([…]) |
A convenience function to compute everything we think might be important. |
timeseries.SpaceCurve.lift_and_mass() |
Produce the terms of the force-balance equations, to help derive coefficient-of-lift and mass from pure trajectory information. |
timeseries.SpaceCurve.lift_profile([…]) |
histogram of the lift_and_mass by lift. |
timeseries.SpaceCurve.load(filename) |
Simple CSV reader. |
timeseries.SpaceCurve.mass_profile([…]) |
histogram of the lift_and_mass by mass. |
timeseries.SpaceCurve.plot(canvas[, title, …]) |
Plot the SpaceCurve in 3D. |
timeseries.SpaceCurve.reparam(rate) |
Change time parametrization, to represent a constant change of speed. |
timeseries.SpaceCurve.reverse() |
Reverse the time parametrization of the SpaceCurve. |
timeseries.SpaceCurve.signature_curve() |
Olver/Boutin signature curve. |
timeseries.SpaceCurve.slide([window, …]) |
Produce equal-time SpaceCurves using a sliding-window on self. |
timeseries.SpaceCurve.snip([time_step, …]) |
Cut this SpaceCurve into equal-time snippets. |
timeseries.test_mollifier |
Test the mollifier code |
timeseries.test_mollifier.TestMollifier |
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timeseries.test_mollifier.TestMollifier.setup() |
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timeseries.test_mollifier.TestMollifier.setup_method(…) |
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timeseries.test_mollifier.TestMollifier.teardown() |
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timeseries.test_mollifier.TestMollifier.teardown_method(…) |
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timeseries.test_mollifier.TestMollifier.test_refinement_counts() |
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timeseries.test_mollifier.TestMollifier.test_resonable_reconstruction() |