edu.stanford.math.plex4.streams.impl

Class VietorisRipsStream<T>

java.lang.Object

edu.stanford.math.plex4.streams.interfaces.PrimitiveStream<Simplex>

edu.stanford.math.plex4.streams.impl.FlagComplexStream

edu.stanford.math.plex4.streams.impl.FlexibleVietorisRipsStream<T>

edu.stanford.math.plex4.streams.impl.VietorisRipsStream<T>

Type Parameters:

T - the base type of the underlying metric space

All Implemented Interfaces:

AbstractFilteredStream<Simplex>, java.lang.Iterable<Simplex>

public class VietorisRipsStream<T>
extends FlexibleVietorisRipsStream<T>

This class implements the Vietoris-Rips filtered simplicial complex. A simplex [v_0, ..., v_k] is in VR(r) if and only if the pairwise distances d(v_i, v_j) are less than r for all 0 <= i, j <= k. Thus a Vietoris-Rips complex is fully defined by its 1-skeleton, in that it is the maximal simplicial complex given such a 1-skeleton. For this reason, we simply derive from the FlagComplexStream abstract class, and implement the pairwise thresholding in order to generate the 1-skeleton.

Author:

Andrew Tausz, Mikael Vejdemo-Johansson

Field Summary

Fields inherited from class edu.stanford.math.plex4.streams.impl.FlexibleVietorisRipsStream

maxDistance, metricSpace

Fields inherited from class edu.stanford.math.plex4.streams.impl.FlagComplexStream

converter, indices, maxAllowableDimension, neighborhoodGraph

Fields inherited from class edu.stanford.math.plex4.streams.interfaces.PrimitiveStream

storageStructure

Constructor Summary

Constructors

Constructor and Description
VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double[] filtrationValues, int maxDimension)
VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension) Constructor which initializes the complex with a metric space.
VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension, int numDivisions)
VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension, int[] indices)
VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension, int numDivisions, StreamStorageStructure<Simplex> storageStructure)

Method Summary

Methods inherited from class edu.stanford.math.plex4.streams.impl.FlexibleVietorisRipsStream

constructEdges

Methods inherited from class edu.stanford.math.plex4.streams.impl.FlagComplexStream

addCofaces, constructComplex, getConverter, getFiltrationValue, getNeighborhoodGraph, incrementalExpansion, transform

Methods inherited from class edu.stanford.math.plex4.streams.interfaces.PrimitiveStream

containsElement, finalizeStream, getBasisComparator, getBoundary, getBoundaryCoefficients, getDimension, getFiltrationIndex, getMaximumFiltrationIndex, getMinimumFiltrationIndex, getSize, isFinalized, iterator, validate, validateVerbose

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

VietorisRipsStream

public VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                  double maxDistance,
                  int maxDimension)

Constructor which initializes the complex with a metric space.

Parameters:

metricSpace - the metric space to use in the construction of the complex

maxDistance - the maximum allowable distance

maxDimension - the maximum dimension of the complex

VietorisRipsStream

public VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                  double maxDistance,
                  int maxDimension,
                  int numDivisions)

VietorisRipsStream

public VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                  double maxDistance,
                  int maxDimension,
                  int numDivisions,
                  StreamStorageStructure<Simplex> storageStructure)

VietorisRipsStream

public VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                  double maxDistance,
                  int maxDimension,
                  int[] indices)

VietorisRipsStream

public VietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                  double[] filtrationValues,
                  int maxDimension)