edu.stanford.math.plex4.examples

Class SimplexStreamExamples

java.lang.Object

edu.stanford.math.plex4.examples.SimplexStreamExamples

public class SimplexStreamExamples
extends java.lang.Object

This class contains various functions for producing examples of filtered and static simplicial complexes. Note that we use the term static complex to refer to the fact that all filtration values are zero.

Author:

Andrew Tausz

Constructor Summary

Constructors

Constructor and Description
SimplexStreamExamples()

Method Summary

Methods

Modifier and Type	Method and Description
static ExplicitSimplexStream	createGraphComplex(AbstractUndirectedGraph graph) This function produces a simplicial complex from a given undirected graph.
static ExplicitSimplexStream	createGraphComplex(int[][] adjacencyMatrix) This function produces a simplicial complex from the adjacency matrix of a given graph.
static ExplicitSimplexStream	getAnnulus(int width, int length)
static ExplicitStream<Simplex>	getCircle(int m) This function returns a simplicial circle with m vertices in it.
static ExplicitStream<Simplex>	getFilteredTriangle() This function returns a filtered triangle where each simplex enters at a new filtration index.
static ExplicitSimplexStream	getIcosahedron()
static ExplicitStream<Simplex>	getOctahedron() This function returns a simplicial octahedron.
static ExplicitStream<Simplex>	getSimplicialSphere(int dimension) This function returns a static simplicial complex containing an n-sphere.
static ExplicitStream<Simplex>	getTetrahedron() This function returns a simplicial tetrahedron (which happens to be equal to a simplicial 2-sphere).
static ExplicitStream<Simplex>	getTorus() This function returns a simplicial 2-torus.
static ExplicitStream<Simplex>	getTriangle() This function returns a simplicial triangle (which happens to be equal to a simplicial 1-sphere).
static ExplicitStream<Simplex>	getZomorodianCarlssonExample() This function returns a filtered simplicial complex which is shown in Figure 1 of the paper "Computing Persistent Homology" by Zomorodian and Carlsson.

Methods inherited from class java.lang.Object

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

Constructor Detail

SimplexStreamExamples

public SimplexStreamExamples()

Method Detail

getZomorodianCarlssonExample

public static ExplicitStream<Simplex> getZomorodianCarlssonExample()

This function returns a filtered simplicial complex which is shown in Figure 1 of the paper "Computing Persistent Homology" by Zomorodian and Carlsson.

Returns:

a filtered simplex stream

getFilteredTriangle

public static ExplicitStream<Simplex> getFilteredTriangle()

This function returns a filtered triangle where each simplex enters at a new filtration index.

Returns:

a filtered triangle

getTriangle

public static ExplicitStream<Simplex> getTriangle()

This function returns a simplicial triangle (which happens to be equal to a simplicial 1-sphere).

Returns:

a simplicial triangle

getTetrahedron

public static ExplicitStream<Simplex> getTetrahedron()

This function returns a simplicial tetrahedron (which happens to be equal to a simplicial 2-sphere).

Returns:

a simplicial tetrahedron

getSimplicialSphere

public static ExplicitStream<Simplex> getSimplicialSphere(int dimension)

This function returns a static simplicial complex containing an n-sphere.

Parameters:

dimension - the dimension of the sphere to produce

Returns:

a simplicial sphere

getTorus

public static ExplicitStream<Simplex> getTorus()

This function returns a simplicial 2-torus. This construction was taken from the original version of Javaplex. Note that the complex returned is static meaning that all filtration values are zero.

Returns:

a simplicial complex containing a 2-torus.

getCircle

public static ExplicitStream<Simplex> getCircle(int m)

This function returns a simplicial circle with m vertices in it. It requires that m >= 3.

Parameters:

m - the number of vertices in the circle

Returns:

a simplicial circle with m vertices

getOctahedron

public static ExplicitStream<Simplex> getOctahedron()

This function returns a simplicial octahedron.

Returns:

a simplicial octahedron.

getIcosahedron

public static ExplicitSimplexStream getIcosahedron()

getAnnulus

public static ExplicitSimplexStream getAnnulus(int width,
                               int length)

createGraphComplex

public static ExplicitSimplexStream createGraphComplex(AbstractUndirectedGraph graph)

This function produces a simplicial complex from a given undirected graph. The resulting complex contains the same vertices and edges as the given graph.

Parameters:

graph - the graph to convert to a simplicial complex

Returns:

a simplicial complex containing the same vertices and edges as the given graph

createGraphComplex

public static ExplicitSimplexStream createGraphComplex(int[][] adjacencyMatrix)

This function produces a simplicial complex from the adjacency matrix of a given graph. The resulting complex contains the same vertices and edges as the given graph.

Parameters:

adjacencyMatrix - the adjacency matrix of the graph to convert to a simplicial complex

Returns:

a simplicial complex containing the same vertices and edges as the given graph