edu.stanford.math.plex

Class Persistence

java.lang.Object

edu.stanford.math.plex.Persistence

public class Persistence
extends java.lang.Object

The Persistence class class implements the algorithm of Zomorodian and Carlsson for computing the persistent homology groups with coefficients in a finite field. The details of this are too complex to explain here. See A. Zomorodian and G. Carlsson, "Computing persistent homology," Discrete and Computational Geometry, 33 (2), pp. 247-274.

The algorithm needs to be extended to return useful basis elements for the homology, and do cohomology calculations. And a really big, open question is how to do the same sort of calculation when using some representation (possibly simplicial sets) that will scale better at the persistence parameter increases.

Version:

$Id$

Constructor Summary

Constructors

Constructor and Description
Persistence()

Method Summary

Methods

Modifier and Type	Method and Description
static int	baseModulus() What is modulus of the coefficient field?
PersistenceInterval.Float[]	computeIntervals(SimplexStream stream) Calculate the persistent homology.
PersistenceInterval.Float[]	computeIntervals(SimplexStream stream, boolean preserveStream, int prime) Calculate the persistent homology with a specified Zp.
PersistenceInterval[]	computeRawIntervals(SimplexStream stream, boolean preserveStream, int prime) Calculate the raw persistent intervals for a stream, using a specified Zp.
int	cycleSpaceDimension() Return the dimension of the cycle space.
static void	setBaseModulus(int modulus) Set or reset the coefficient field.

Methods inherited from class java.lang.Object

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

Constructor Detail

Persistence

public Persistence()

Method Detail

baseModulus

public static int baseModulus()

What is modulus of the coefficient field?

setBaseModulus

public static void setBaseModulus(int modulus)

Set or reset the coefficient field.

Parameters:

modulus - Must be a prime in [2,255].

Throws:

java.lang.IllegalArgumentException

cycleSpaceDimension

public int cycleSpaceDimension()

Return the dimension of the cycle space.

This function is for performance tuning and pandering to aimless curiosity.

Returns:

number of basis cycles.

computeIntervals

public PersistenceInterval.Float[] computeIntervals(SimplexStream stream)

Calculate the persistent homology.

Parameters:

stream - generates simplices in persistence/dimension order.

Returns:

PersistenceInterval.Float[] instances describing the homology.

computeIntervals

public PersistenceInterval.Float[] computeIntervals(SimplexStream stream,
                                           boolean preserveStream,
                                           int prime)

Calculate the persistent homology with a specified Zp.

Parameters:

stream - generates simplices in persistence/dimension order.

preserveStream - If true, don't deplete the stream.

prime - Set the base field to be Z/prime.

Returns:

PersistenceInterval.Float[] instances describing the homology.

computeRawIntervals

public PersistenceInterval[] computeRawIntervals(SimplexStream stream,
                                        boolean preserveStream,
                                        int prime)

Calculate the raw persistent intervals for a stream, using a specified Zp. This method will probably be used only by internal tests.

Parameters:

stream - generates simplices in persistence/dimension order.

preserveStream - If true, don't deplete the stream.

prime - Set the base field to be Z/prime.

Returns:

PersistenceInterval[] instances describing the homology in terms of the raw filtration indices.