edu.stanford.math.plex4.homology.zigzag

Class ZigZagHomology<U extends PrimitiveBasisElement>

java.lang.Object

edu.stanford.math.plex4.homology.interfaces.AbstractPersistenceAlgorithm<U>

edu.stanford.math.plex4.homology.zigzag.ZigZagHomology<U>

public class ZigZagHomology<U extends PrimitiveBasisElement>
extends AbstractPersistenceAlgorithm<U>

Field Summary

Fields

Modifier and Type	Field and Description
protected java.util.Comparator<U>	basisComparator This comparator defines the ordering on the basis elements.
protected edu.stanford.math.primitivelib.autogen.formal_sum.IntAlgebraicFreeModule<U>	chainModule This objects performs the chain computations.
protected edu.stanford.math.primitivelib.autogen.algebraic.IntAbstractField	field This is the field over which we perform the arithmetic computations.
protected java.util.Comparator<U>	filteredComparator This comparator provides the dictionary ordering on filtration value - basis element pairs.
protected int	maxDimension This stores the maximum dimension for which to compute (co)homology.
protected int	minDimension This stores the minimum dimension for which to compute (co)homology.

Constructor Summary

Constructors

Constructor and Description
ZigZagHomology(edu.stanford.math.primitivelib.autogen.algebraic.IntAbstractField field, java.util.Comparator<U> basisComparator, int minDimension, int maxDimension) This constructor initializes the object with a field and a comparator on the basis type.

Method Summary

Methods

Modifier and Type	Method and Description
BarcodeCollection<java.lang.Integer>	computeIndexIntervals(AbstractFilteredStream<U> stream) This function computes the persistence index intervals of a filtered chain complex.
protected void	initializeFilteredComparator(AbstractFilteredStream<U> stream) This function simply updates the filtered comparator to the one induced by the given filtered stream.

Methods inherited from class edu.stanford.math.plex4.homology.interfaces.AbstractPersistenceAlgorithm

computeIntervals

Methods inherited from class java.lang.Object

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

Field Detail

field

protected final edu.stanford.math.primitivelib.autogen.algebraic.IntAbstractField field

This is the field over which we perform the arithmetic computations.

chainModule

protected final edu.stanford.math.primitivelib.autogen.formal_sum.IntAlgebraicFreeModule<U extends PrimitiveBasisElement> chainModule

This objects performs the chain computations.

basisComparator

protected final java.util.Comparator<U extends PrimitiveBasisElement> basisComparator

This comparator defines the ordering on the basis elements.

filteredComparator

protected java.util.Comparator<U extends PrimitiveBasisElement> filteredComparator

This comparator provides the dictionary ordering on filtration value - basis element pairs.

minDimension

protected int minDimension

This stores the minimum dimension for which to compute (co)homology.

maxDimension

protected int maxDimension

This stores the maximum dimension for which to compute (co)homology.

Constructor Detail

ZigZagHomology

public ZigZagHomology(edu.stanford.math.primitivelib.autogen.algebraic.IntAbstractField field,
              java.util.Comparator<U> basisComparator,
              int minDimension,
              int maxDimension)

This constructor initializes the object with a field and a comparator on the basis type.

Parameters:

field - a field structure on the type int

basisComparator - a comparator on the basis type U

minDimension - the minimum dimension to compute

maxDimension - the maximum dimension to compute

Method Detail

initializeFilteredComparator

protected void initializeFilteredComparator(AbstractFilteredStream<U> stream)

This function simply updates the filtered comparator to the one induced by the given filtered stream.

Parameters:

stream - the AbstractFilteredStream that provides the filtration index information

computeIndexIntervals

public BarcodeCollection<java.lang.Integer> computeIndexIntervals(AbstractFilteredStream<U> stream)

Description copied from class: AbstractPersistenceAlgorithm

This function computes the persistence index intervals of a filtered chain complex. In other words, it returns intervals corresponding to the internal filtration indices of the basis elements.

Specified by:

computeIndexIntervals in class AbstractPersistenceAlgorithm<U extends PrimitiveBasisElement>

Parameters:

stream - the filtered chain complex

Returns:

the persistence intervals of the given complex