edu.stanford.math.plex4.autogen.homology

Class IntPersistenceAlgorithm<U>

java.lang.Object

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

edu.stanford.math.plex4.homology.interfaces.AbstractPersistenceBasisAlgorithm<U,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>>

edu.stanford.math.plex4.autogen.homology.IntPersistenceAlgorithm<U>

Direct Known Subclasses:

IntPersistentHomology

public abstract class IntPersistenceAlgorithm<U>
extends AbstractPersistenceBasisAlgorithm<U,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>>

This class defines the functionality for a persistence algorithm with underlying field type being int and underlying basis element type being U. It acts as an intermediate layer between the interface AbstractPersistenceBasisAlgorithm and the actual implementations of the persistent homology/cohomology algorithms.

int the underlying type of the coefficient field

U the underlying basis type

Author:

autogen

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
IntPersistenceAlgorithm(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
AnnotatedBarcodeCollection<java.lang.Integer,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>>	computeAnnotatedIndexIntervals(AbstractFilteredStream<U> stream) This function computes the augmented persistence index intervals for a supplied filtered chain complex.
protected abstract AnnotatedBarcodeCollection<java.lang.Integer,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>>	computeAnnotatedIntervalsImpl(AbstractFilteredStream<U> stream) This function provides the implementation of computeAnnotatedIntervals.
BarcodeCollection<java.lang.Integer>	computeIndexIntervals(AbstractFilteredStream<U> stream) This function computes the persistence index intervals of a filtered chain complex.
protected abstract BarcodeCollection<java.lang.Integer>	computeIntervalsImpl(AbstractFilteredStream<U> stream) This function provides the implementation of computeIntervals.
edu.stanford.math.primitivelib.autogen.formal_sum.IntAlgebraicFreeModule<U>	getChainModule() This function returns the free module used for the arithmetic computations.
edu.stanford.math.primitivelib.autogen.algebraic.IntAbstractField	getField() This function returns the field over which the homology is computed.
protected void	initializeFilteredComparator(AbstractFilteredStream<U> stream) This function simply updates the filtered comparator to the one induced by the given filtered stream.
protected U	low(edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U> chain) This function computes the operation low_A(j) as described in the paper.

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

computeAnnotatedIntervals

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> chainModule

This objects performs the chain computations.

basisComparator

protected final java.util.Comparator<U> basisComparator

This comparator defines the ordering on the basis elements.

filteredComparator

protected java.util.Comparator<U> 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

IntPersistenceAlgorithm

public IntPersistenceAlgorithm(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

getChainModule

public edu.stanford.math.primitivelib.autogen.formal_sum.IntAlgebraicFreeModule<U> getChainModule()

This function returns the free module used for the arithmetic computations.

Returns:

the free module over chains in U

getField

public edu.stanford.math.primitivelib.autogen.algebraic.IntAbstractField getField()

This function returns the field over which the homology is computed.

Returns:

the field over type int

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>

Parameters:

stream - the filtered chain complex

Returns:

the persistence intervals of the given complex

computeAnnotatedIndexIntervals

public AnnotatedBarcodeCollection<java.lang.Integer,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>> computeAnnotatedIndexIntervals(AbstractFilteredStream<U> stream)

Description copied from class: AbstractPersistenceBasisAlgorithm

This function computes the augmented persistence index intervals for a supplied filtered chain complex. The augmented persistence intervals are the same as the regular persistence intervals, except that each interval is annotated with a generator of type B. Note that it returns intervals corresponding to the internal filtration indices of the basis elements.

Specified by:

computeAnnotatedIndexIntervals in class AbstractPersistenceBasisAlgorithm<U,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>>

Parameters:

stream - the filtered chain complex

Returns:

the augmented persistence intervals

computeIntervalsImpl

protected abstract BarcodeCollection<java.lang.Integer> computeIntervalsImpl(AbstractFilteredStream<U> stream)

This function provides the implementation of computeIntervals.

Parameters:

stream - the filtered chain complex

Returns:

the persistence intervals of the given complex

computeAnnotatedIntervalsImpl

protected abstract AnnotatedBarcodeCollection<java.lang.Integer,edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U>> computeAnnotatedIntervalsImpl(AbstractFilteredStream<U> stream)

This function provides the implementation of computeAnnotatedIntervals.

Parameters:

stream - the filtered chain complex

Returns:

the augmented persistence intervals

low

protected U low(edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<U> chain)

This function computes the operation low_A(j) as described in the paper. Note that if the chain is empty (for example the column contains only zeros), then this function returns null.

Parameters:

chain - the chain to search

Returns:

the lowest element of the chain