edu.stanford.math.plex4.streams.utility

Class StreamUtility

java.lang.Object

edu.stanford.math.plex4.streams.utility.StreamUtility

public class StreamUtility
extends java.lang.Object

This class contains various static functions for querying and manipulating filtered chain complexes.

Author:

Andrew Tausz

Constructor Summary

Constructors

Constructor and Description
StreamUtility()

Method Summary

Methods

Modifier and Type	Method and Description
static java.util.List<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<Simplex,Simplex>>	alexanderWhitneyDiagonal(Simplex simplex) This function computes the Alexander-Whitney diagonal map of a given simplex defined by Delta([v_0, ...
static edu.stanford.math.primitivelib.autogen.matrix.IntSparseMatrix	createAlexanderWhitneyMatrix(AbstractFilteredStream<Simplex> stream)
static <T> edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>>	createBoundaryMatrixAsDoubleSum(AbstractFilteredStream<T> stream) This function returns the boundary matrix for the entire complex.
static <T> edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>>	createBoundaryMatrixAsDoubleSum(AbstractFilteredStream<T> stream, int dimension) This function returns the boundary matrix for the entire complex.
static <T> edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>>	createBoundaryMatrixAsIntSum(AbstractFilteredStream<T> stream) This function returns the boundary matrix for the entire complex.
static <T> edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>>	createBoundaryMatrixAsIntSum(AbstractFilteredStream<T> stream, int dimension) This function returns the boundary matrix for the entire complex.
static <T> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<T>>	getBoundaryMatrixColumns(AbstractFilteredStream<T> stream, int dimension) This function returns the boundary matrix at the specified dimension as a list of columns
static <R,T> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,T>>	getBoundaryMatrixColumns(AbstractFilteredStream<T> stream, int dimension, edu.stanford.math.primitivelib.autogen.formal_sum.ObjectAlgebraicFreeModule<R,T> chainModule) This function produces a list of formal sums which are the columns of the boundary matrix at the requested dimension.
static AbstractUndirectedGraph	getNeighborhoodGraph(AbstractFilteredStream<Simplex> stream) This function returns the 1-skeleton of a filtered simplicial complex in the form of an undirected graph.
static UndirectedListGraph	getNeighborhoodGraph(AbstractFilteredStream<Simplex> stream, int minFiltrationIndex) This function returns a graph containing the 1-skeleton of a given filtered simplicial complex.
static <T> java.util.List<T>	getSkeleton(AbstractFilteredStream<T> stream, int k) This function dumps the k-skeleton of a chain complex into a list.
static <T> int	getSkeletonSize(AbstractFilteredStream<T> stream, int k) This function computes the size of the k-skeleton of a chain complex.

Methods inherited from class java.lang.Object

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

Constructor Detail

StreamUtility

public StreamUtility()

Method Detail

getSkeleton

public static <T> java.util.List<T> getSkeleton(AbstractFilteredStream<T> stream,
                                int k)

This function dumps the k-skeleton of a chain complex into a list.

Type Parameters:

T - the type of the basis elements

Parameters:

stream - the stream to search

k - the dimension of the objects to retrieve

Returns:

the objects with the requested dimension

getSkeletonSize

public static <T> int getSkeletonSize(AbstractFilteredStream<T> stream,
                      int k)

This function computes the size of the k-skeleton of a chain complex.

Type Parameters:

T - the type of the basis elements

Parameters:

stream - the stream to search

k - the dimension of the objects to retrieve

Returns:

the size of the k-seleton of the complex

createBoundaryMatrixAsIntSum

public static <T> edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>> createBoundaryMatrixAsIntSum(AbstractFilteredStream<T> stream)

This function returns the boundary matrix for the entire complex.

Type Parameters:

T - the underlying basis type

Parameters:

stream - the complex

Returns:

the boundary matrix as an IntSparseFormalSum

createBoundaryMatrixAsDoubleSum

public static <T> edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>> createBoundaryMatrixAsDoubleSum(AbstractFilteredStream<T> stream)

This function returns the boundary matrix for the entire complex.

Type Parameters:

T - the underlying basis type

Parameters:

stream - the complex

Returns:

the boundary matrix as a DoubleSparseFormalSum

createBoundaryMatrixAsIntSum

public static <T> edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>> createBoundaryMatrixAsIntSum(AbstractFilteredStream<T> stream,
                                                                                                                                                                       int dimension)

This function returns the boundary matrix for the entire complex.

Type Parameters:

T - the underlying basis type

Parameters:

stream - the complex

dimension - the dimension to get the boundary for

Returns:

the boundary matrix as an IntSparseFormalSum

createBoundaryMatrixAsDoubleSum

public static <T> edu.stanford.math.primitivelib.autogen.formal_sum.DoubleSparseFormalSum<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<T,T>> createBoundaryMatrixAsDoubleSum(AbstractFilteredStream<T> stream,
                                                                                                                                                                             int dimension)

This function returns the boundary matrix for the entire complex.

Type Parameters:

T - the underlying basis type

Parameters:

stream - the complex

dimension - the dimension to get the boundary for

Returns:

the boundary matrix as a DoubleSparseFormalSum

getBoundaryMatrixColumns

public static <T> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.IntSparseFormalSum<T>> getBoundaryMatrixColumns(AbstractFilteredStream<T> stream,
                                                                                                                   int dimension)

This function returns the boundary matrix at the specified dimension as a list of columns

Type Parameters:

T - the underlying basis type

Parameters:

stream - the complex

dimension - the dimension to get the boundary for

Returns:

the boundary matrix as a list of formal sums

getBoundaryMatrixColumns

public static <R,T> java.util.List<edu.stanford.math.primitivelib.autogen.formal_sum.ObjectSparseFormalSum<R,T>> getBoundaryMatrixColumns(AbstractFilteredStream<T> stream,
                                                                                                                          int dimension,
                                                                                                                          edu.stanford.math.primitivelib.autogen.formal_sum.ObjectAlgebraicFreeModule<R,T> chainModule)

This function produces a list of formal sums which are the columns of the boundary matrix at the requested dimension.

Type Parameters:

R - the type of the ring in which to compute

T - the type of the basis elements

Parameters:

stream - the stream to perform the operation on

dimension - the dimension

chainModule - the module which performs the algebraic operations (forming the sums)

Returns:

the columns of the boundary matrix at the request dimension

getNeighborhoodGraph

public static UndirectedListGraph getNeighborhoodGraph(AbstractFilteredStream<Simplex> stream,
                                       int minFiltrationIndex)

This function returns a graph containing the 1-skeleton of a given filtered simplicial complex. It only adds edges whose filtration index is greater than the specified value.

Parameters:

stream - the stream to perform the operation on

minFiltrationIndex - the minimum filtration index

Returns:

the 1-skeleton of the complex in the form of an undirected graph

getNeighborhoodGraph

public static AbstractUndirectedGraph getNeighborhoodGraph(AbstractFilteredStream<Simplex> stream)

This function returns the 1-skeleton of a filtered simplicial complex in the form of an undirected graph.

Parameters:

stream - the stream to perform the operation on

Returns:

the 1-skeleton of the complex

createAlexanderWhitneyMatrix

public static edu.stanford.math.primitivelib.autogen.matrix.IntSparseMatrix createAlexanderWhitneyMatrix(AbstractFilteredStream<Simplex> stream)

alexanderWhitneyDiagonal

public static java.util.List<edu.stanford.math.primitivelib.autogen.pair.ObjectObjectPair<Simplex,Simplex>> alexanderWhitneyDiagonal(Simplex simplex)

This function computes the Alexander-Whitney diagonal map of a given simplex defined by Delta([v_0, ... v_n]) = sum_i [v_0, ... v_i] tensor [v_i, ... v_n]

Parameters:

simplex - the simplex argument

Returns:

the Alexander-Whitney diagonal map of the given simplex