PrimitiveStream

java.lang.Object
- edu.stanford.math.plex4.streams.interfaces.PrimitiveStream<T>

Type Parameters:
T - the underlying basis type of the stream

All Implemented Interfaces:

AbstractFilteredStream<T>, java.lang.Iterable<T>

Direct Known Subclasses:

ExplicitStream, FlagComplexStream, WitnessStream
```
public abstract class PrimitiveStream<T extends PrimitiveBasisElement>
extends java.lang.Object
implements AbstractFilteredStream<T>
```
This class implements a filtered chain complex where the underlying type is a geometric primitive (a Simplex or a Cell). Thus the appropriate homological functions are defined by the geometric properties of the underlying type. For example, the homological dimension is given by the actual geometric dimension, and the boundary is the geometric boundary of the cell or simplex in question.

Note that this class does not actually implement a storage mechanism, but allows a user to define one via a supplied StreamStorageStructure object. In the event that the user does not supply one, it reverts to the default one.

Author:

Andrew Tausz

Field Summary

Fields
Modifier and Type Field and Description

protected StreamStorageStructure<T> storageStructure
This object implements the actual storage structure for the stream.

Fields
Modifier and Type	Field and Description
`protected StreamStorageStructure<T>`	`storageStructure` This object implements the actual storage structure for the stream.

Constructor Summary

Constructors
Modifier	Constructor and Description
`protected`	`PrimitiveStream(java.util.Comparator<T> comparator)` This constructor construct the stream with the default storage scheme.
`protected`	`PrimitiveStream(StreamStorageStructure<T> storageStructure)` This constructor constructs the stream with the supplied StreamStorageStructure.

Method Summary

Methods
Modifier and Type	Method and Description
`protected abstract void`	`constructComplex()` This abstract function performs the construction of the filtered chain complex.
`boolean`	`containsElement(T basisElement)` This function returns whether an element is contained in the stream.
`void`	`finalizeStream()` This function prepares the stream for use by a consumer, such as the PersistentHomology class.
`java.util.Comparator<T>`	`getBasisComparator()` This function returns a comparator on the underlying basis type.
`T[]`	`getBoundary(T basisElement)` This function returns the elements in the boundary of the supplied basisElement, without the coefficients.
`int[]`	`getBoundaryCoefficients(T basisElement)` This function returns the coefficients of the boundary of the supplied basis element.
`int`	`getDimension(T basisElement)` This function returns the dimension of a basis element within the chain complex.
`int`	`getFiltrationIndex(T basisElement)` This function returns the filtration index of the requested basis element.
`int`	`getMaximumFiltrationIndex()` This function gets the maximum filtration index in the complex.
`int`	`getMinimumFiltrationIndex()` This function gets the minimum filtration index in the complex.
`int`	`getSize()` This function returns the total number of elements in the stream.
`boolean`	`isFinalized()` This function checks whether the finalize() function has been called.
`java.util.Iterator<T>`	`iterator()`
`boolean`	`validate()` This function validates the stream to make sure that it contains a valid filtered simplicial or cell complex.
`boolean`	`validateVerbose()` This function validates the stream to make sure that it contains a valid filtered simplicial or cell complex.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface edu.stanford.math.plex4.streams.interfaces.AbstractFilteredStream
getFiltrationValue, transform

- Field Detail
  - storageStructure
```
protected final StreamStorageStructure<T extends PrimitiveBasisElement> storageStructure
```
    This object implements the actual storage structure for the stream.
- Constructor Detail
  - PrimitiveStream
```
protected PrimitiveStream(StreamStorageStructure<T> storageStructure)
```
    This constructor constructs the stream with the supplied StreamStorageStructure.
    
    Parameters:
    storageStructure - the StreamStorageStructure to use
  - PrimitiveStream
```
protected PrimitiveStream(java.util.Comparator<T> comparator)
```
    This constructor construct the stream with the default storage scheme.
    
    Parameters:
    comparator - a Comparator which defines an ordering for the storage scheme
- Method Detail
  - constructComplex
```
protected abstract void constructComplex()
```
    This abstract function performs the construction of the filtered chain complex. For example, this might construct the complex from a metric space via a Vietoris-Rips or witness construction.
  - getBoundary
```
public final T[] getBoundary(T basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the elements in the boundary of the supplied basisElement, without the coefficients. We do not integrate the elements of the boundary array with their respective coefficients since this interface is designed to be independent of the algebraic environment.
    
    Specified by:
    
    getBoundary in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Parameters:
    basisElement - the element to get the boundary of
    
    Returns:
    an array containing the boundary elements of the queried element
  - getBoundaryCoefficients
```
public final int[] getBoundaryCoefficients(T basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the coefficients of the boundary of the supplied basis element. Note that in many cases, this will be the standard array consisting of alternating signs: [1, -1, 1, -1, ...]. However, this will not always be the case. Thus this must be left abstract. Also note that the coefficients will always be integers.
    
    Specified by:
    
    getBoundaryCoefficients in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Parameters:
    basisElement - the element to get the boundary coefficients of
    
    Returns:
    an array containing the boundary coefficients of the queried element
  - getDimension
```
public final int getDimension(T basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the dimension of a basis element within the chain complex.
    
    Specified by:
    
    getDimension in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Parameters:
    basisElement - the element to get the dimension of
    
    Returns:
    the dimension of the basis element within the chain complex
  - iterator
```
public final java.util.Iterator<T> iterator()
```
    Specified by:
    
    iterator in interface java.lang.Iterable<T extends PrimitiveBasisElement>
  - finalizeStream
```
public final void finalizeStream()
```
    Description copied from interface: AbstractFilteredStream
    
    This function prepares the stream for use by a consumer, such as the PersistentHomology class. After finalization, the stream cannot not be modified by adding or removing elements. In practice, the finalize procedure will probably do some sorting and construction of data structures necessary for iterating through the stream.
    
    Specified by:
    
    finalizeStream in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
  - getFiltrationIndex
```
public final int getFiltrationIndex(T basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the filtration index of the requested basis element.
    
    Specified by:
    
    getFiltrationIndex in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Parameters:
    basisElement - the basis element to get the filtration index for
    
    Returns:
    the filtration index of the specified basis element
  - containsElement
```
public boolean containsElement(T basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns whether an element is contained in the stream.
    
    Specified by:
    
    containsElement in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Parameters:
    basisElement - the basis element to be tested
  - isFinalized
```
public final boolean isFinalized()
```
    Description copied from interface: AbstractFilteredStream
    
    This function checks whether the finalize() function has been called.
    
    Specified by:
    
    isFinalized in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Returns:
    true if the stream has been finalized, and false otherwise
  - getSize
```
public final int getSize()
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the total number of elements in the stream.
    
    Specified by:
    
    getSize in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Returns:
    the size of the stream
  - getMaximumFiltrationIndex
```
public int getMaximumFiltrationIndex()
```
    Description copied from interface: AbstractFilteredStream
    
    This function gets the maximum filtration index in the complex.
    
    Specified by:
    
    getMaximumFiltrationIndex in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Returns:
    the maximum filtration index
  - getMinimumFiltrationIndex
```
public int getMinimumFiltrationIndex()
```
    Description copied from interface: AbstractFilteredStream
    
    This function gets the minimum filtration index in the complex.
    
    Specified by:
    
    getMinimumFiltrationIndex in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Returns:
    the minimum filtration index
  - getBasisComparator
```
public java.util.Comparator<T> getBasisComparator()
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns a comparator on the underlying basis type.
    
    Specified by:
    
    getBasisComparator in interface AbstractFilteredStream<T extends PrimitiveBasisElement>
    
    Returns:
    a comparator on the underlying basis type
  - validate
```
public boolean validate()
```
    This function validates the stream to make sure that it contains a valid filtered simplicial or cell complex. It checks the two following conditions: 1. For each element in the complex, all of the faces of the simplex also belong to the complex. 2. The faces of each simplex have filtration values that are less than or equal to those of its cofaces.
    
    Returns:
    true if the stream is consistent, false otherwise
  - validateVerbose
```
public boolean validateVerbose()
```
    This function validates the stream to make sure that it contains a valid filtered simplicial or cell complex. It checks the two following conditions: 1. For each element in the complex, all of the faces of the simplex also belong to the complex. 2. The faces of each simplex have filtration values that are less than or equal to those of its cofaces.
    
    Returns:
    true if the stream is consistent, false otherwise

Class PrimitiveStream<T extends PrimitiveBasisElement>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.stanford.math.plex4.streams.interfaces.AbstractFilteredStream

Field Detail

storageStructure

Constructor Detail

PrimitiveStream

PrimitiveStream

Method Detail

constructComplex

getBoundary

getBoundaryCoefficients

getDimension

iterator

finalizeStream

getFiltrationIndex

containsElement

isFinalized

getSize

getMaximumFiltrationIndex

getMinimumFiltrationIndex

getBasisComparator

validate

validateVerbose