GeometricSimplexStream

java.lang.Object
- edu.stanford.math.plex4.streams.impl.GeometricSimplexStream

All Implemented Interfaces:

AbstractIntMetricSpace, AbstractObjectMetric<double[]>, AbstractObjectMetricSpace<double[]>, AbstractFilteredStream<Simplex>, java.lang.Iterable<Simplex>
```
public class GeometricSimplexStream
extends java.lang.Object
implements AbstractFilteredStream<Simplex>, AbstractObjectMetricSpace<double[]>
```
This class defines a geometric realization of a filtered simplicial complex, ie. one in which the vertices are elements of Euclidean space. A geometric simplex stream is defined to be a simplex stream along with a mapping of the set of vertices to Euclidean space, which in this case is an object of type AbstractObjectMetricSpace.

Author:

Andrew Tausz

Constructor Summary

Constructors
Constructor and Description
`GeometricSimplexStream(AbstractFilteredStream<Simplex> stream, AbstractObjectMetricSpace<double[]> metricSpace)` This constructor initializes the geometric complex from an abstract filtered complex and a metric space.
`GeometricSimplexStream(AbstractFilteredStream<Simplex> stream, double[][] points)` This constructor initializes the geometric complex from an abstract simplicial complex and double array whose rows consist of the Euclidean coordinates of the vertices.

Method Summary

Methods
Modifier and Type	Method and Description
`boolean`	`containsElement(Simplex basisElement)` This function returns whether an element is contained in the stream.
`double`	`distance(double[] a, double[] b)` This function returns the distance between two points.
`double`	`distance(int i, int j)` This function returns the distance between the object at index i and the object at index j.
`void`	`finalizeStream()` This function prepares the stream for use by a consumer, such as the PersistentHomology class.
`java.util.Comparator<Simplex>`	`getBasisComparator()` This function returns a comparator on the underlying basis type.
`Simplex[]`	`getBoundary(Simplex simplex)` This function returns the elements in the boundary of the supplied basisElement, without the coefficients.
`int[]`	`getBoundaryCoefficients(Simplex simplex)` This function returns the coefficients of the boundary of the supplied basis element.
`int`	`getDimension(Simplex element)` This function returns the dimension of a basis element within the chain complex.
`int`	`getFiltrationIndex(Simplex basisElement)` This function returns the filtration index of the requested basis element.
`double`	`getFiltrationValue(Simplex basisElement)`
`int`	`getMaximumFiltrationIndex()` This function gets the maximum filtration index in the complex.
`int`	`getMinimumFiltrationIndex()` This function gets the minimum filtration index in the complex.
`double[]`	`getPoint(int index)` This function returns the point at the specified index.
`double[][]`	`getPoints()` This function returns the set of points in the metric space as an array.
`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<Simplex>`	`iterator()`
`int`	`size()` This function returns the number of points in the metric space.
`<G> PersistenceInvariantDescriptor<Interval<java.lang.Double>,G>`	`transform(PersistenceInvariantDescriptor<Interval<java.lang.Integer>,G> barcodeCollection)` This function transforms the given collection of filtration index barcodes into filtration value barcodes.

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

- Constructor Detail
  - GeometricSimplexStream
```
public GeometricSimplexStream(AbstractFilteredStream<Simplex> stream,
                      AbstractObjectMetricSpace<double[]> metricSpace)
```
    This constructor initializes the geometric complex from an abstract filtered complex and a metric space.
    
    Parameters:
    stream - the abstract simplicial complex
    metricSpace - the Euclidean metric space of vertices
  - GeometricSimplexStream
```
public GeometricSimplexStream(AbstractFilteredStream<Simplex> stream,
                      double[][] points)
```
    This constructor initializes the geometric complex from an abstract simplicial complex and double array whose rows consist of the Euclidean coordinates of the vertices.
    
    Parameters:
    stream - the abstract simplicial complex
    points - the array of points
- Method Detail
  - finalizeStream
```
public 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<Simplex>
  - getFiltrationIndex
```
public int getFiltrationIndex(Simplex basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the filtration index of the requested basis element.
    
    Specified by:
    
    getFiltrationIndex in interface AbstractFilteredStream<Simplex>
    
    Parameters:
    basisElement - the basis element to get the filtration index for
    
    Returns:
    the filtration index of the specified basis element
  - containsElement
```
public boolean containsElement(Simplex basisElement)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns whether an element is contained in the stream.
    
    Specified by:
    
    containsElement in interface AbstractFilteredStream<Simplex>
    
    Parameters:
    basisElement - the basis element to be tested
  - isFinalized
```
public boolean isFinalized()
```
    Description copied from interface: AbstractFilteredStream
    
    This function checks whether the finalize() function has been called.
    
    Specified by:
    
    isFinalized in interface AbstractFilteredStream<Simplex>
    
    Returns:
    true if the stream has been finalized, and false otherwise
  - iterator
```
public java.util.Iterator<Simplex> iterator()
```
    Specified by:
    
    iterator in interface java.lang.Iterable<Simplex>
  - getPoint
```
public double[] getPoint(int index)
```
    Description copied from interface: AbstractObjectMetricSpace
    
    This function returns the point at the specified index.
    
    Specified by:
    
    getPoint in interface AbstractObjectMetricSpace<double[]>
    
    Parameters:
    index - the index of the point to retrieve
    
    Returns:
    the point at the given index
  - size
```
public int size()
```
    Description copied from interface: AbstractIntMetricSpace
    
    This function returns the number of points in the metric space.
    
    Specified by:
    
    size in interface AbstractIntMetricSpace
    
    Returns:
    the number of points in the metric space.
  - distance
```
public double distance(int i,
              int j)
```
    Description copied from interface: AbstractIntMetricSpace
    
    This function returns the distance between the object at index i and the object at index j.
    
    Specified by:
    
    distance in interface AbstractIntMetricSpace
    
    Parameters:
    i - the index of the first object
    j - the index of the second object
    
    Returns:
    the distance between the objects at the two given indices
  - distance
```
public double distance(double[] a,
              double[] b)
```
    Description copied from interface: AbstractObjectMetric
    
    This function returns the distance between two points.
    
    Specified by:
    
    distance in interface AbstractObjectMetric<double[]>
    
    Parameters:
    a - the first point
    b - the second point
    
    Returns:
    the distance between the two points
  - getBoundary
```
public Simplex[] getBoundary(Simplex simplex)
```
    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<Simplex>
    
    Parameters:
    simplex - the element to get the boundary of
    
    Returns:
    an array containing the boundary elements of the queried element
  - getBoundaryCoefficients
```
public int[] getBoundaryCoefficients(Simplex simplex)
```
    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<Simplex>
    
    Parameters:
    simplex - the element to get the boundary coefficients of
    
    Returns:
    an array containing the boundary coefficients of the queried element
  - getDimension
```
public int getDimension(Simplex element)
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the dimension of a basis element within the chain complex.
    
    Specified by:
    
    getDimension in interface AbstractFilteredStream<Simplex>
    
    Parameters:
    element - the element to get the dimension of
    
    Returns:
    the dimension of the basis element within the chain complex
  - getPoints
```
public double[][] getPoints()
```
    Description copied from interface: AbstractObjectMetricSpace
    
    This function returns the set of points in the metric space as an array. The returned array satisfies the requirement that the indices of the points in the array are equal to the indices of the points within the metric space.
    
    Specified by:
    
    getPoints in interface AbstractObjectMetricSpace<double[]>
    
    Returns:
    an array containing the points of the metric space
  - getSize
```
public int getSize()
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns the total number of elements in the stream.
    
    Specified by:
    
    getSize in interface AbstractFilteredStream<Simplex>
    
    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<Simplex>
    
    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<Simplex>
    
    Returns:
    the minimum filtration index
  - getBasisComparator
```
public java.util.Comparator<Simplex> getBasisComparator()
```
    Description copied from interface: AbstractFilteredStream
    
    This function returns a comparator on the underlying basis type.
    
    Specified by:
    
    getBasisComparator in interface AbstractFilteredStream<Simplex>
    
    Returns:
    a comparator on the underlying basis type
  - transform
```
public <G> PersistenceInvariantDescriptor<Interval<java.lang.Double>,G> transform(PersistenceInvariantDescriptor<Interval<java.lang.Integer>,G> barcodeCollection)
```
    Description copied from interface: AbstractFilteredStream
    
    This function transforms the given collection of filtration index barcodes into filtration value barcodes.
    
    Specified by:
    
    transform in interface AbstractFilteredStream<Simplex>
    
    Parameters:
    barcodeCollection - the set of filtration index barcodes
    
    Returns:
    the barcodes transformed into filtration value form
  - getFiltrationValue
```
public double getFiltrationValue(Simplex basisElement)
```
    Specified by:
    
    getFiltrationValue in interface AbstractFilteredStream<Simplex>

Class GeometricSimplexStream

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

GeometricSimplexStream

GeometricSimplexStream

Method Detail

finalizeStream

getFiltrationIndex

containsElement

isFinalized

iterator

getPoint

size

distance

distance

getBoundary

getBoundaryCoefficients

getDimension

getPoints

getSize

getMaximumFiltrationIndex

getMinimumFiltrationIndex

getBasisComparator

transform

getFiltrationValue