edu.stanford.math.plex

Class Chain

java.lang.Object

edu.stanford.math.plex.Chain

public class Chain
extends java.lang.Object

A Chain instance is an element of the module constructed by taking formal sums of ring elements times simplices. In our case the ring will always be a field, so the module is a vector space where the basis elements are indexed by simplices. The dimension of the space of chains is huge, so instead of making vectors of length the dimension of the space, we use a sparse representation with (sorted) Simplex[] arrays and corresponding int[] coefficient arrays. Addition and finding the coefficient of the largest (non-zero) basis element are the most important in persistence calculations, and this representation is suited to these operations.

See Persistence, and references therein for the real story.

Version:

$Id$

See Also:

Persistence

Constructor Summary

Constructors

Constructor and Description
Chain(int modulus)
Chain(int modulus, int[] cvec, Simplex[] elts)
Chain(int modulus, int coeff, Simplex elt)

Method Summary

Methods

Modifier and Type	Method and Description
Chain	add(Chain x, int c) Add one chain to another.
protected static int[]	alternatingCoefficients(int mod, int len)
protected static void	chain_sort(Simplex[] b, int[] c)
int	coefficientOf(Simplex s)
boolean	equals(Chain c) Chain equals implementation.
Chain	filter(java.util.List<Simplex> simplexList)
Chain	filter(SimplexTable simplexList) Filter simplices.
int	HashCode() Because we override equals, we also need to override HashCode.
boolean	isZero()
static boolean	isZero(Chain c)
int	maxC() Return the coefficient of the largetst basis element.
Simplex	maxS() Return the largest basis element.
protected Chain	mergeBasisElts(Simplex[] first, int[] fc, Simplex[] second, int[] sc, int c)
protected static Chain	normalize(Simplex[] s, int[] c, int p)
int	rewriteModP(int elt) Rewrite an element in Z/p from the representation in the interval [0,p) to the representation in (-p/2,p/2).
protected static boolean	s_and_c_okay(Simplex[] s, int[] c, int p)
java.lang.String	toString() Represent a Chain as a String.
static Chain	zero(int modulus)

Methods inherited from class java.lang.Object

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

Constructor Detail

Chain

public Chain(int modulus,
     int[] cvec,
     Simplex[] elts)

Chain

public Chain(int modulus)

Chain

public Chain(int modulus,
     int coeff,
     Simplex elt)

Method Detail

maxS

public Simplex maxS()

Return the largest basis element.

Returns:

Largest simplex with nonzero coefficient.

maxC

public int maxC()

Return the coefficient of the largetst basis element.

Returns:

Coefficient of largest simplex with nonzero coefficient.

zero

public static Chain zero(int modulus)

isZero

public static boolean isZero(Chain c)

isZero

public boolean isZero()

mergeBasisElts

protected Chain mergeBasisElts(Simplex[] first,
                   int[] fc,
                   Simplex[] second,
                   int[] sc,
                   int c)

add

public Chain add(Chain x,
        int c)

Add one chain to another.

Parameters:

x - the chain to add

c - a coefficient to apply to the argument chain before adding.

Returns:

the result of the addition

normalize

protected static Chain normalize(Simplex[] s,
              int[] c,
              int p)

chain_sort

protected static void chain_sort(Simplex[] b,
              int[] c)

alternatingCoefficients

protected static int[] alternatingCoefficients(int mod,
                            int len)

rewriteModP

public int rewriteModP(int elt)

Rewrite an element in Z/p from the representation in the interval [0,p) to the representation in (-p/2,p/2).

Parameters:

elt - Element

Returns:

Rewritten element.

toString

public java.lang.String toString()

Represent a Chain as a String.

Overrides:

toString in class java.lang.Object

Returns:

A string that describes a Chain.

filter

public Chain filter(SimplexTable simplexList)

Filter simplices. In several cases, we'll want to extract only a portion of a chain spanned by specific simplices. In the non-basis supported persistent interval computation this is an optimization step.

This function also gets used to replace generated (and thus filtration agnostic) simplices by the singleton instances equipped with the correct filtration index.

Parameters:

simplexList - The list of simplices onto which the chain is projected

Returns:

A chain with only the simplices form the list, and with references to each simplex updated to point at those in the list.

filter

public Chain filter(java.util.List<Simplex> simplexList)

coefficientOf

public int coefficientOf(Simplex s)

equals

public boolean equals(Chain c)

Chain equals implementation. Allows for standard style compliant comparisons.

Parameters:

c - Chain to compare

Returns:

true if equal, else false.

HashCode

public int HashCode()

Because we override equals, we also need to override HashCode. We don't claim to do any kind of an informed choice here.

Returns:

Always returns 0.

s_and_c_okay

protected static boolean s_and_c_okay(Simplex[] s,
                   int[] c,
                   int p)