orbital.math
Interface Metric

public interface Metric

This interface imposes a metric on the objects supported by it. A metric is a measure for distances.

d:A×A→R is a metric (or distance function) on A if ∀x,y,z,w∈A
(def)	d(x,y)=0 ⇔ x=y	"(positive?) definite"
(s)	d(x,y) = d(y,x)	"symmetric"
(Δ)	d(x,y) ≤ d(x,z) + d(z,y)	"triangular inequality"
⇒ (even for half-metrics, i.e. without definite)
(□)	|d(x,y) - d(z,w)| ≤ d(x,z) + d(y,w)	"rectangular inequality"
(pos)	d(x,y)≥0	"positive"

Author:

André Platzer

See Also:

Normed, INDUCED, Comparator

Field Summary

static Metric

INDUCED The metric induced by a norm ||.||.

Method Summary

Real	distance(java.lang.Object x, java.lang.Object y) Returns the distance of two objects.

Field Detail

INDUCED

static final Metric INDUCED

The metric induced by a norm ||.||.

A norm ||.|| on arithmetic objects induces a metric d:A×A→R; (a,b)↦d(a,b) := ||a-b||.

See Also:

Normed

Method Detail

distance

Real distance(java.lang.Object x,
              java.lang.Object y)

Returns the distance of two objects.

Returns:

the distance of the objects a and b, or Double.NaN if it is symbolic and has no numeric distance.

Postconditions:

RES >= 0 && RES==0 <=> x==y && distance(x,y) == distance(y,x) && distance(x,y) <= distance(x,z) + distance(z,y) && RES≠null