Orbital library

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"

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


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:
Method Detail


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

the distance of the objects a and b, or Double.NaN if it is symbolic and has no numeric distance.
RES >= 0 && RES==0 <=> x==y && distance(x,y) == distance(y,x) && distance(x,y) <= distance(x,z) + distance(z,y) && RES≠null

Orbital library
1.3.0: 11 Apr 2009

Copyright © 1996-2009 André Platzer
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