smile.math.distance.Distance Maven / Gradle / Ivy
/*
* Copyright (c) 2010-2021 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Smile is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Smile. If not, see .
*/
package smile.math.distance;
import java.io.Serializable;
import java.util.function.ToDoubleBiFunction;
import java.util.stream.IntStream;
import smile.math.blas.UPLO;
import smile.math.matrix.Matrix;
/**
* An interface to calculate a distance measure between two objects. A distance
* function maps pairs of points into the non-negative reals and has to satisfy
*
* - non-negativity: {@code d(x, y) >= 0}
*
- isolation: {@code d(x, y) = 0} if and only if {@code x = y}
*
- symmetry: {@code d(x, y) = d(x, y)}
*
* Note that a distance function is not required to satisfy triangular inequality
* {@code |x - y| + |y - z| >= |x - z|}, which is necessary for a metric.
*
* @param the input type of distance function.
*
* @author Haifeng Li
*/
public interface Distance extends ToDoubleBiFunction, Serializable {
/**
* Returns the distance measure between two objects.
* @param x an object.
* @param y an object.
* @return the distance.
*/
double d(T x, T y);
/**
* Returns the distance measure between two objects.
* This is simply for Scala convenience.
* @param x an object.
* @param y an object.
* @return the distance.
*/
default double apply(T x, T y) {
return d(x, y);
}
@Override
default double applyAsDouble(T x, T y) {
return d(x, y);
}
/**
* Returns the pairwise distance matrix.
*
* @param x samples.
* @return the pairwise distance matrix.
*/
default Matrix D(T[] x) {
int n = x.length;
int N = n * (n - 1) / 2;
Matrix D = new Matrix(n, n);
IntStream.range(0, N).parallel().forEach(k -> {
int j = n - 2 - (int) Math.floor(Math.sqrt(-8*k + 4*n*(n-1)-7)/2.0 - 0.5);
int i = k + j + 1 - n*(n-1)/2 + (n-j)*((n-j)-1)/2;
D.set(i, j, d(x[i], x[j]));
});
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
D.set(i, j, D.get(j, i));
}
}
D.uplo(UPLO.LOWER);
return D;
}
/**
* Returns the pairwise distance matrix.
*
* @param x samples.
* @param y samples.
* @return the pairwise distance matrix.
*/
default Matrix D(T[] x, T[] y) {
int m = x.length;
int n = y.length;
Matrix D = new Matrix(m, n);
IntStream.range(0, m).parallel().forEach(i -> {
T xi = x[i];
for (int j = 0; j < n; j++) {
D.set(i, j, d(xi, y[j]));
}
});
return D;
}
}