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/*
 * 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; } }




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