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/*******************************************************************************
* Copyright (c) 2010-2020 Haifeng Li. All rights reserved.
*
* Smile is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Smile. If not, see .
******************************************************************************/
package smile.math.distance;
import java.util.Arrays;
/**
* Minkowski distance of order p or Lp-norm, is a generalization of
* Euclidean distance that is actually L2-norm. You may also provide
* a specified weight vector. For float or double arrays, missing values (i.e. NaN)
* are also handled.
*
* @see SparseMinkowskiDistance
*
* @author Haifeng Li
*/
public class MinkowskiDistance implements Metric {
private static final long serialVersionUID = 1L;
/**
* The order of Minkowski distance.
*/
private int p;
/**
* The weights used in weighted distance.
*/
private double[] weight = null;
/**
* Constructor.
*/
public MinkowskiDistance(int p) {
if (p <= 0) {
throw new IllegalArgumentException(String.format("The order p has to be larger than 0: p = d", p));
}
this.p = p;
}
/**
* Constructor.
*
* @param weight the weight vector.
*/
public MinkowskiDistance(int p, double[] weight) {
if (p <= 0) {
throw new IllegalArgumentException(String.format("The order p has to be larger than 0: p = d", p));
}
for (int i = 0; i < weight.length; i++) {
if (weight[i] < 0) {
throw new IllegalArgumentException(String.format("Weight has to be nonnegative: %f", weight[i]));
}
}
this.p = p;
this.weight = weight;
}
@Override
public String toString() {
if (weight != null) {
return String.format("Weighted Minkowski Distance(p = %d, weight = %s)", p, Arrays.toString(weight));
} else {
return String.format("Minkowski Distance(p = %d)", p);
}
}
/**
* Minkowski distance between the two arrays of type integer.
*/
public double d(int[] x, int[] y) {
if (x.length != y.length) {
throw new IllegalArgumentException(String.format("Arrays have different length: x[%d], y[%d]", x.length, y.length));
}
double dist = 0.0;
if (weight == null) {
for (int i = 0; i < x.length; i++) {
double d = Math.abs(x[i] - y[i]);
dist += Math.pow(d, p);
}
} else {
if (x.length != weight.length) {
throw new IllegalArgumentException(String.format("Input vectors and weight vector have different length: %d, %d", x.length, weight.length));
}
for (int i = 0; i < x.length; i++) {
double d = Math.abs(x[i] - y[i]);
dist += weight[i] * Math.pow(d, p);
}
}
return Math.pow(dist, 1.0/p);
}
/**
* Minkowski distance between the two arrays of type float.
* NaN will be treated as missing values and will be excluded from the
* calculation. Let m be the number non-missing values, and n be the
* number of all values. The returned distance is pow(n * d / m, 1/p),
* where d is the p-pow of distance between non-missing values.
*/
public double d(float[] x, float[] y) {
if (x.length != y.length) {
throw new IllegalArgumentException(String.format("Arrays have different length: x[%d], y[%d]", x.length, y.length));
}
int n = x.length;
int m = 0;
double dist = 0.0;
if (weight == null) {
for (int i = 0; i < x.length; i++) {
if (!Float.isNaN(x[i]) && !Float.isNaN(y[i])) {
m++;
double d = Math.abs(x[i] - y[i]);
dist += Math.pow(d, p);
}
}
} else {
if (x.length != weight.length) {
throw new IllegalArgumentException(String.format("Input vectors and weight vector have different length: %d, %d", x.length, weight.length));
}
for (int i = 0; i < x.length; i++) {
if (!Float.isNaN(x[i]) && !Float.isNaN(y[i])) {
m++;
double d = Math.abs(x[i] - y[i]);
dist += weight[i] * Math.pow(d, p);
}
}
}
dist = n * dist / m;
return Math.pow(dist, 1.0/p);
}
/**
* Minkowski distance between the two arrays of type double.
* NaN will be treated as missing values and will be excluded from the
* calculation. Let m be the number non-missing values, and n be the
* number of all values. The returned distance is pow(n * d / m, 1/p),
* where d is the p-pow of distance between non-missing values.
*/
@Override
public double d(double[] x, double[] y) {
if (x.length != y.length) {
throw new IllegalArgumentException(String.format("Arrays have different length: x[%d], y[%d]", x.length, y.length));
}
int n = x.length;
int m = 0;
double dist = 0.0;
if (weight == null) {
for (int i = 0; i < x.length; i++) {
if (!Double.isNaN(x[i]) && !Double.isNaN(y[i])) {
m++;
double d = Math.abs(x[i] - y[i]);
dist += Math.pow(d, p);
}
}
} else {
if (x.length != weight.length) {
throw new IllegalArgumentException(String.format("Input vectors and weight vector have different length: %d, %d", x.length, weight.length));
}
for (int i = 0; i < x.length; i++) {
if (!Double.isNaN(x[i]) && !Double.isNaN(y[i])) {
m++;
double d = Math.abs(x[i] - y[i]);
dist += weight[i] * Math.pow(d, p);
}
}
}
dist = n * dist / m;
return Math.pow(dist, 1.0/p);
}
}
