/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.distribution;
import org.apache.commons.math3.stat.correlation.Covariance;
import org.apache.commons.math3.linear.RealMatrix;
import java.util.Random;
import org.junit.After;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;
/**
* Test cases for {@link MultivariateNormalDistribution}.
*/
public class MultivariateNormalDistributionTest {
/**
* Test the ability of the distribution to report its mean value parameter.
*/
@Test
public void testGetMean() {
final double[] mu = { -1.5, 2 };
final double[][] sigma = { { 2, -1.1 },
{ -1.1, 2 } };
final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
final double[] m = d.getMeans();
for (int i = 0; i < m.length; i++) {
Assert.assertEquals(mu[i], m[i], 0);
}
}
/**
* Test the ability of the distribution to report its covariance matrix parameter.
*/
@Test
public void testGetCovarianceMatrix() {
final double[] mu = { -1.5, 2 };
final double[][] sigma = { { 2, -1.1 },
{ -1.1, 2 } };
final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
final RealMatrix s = d.getCovariances();
final int dim = d.getDimension();
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
Assert.assertEquals(sigma[i][j], s.getEntry(i, j), 0);
}
}
}
/**
* Test the accuracy of sampling from the distribution.
*/
@Test
public void testSampling() {
final double[] mu = { -1.5, 2 };
final double[][] sigma = { { 2, -1.1 },
{ -1.1, 2 } };
final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
d.reseedRandomGenerator(50);
final int n = 500000;
final double[][] samples = d.sample(n);
final int dim = d.getDimension();
final double[] sampleMeans = new double[dim];
for (int i = 0; i < samples.length; i++) {
for (int j = 0; j < dim; j++) {
sampleMeans[j] += samples[i][j];
}
}
final double sampledValueTolerance = 1e-2;
for (int j = 0; j < dim; j++) {
sampleMeans[j] /= samples.length;
Assert.assertEquals(mu[j], sampleMeans[j], sampledValueTolerance);
}
final double[][] sampleSigma = new Covariance(samples).getCovarianceMatrix().getData();
for (int i = 0; i < dim; i++) {
for (int j = 0; j < dim; j++) {
Assert.assertEquals(sigma[i][j], sampleSigma[i][j], sampledValueTolerance);
}
}
}
/**
* Test the accuracy of the distribution when calculating densities.
*/
@Test
public void testDensities() {
final double[] mu = { -1.5, 2 };
final double[][] sigma = { { 2, -1.1 },
{ -1.1, 2 } };
final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
final double[][] testValues = { { -1.5, 2 },
{ 4, 4 },
{ 1.5, -2 },
{ 0, 0 } };
final double[] densities = new double[testValues.length];
for (int i = 0; i < densities.length; i++) {
densities[i] = d.density(testValues[i]);
}
// From dmvnorm function in R 2.15 CRAN package Mixtools v0.4.5
final double[] correctDensities = { 0.09528357207691344,
5.80932710124009e-09,
0.001387448895173267,
0.03309922090210541 };
for (int i = 0; i < testValues.length; i++) {
Assert.assertEquals(correctDensities[i], densities[i], 1e-16);
}
}
/**
* Test the accuracy of the distribution when calculating densities.
*/
@Test
public void testUnivariateDistribution() {
final double[] mu = { -1.5 };
final double[][] sigma = { { 1 } };
final MultivariateNormalDistribution multi = new MultivariateNormalDistribution(mu, sigma);
final NormalDistribution uni = new NormalDistribution(mu[0], sigma[0][0]);
final Random rng = new Random();
final int numCases = 100;
final double tol = Math.ulp(1d);
for (int i = 0; i < numCases; i++) {
final double v = rng.nextDouble() * 10 - 5;
Assert.assertEquals(uni.density(v), multi.density(new double[] { v }), tol);
}
}
}