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Java example source code file (MultivariateNormalDistributionTest.java)

This example Java source code file (MultivariateNormalDistributionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

multivariatenormaldistribution, multivariatenormaldistributiontest, normaldistribution, random, realmatrix, test, util

The MultivariateNormalDistributionTest.java Java example source code

/*
 * 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.Assert;
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);
        }
    }
}

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