src/test/java/org/apache/commons/math3/distribution/MultivariateNormalMixtureModelDistributionTest.java - commons-math - Git at Google

 /*
  * 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 java.util.List;
 import java.util.ArrayList;
 import org.apache.commons.math3.exception.NotPositiveException;
 import org.apache.commons.math3.exception.MathArithmeticException;
 import org.apache.commons.math3.util.Pair;
 import org.junit.Assert;
 import org.junit.Test;

 /**
  * Test that demonstrates the use of {@link MixtureMultivariateRealDistribution}
  * in order to create a mixture model composed of {@link MultivariateNormalDistribution
  * normal distributions}.
  */
 public class MultivariateNormalMixtureModelDistributionTest {

     @Test
     public void testNonUnitWeightSum() {
         final double[] weights = { 1, 2 };
         final double[][] means = { { -1.5, 2.0 },
                                    { 4.0, 8.2 } };
         final double[][][] covariances = { { { 2.0, -1.1 },
                                              { -1.1, 2.0 } },
                                            { { 3.5, 1.5 },
                                              { 1.5, 3.5 } } };
         final MultivariateNormalMixtureModelDistribution d
             = create(weights, means, covariances);

         final List<Pair<Double, MultivariateNormalDistribution>> comp = d.getComponents();

         Assert.assertEquals(1d / 3, comp.get(0).getFirst().doubleValue(), Math.ulp(1d));
         Assert.assertEquals(2d / 3, comp.get(1).getFirst().doubleValue(), Math.ulp(1d));
     }

     @Test(expected=MathArithmeticException.class)
     public void testWeightSumOverFlow() {
         final double[] weights = { 0.5 * Double.MAX_VALUE, 0.51 * Double.MAX_VALUE };
         final double[][] means = { { -1.5, 2.0 },
                                    { 4.0, 8.2 } };
         final double[][][] covariances = { { { 2.0, -1.1 },
                                              { -1.1, 2.0 } },
                                            { { 3.5, 1.5 },
                                              { 1.5, 3.5 } } };
         create(weights, means, covariances);
     }

     @Test(expected=NotPositiveException.class)
     public void testPreconditionPositiveWeights() {
         final double[] negativeWeights = { -0.5, 1.5 };
         final double[][] means = { { -1.5, 2.0 },
                                    { 4.0, 8.2 } };
         final double[][][] covariances = { { { 2.0, -1.1 },
                                              { -1.1, 2.0 } },
                                            { { 3.5, 1.5 },
                                              { 1.5, 3.5 } } };
         create(negativeWeights, means, covariances);
     }

     /**
      * Test the accuracy of the density calculation.
      */
     @Test
     public void testDensities() {
         final double[] weights = { 0.3, 0.7 };
         final double[][] means = { { -1.5, 2.0 },
                                    { 4.0, 8.2 } };
         final double[][][] covariances = { { { 2.0, -1.1 },
                                              { -1.1, 2.0 } },
                                            { { 3.5, 1.5 },
                                              { 1.5, 3.5 } } };
         final MultivariateNormalMixtureModelDistribution d
             = create(weights, means, covariances);

         // Test vectors
         final double[][] testValues = { { -1.5, 2 },
                                         { 4, 8.2 },
                                         { 1.5, -2 },
                                         { 0, 0 } };

         // Densities that we should get back.
         // Calculated by assigning weights to multivariate normal distribution
         // and summing
         // values from dmvnorm function in R 2.15 CRAN package Mixtools v0.4.
         // Like: .3*dmvnorm(val,mu1,sigma1)+.7*dmvnorm(val,mu2,sigma2)
         final double[] correctDensities = { 0.02862037278930575,
                                             0.03523044847314091,
                                             0.000416241365629767,
                                             0.009932042831700297 };

         for (int i = 0; i < testValues.length; i++) {
             Assert.assertEquals(correctDensities[i], d.density(testValues[i]), Math.ulp(1d));
         }
     }

     /**
      * Test the accuracy of sampling from the distribution.
      */
     @Test
     public void testSampling() {
         final double[] weights = { 0.3, 0.7 };
         final double[][] means = { { -1.5, 2.0 },
                                    { 4.0, 8.2 } };
         final double[][][] covariances = { { { 2.0, -1.1 },
                                              { -1.1, 2.0 } },
                                            { { 3.5, 1.5 },
                                              { 1.5, 3.5 } } };
         final MultivariateNormalMixtureModelDistribution d
             = create(weights, means, covariances);
         d.reseedRandomGenerator(50);

         final double[][] correctSamples = getCorrectSamples();
         final int n = correctSamples.length;
         final double[][] samples = d.sample(n);

         for (int i = 0; i < n; i++) {
             for (int j = 0; j < samples[i].length; j++) {
                 Assert.assertEquals(correctSamples[i][j], samples[i][j], 1e-16);
             }
         }
     }

     /**
      * Creates a mixture of Gaussian distributions.
      *
      * @param weights Weights.
      * @param means Means.
      * @param covariances Covariances.
      * @return the mixture distribution.
      */
     private MultivariateNormalMixtureModelDistribution create(double[] weights,
                                                               double[][] means,
                                                               double[][][] covariances) {
         final List<Pair<Double, MultivariateNormalDistribution>> mvns
             = new ArrayList<Pair<Double, MultivariateNormalDistribution>>();

         for (int i = 0; i < weights.length; i++) {
             final MultivariateNormalDistribution dist
                 = new MultivariateNormalDistribution(means[i], covariances[i]);
             mvns.add(new Pair<Double, MultivariateNormalDistribution>(weights[i], dist));
         }

         return new MultivariateNormalMixtureModelDistribution(mvns);
     }

     /**
      * Values used in {@link #testSampling()}.
      */
     private double[][] getCorrectSamples() {
         // These were sampled from the MultivariateNormalMixtureModelDistribution class
         // with seed 50.
         //
         // They were then fit to a MVN mixture model in R using mixtools.
         //
         // The optimal parameters were:
         // - component weights: {0.3595186, 0.6404814}
         // - mean vectors: {-1.645879, 1.989797}, {3.474328, 7.782232}
         // - covariance matrices:
         //     { 1.397738 -1.167732
         //       -1.167732 1.801782 }
         //   and
         //     { 3.934593 2.354787
         //       2.354787 4.428024 }
         //
         // It is considered fairly close to the actual test parameters,
         // considering that the sample size is only 100.
         return new double[][] {
             { 6.259990922080121, 11.972954175355897 },
             { -2.5296544304801847, 1.0031292519854365 },
             { 0.49037886081440396, 0.9758251727325711 },
             { 5.022970993312015, 9.289348879616787 },
             { -1.686183146603914, 2.007244382745706 },
             { -1.4729253946002685, 2.762166644212484 },
             { 4.329788143963888, 11.514016497132253 },
             { 3.008674596114442, 4.960246550446107 },
             { 3.342379304090846, 5.937630105198625 },
             { 2.6993068328674754, 7.42190871572571 },
             { -2.446569340219571, 1.9687117791378763 },
             { 1.922417883170056, 4.917616702617099 },
             { -1.1969741543898518, 2.4576126277884387 },
             { 2.4216948702967196, 8.227710158117134 },
             { 6.701424725804463, 9.098666475042428 },
             { 2.9890253545698964, 9.643807939324331 },
             { 0.7162632354907799, 8.978811120287553 },
             { -2.7548699149775877, 4.1354812280794215 },
             { 8.304528180745018, 11.602319388898287 },
             { -2.7633253389165926, 2.786173883989795 },
             { 1.3322228389460813, 5.447481218602913 },
             { -1.8120096092851508, 1.605624499560037 },
             { 3.6546253437206504, 8.195304526564376 },
             { -2.312349539658588, 1.868941220444169 },
             { -1.882322136356522, 2.033795570464242 },
             { 4.562770714939441, 7.414967958885031 },
             { 4.731882017875329, 8.890676665580747 },
             { 3.492186010427425, 8.9005225241848 },
             { -1.619700190174894, 3.314060142479045 },
             { 3.5466090064003315, 7.75182101001913 },
             { 5.455682472787392, 8.143119287755635 },
             { -2.3859602945473197, 1.8826732217294837 },
             { 3.9095306088680015, 9.258129209626317 },
             { 7.443020189508173, 7.837840713329312 },
             { 2.136004873917428, 6.917636475958297 },
             { -1.7203379410395119, 2.3212878757611524 },
             { 4.618991257611526, 12.095065976419436 },
             { -0.4837044029854387, 0.8255970441255125 },
             { -4.438938966557163, 4.948666297280241 },
             { -0.4539625134045906, 4.700922454655341 },
             { 2.1285488271265356, 8.457941480487563 },
             { 3.4873561871454393, 11.99809827845933 },
             { 4.723049431412658, 7.813095742563365 },
             { 1.1245583037967455, 5.20587873556688 },
             { 1.3411933634409197, 6.069796875785409 },
             { 4.585119332463686, 7.967669543767418 },
             { 1.3076522817963823, -0.647431033653445 },
             { -1.4449446442803178, 1.9400424267464862 },
             { -2.069794456383682, 3.5824162107496544 },
             { -0.15959481421417276, 1.5466782303315405 },
             { -2.0823081278810136, 3.0914366458581437 },
             { 3.521944615248141, 10.276112932926408 },
             { 1.0164326704884257, 4.342329556442856 },
             { 5.3718868590295275, 8.374761158360922 },
             { 0.3673656866959396, 8.75168581694866 },
             { -2.250268955954753, 1.4610850300996527 },
             { -2.312739727403522, 1.5921126297576362 },
             { 3.138993360831055, 6.7338392374947365 },
             { 2.6978650950790115, 7.941857288979095 },
             { 4.387985088655384, 8.253499976968 },
             { -1.8928961721456705, 0.23631082388724223 },
             { 4.43509029544109, 8.565290285488782 },
             { 4.904728034106502, 5.79936660133754 },
             { -1.7640371853739507, 2.7343727594167433 },
             { 2.4553674733053463, 7.875871017408807 },
             { -2.6478965122565006, 4.465127753193949 },
             { 3.493873671142299, 10.443093773532448 },
             { 1.1321916197409103, 7.127108479263268 },
             { -1.7335075535240392, 2.550629648463023 },
             { -0.9772679734368084, 4.377196298969238 },
             { 3.6388366973980357, 6.947299283206256 },
             { 0.27043799318823325, 6.587978599614367 },
             { 5.356782352010253, 7.388957912116327 },
             { -0.09187745751354681, 0.23612399246659743 },
             { 2.903203580353435, 3.8076727621794415 },
             { 5.297014824937293, 8.650985262326508 },
             { 4.934508602170976, 9.164571423190052 },
             { -1.0004911869654256, 4.797064194444461 },
             { 6.782491700298046, 11.852373338280497 },
             { 2.8983678524536014, 8.303837362117521 },
             { 4.805003269830865, 6.790462904325329 },
             { -0.8815799740744226, 1.3015810062131394 },
             { 5.115138859802104, 6.376895810201089 },
             { 4.301239328205988, 8.60546337560793 },
             { 3.276423626317666, 9.889429652591947 },
             { -4.001924973153122, 4.3353864592328515 },
             { 3.9571892554119517, 4.500569057308562 },
             { 4.783067027436208, 7.451125480601317 },
             { 4.79065438272821, 9.614122776979698 },
             { 2.677655270279617, 6.8875223698210135 },
             { -1.3714746289327362, 2.3992153193382437 },
             { 3.240136859745249, 7.748339397522042 },
             { 5.107885374416291, 8.508324480583724 },
             { -1.5830830226666048, 0.9139127045208315 },
             { -1.1596156791652918, -0.04502759384531929 },
             { -0.4670021307952068, 3.6193633227841624 },
             { -0.7026065228267798, 0.4811423031997131 },
             { -2.719979836732917, 2.5165041618080104 },
             { 1.0336754331123372, -0.34966029029320644 },
             { 4.743217291882213, 5.750060115251131 }
         };
     }
 }

 /**
  * Class that implements a mixture of Gaussian ditributions.
  */
 class MultivariateNormalMixtureModelDistribution
     extends MixtureMultivariateRealDistribution<MultivariateNormalDistribution> {

     public MultivariateNormalMixtureModelDistribution(List<Pair<Double, MultivariateNormalDistribution>> components) {
         super(components);
     }
 }
	/*
	* 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 java.util.List;
	import java.util.ArrayList;
	import org.apache.commons.math3.exception.NotPositiveException;
	import org.apache.commons.math3.exception.MathArithmeticException;
	import org.apache.commons.math3.util.Pair;
	import org.junit.Assert;
	import org.junit.Test;

	/**
	* Test that demonstrates the use of {@link MixtureMultivariateRealDistribution}
	* in order to create a mixture model composed of {@link MultivariateNormalDistribution
	* normal distributions}.
	*/
	public class MultivariateNormalMixtureModelDistributionTest {

	@Test
	public void testNonUnitWeightSum() {
	final double[] weights = { 1, 2 };
	final double[][] means = { { -1.5, 2.0 },
	{ 4.0, 8.2 } };
	final double[][][] covariances = { { { 2.0, -1.1 },
	{ -1.1, 2.0 } },
	{ { 3.5, 1.5 },
	{ 1.5, 3.5 } } };
	final MultivariateNormalMixtureModelDistribution d
	= create(weights, means, covariances);

	final List<Pair<Double, MultivariateNormalDistribution>> comp = d.getComponents();

	Assert.assertEquals(1d / 3, comp.get(0).getFirst().doubleValue(), Math.ulp(1d));
	Assert.assertEquals(2d / 3, comp.get(1).getFirst().doubleValue(), Math.ulp(1d));
	}

	@Test(expected=MathArithmeticException.class)
	public void testWeightSumOverFlow() {
	final double[] weights = { 0.5 * Double.MAX_VALUE, 0.51 * Double.MAX_VALUE };
	final double[][] means = { { -1.5, 2.0 },
	{ 4.0, 8.2 } };
	final double[][][] covariances = { { { 2.0, -1.1 },
	{ -1.1, 2.0 } },
	{ { 3.5, 1.5 },
	{ 1.5, 3.5 } } };
	create(weights, means, covariances);
	}

	@Test(expected=NotPositiveException.class)
	public void testPreconditionPositiveWeights() {
	final double[] negativeWeights = { -0.5, 1.5 };
	final double[][] means = { { -1.5, 2.0 },
	{ 4.0, 8.2 } };
	final double[][][] covariances = { { { 2.0, -1.1 },
	{ -1.1, 2.0 } },
	{ { 3.5, 1.5 },
	{ 1.5, 3.5 } } };
	create(negativeWeights, means, covariances);
	}

	/**
	* Test the accuracy of the density calculation.
	*/
	@Test
	public void testDensities() {
	final double[] weights = { 0.3, 0.7 };
	final double[][] means = { { -1.5, 2.0 },
	{ 4.0, 8.2 } };
	final double[][][] covariances = { { { 2.0, -1.1 },
	{ -1.1, 2.0 } },
	{ { 3.5, 1.5 },
	{ 1.5, 3.5 } } };
	final MultivariateNormalMixtureModelDistribution d
	= create(weights, means, covariances);

	// Test vectors
	final double[][] testValues = { { -1.5, 2 },
	{ 4, 8.2 },
	{ 1.5, -2 },
	{ 0, 0 } };

	// Densities that we should get back.
	// Calculated by assigning weights to multivariate normal distribution
	// and summing
	// values from dmvnorm function in R 2.15 CRAN package Mixtools v0.4.
	// Like: .3dmvnorm(val,mu1,sigma1)+.7dmvnorm(val,mu2,sigma2)
	final double[] correctDensities = { 0.02862037278930575,
	0.03523044847314091,
	0.000416241365629767,
	0.009932042831700297 };

	for (int i = 0; i < testValues.length; i++) {
	Assert.assertEquals(correctDensities[i], d.density(testValues[i]), Math.ulp(1d));
	}
	}

	/**
	* Test the accuracy of sampling from the distribution.
	*/
	@Test
	public void testSampling() {
	final double[] weights = { 0.3, 0.7 };
	final double[][] means = { { -1.5, 2.0 },
	{ 4.0, 8.2 } };
	final double[][][] covariances = { { { 2.0, -1.1 },
	{ -1.1, 2.0 } },
	{ { 3.5, 1.5 },
	{ 1.5, 3.5 } } };
	final MultivariateNormalMixtureModelDistribution d
	= create(weights, means, covariances);
	d.reseedRandomGenerator(50);

	final double[][] correctSamples = getCorrectSamples();
	final int n = correctSamples.length;
	final double[][] samples = d.sample(n);

	for (int i = 0; i < n; i++) {
	for (int j = 0; j < samples[i].length; j++) {
	Assert.assertEquals(correctSamples[i][j], samples[i][j], 1e-16);
	}
	}
	}

	/**
	* Creates a mixture of Gaussian distributions.
	*
	* @param weights Weights.
	* @param means Means.
	* @param covariances Covariances.
	* @return the mixture distribution.
	*/
	private MultivariateNormalMixtureModelDistribution create(double[] weights,
	double[][] means,
	double[][][] covariances) {
	final List<Pair<Double, MultivariateNormalDistribution>> mvns
	= new ArrayList<Pair<Double, MultivariateNormalDistribution>>();

	for (int i = 0; i < weights.length; i++) {
	final MultivariateNormalDistribution dist
	= new MultivariateNormalDistribution(means[i], covariances[i]);
	mvns.add(new Pair<Double, MultivariateNormalDistribution>(weights[i], dist));
	}

	return new MultivariateNormalMixtureModelDistribution(mvns);
	}

	/**
	* Values used in {@link #testSampling()}.
	*/
	private double[][] getCorrectSamples() {
	// These were sampled from the MultivariateNormalMixtureModelDistribution class
	// with seed 50.
	//
	// They were then fit to a MVN mixture model in R using mixtools.
	//
	// The optimal parameters were:
	// - component weights: {0.3595186, 0.6404814}
	// - mean vectors: {-1.645879, 1.989797}, {3.474328, 7.782232}
	// - covariance matrices:
	// { 1.397738 -1.167732
	// -1.167732 1.801782 }
	// and
	// { 3.934593 2.354787
	// 2.354787 4.428024 }
	//
	// It is considered fairly close to the actual test parameters,
	// considering that the sample size is only 100.
	return new double[][] {
	{ 6.259990922080121, 11.972954175355897 },
	{ -2.5296544304801847, 1.0031292519854365 },
	{ 0.49037886081440396, 0.9758251727325711 },
	{ 5.022970993312015, 9.289348879616787 },
	{ -1.686183146603914, 2.007244382745706 },
	{ -1.4729253946002685, 2.762166644212484 },
	{ 4.329788143963888, 11.514016497132253 },
	{ 3.008674596114442, 4.960246550446107 },
	{ 3.342379304090846, 5.937630105198625 },
	{ 2.6993068328674754, 7.42190871572571 },
	{ -2.446569340219571, 1.9687117791378763 },
	{ 1.922417883170056, 4.917616702617099 },
	{ -1.1969741543898518, 2.4576126277884387 },
	{ 2.4216948702967196, 8.227710158117134 },
	{ 6.701424725804463, 9.098666475042428 },
	{ 2.9890253545698964, 9.643807939324331 },
	{ 0.7162632354907799, 8.978811120287553 },
	{ -2.7548699149775877, 4.1354812280794215 },
	{ 8.304528180745018, 11.602319388898287 },
	{ -2.7633253389165926, 2.786173883989795 },
	{ 1.3322228389460813, 5.447481218602913 },
	{ -1.8120096092851508, 1.605624499560037 },
	{ 3.6546253437206504, 8.195304526564376 },
	{ -2.312349539658588, 1.868941220444169 },
	{ -1.882322136356522, 2.033795570464242 },
	{ 4.562770714939441, 7.414967958885031 },
	{ 4.731882017875329, 8.890676665580747 },
	{ 3.492186010427425, 8.9005225241848 },
	{ -1.619700190174894, 3.314060142479045 },
	{ 3.5466090064003315, 7.75182101001913 },
	{ 5.455682472787392, 8.143119287755635 },
	{ -2.3859602945473197, 1.8826732217294837 },
	{ 3.9095306088680015, 9.258129209626317 },
	{ 7.443020189508173, 7.837840713329312 },
	{ 2.136004873917428, 6.917636475958297 },
	{ -1.7203379410395119, 2.3212878757611524 },
	{ 4.618991257611526, 12.095065976419436 },
	{ -0.4837044029854387, 0.8255970441255125 },
	{ -4.438938966557163, 4.948666297280241 },
	{ -0.4539625134045906, 4.700922454655341 },
	{ 2.1285488271265356, 8.457941480487563 },
	{ 3.4873561871454393, 11.99809827845933 },
	{ 4.723049431412658, 7.813095742563365 },
	{ 1.1245583037967455, 5.20587873556688 },
	{ 1.3411933634409197, 6.069796875785409 },
	{ 4.585119332463686, 7.967669543767418 },
	{ 1.3076522817963823, -0.647431033653445 },
	{ -1.4449446442803178, 1.9400424267464862 },
	{ -2.069794456383682, 3.5824162107496544 },
	{ -0.15959481421417276, 1.5466782303315405 },
	{ -2.0823081278810136, 3.0914366458581437 },
	{ 3.521944615248141, 10.276112932926408 },
	{ 1.0164326704884257, 4.342329556442856 },
	{ 5.3718868590295275, 8.374761158360922 },
	{ 0.3673656866959396, 8.75168581694866 },
	{ -2.250268955954753, 1.4610850300996527 },
	{ -2.312739727403522, 1.5921126297576362 },
	{ 3.138993360831055, 6.7338392374947365 },
	{ 2.6978650950790115, 7.941857288979095 },
	{ 4.387985088655384, 8.253499976968 },
	{ -1.8928961721456705, 0.23631082388724223 },
	{ 4.43509029544109, 8.565290285488782 },
	{ 4.904728034106502, 5.79936660133754 },
	{ -1.7640371853739507, 2.7343727594167433 },
	{ 2.4553674733053463, 7.875871017408807 },
	{ -2.6478965122565006, 4.465127753193949 },
	{ 3.493873671142299, 10.443093773532448 },
	{ 1.1321916197409103, 7.127108479263268 },
	{ -1.7335075535240392, 2.550629648463023 },
	{ -0.9772679734368084, 4.377196298969238 },
	{ 3.6388366973980357, 6.947299283206256 },
	{ 0.27043799318823325, 6.587978599614367 },
	{ 5.356782352010253, 7.388957912116327 },
	{ -0.09187745751354681, 0.23612399246659743 },
	{ 2.903203580353435, 3.8076727621794415 },
	{ 5.297014824937293, 8.650985262326508 },
	{ 4.934508602170976, 9.164571423190052 },
	{ -1.0004911869654256, 4.797064194444461 },
	{ 6.782491700298046, 11.852373338280497 },
	{ 2.8983678524536014, 8.303837362117521 },
	{ 4.805003269830865, 6.790462904325329 },
	{ -0.8815799740744226, 1.3015810062131394 },
	{ 5.115138859802104, 6.376895810201089 },
	{ 4.301239328205988, 8.60546337560793 },
	{ 3.276423626317666, 9.889429652591947 },
	{ -4.001924973153122, 4.3353864592328515 },
	{ 3.9571892554119517, 4.500569057308562 },
	{ 4.783067027436208, 7.451125480601317 },
	{ 4.79065438272821, 9.614122776979698 },
	{ 2.677655270279617, 6.8875223698210135 },
	{ -1.3714746289327362, 2.3992153193382437 },
	{ 3.240136859745249, 7.748339397522042 },
	{ 5.107885374416291, 8.508324480583724 },
	{ -1.5830830226666048, 0.9139127045208315 },
	{ -1.1596156791652918, -0.04502759384531929 },
	{ -0.4670021307952068, 3.6193633227841624 },
	{ -0.7026065228267798, 0.4811423031997131 },
	{ -2.719979836732917, 2.5165041618080104 },
	{ 1.0336754331123372, -0.34966029029320644 },
	{ 4.743217291882213, 5.750060115251131 }
	};
	}
	}

	/**
	* Class that implements a mixture of Gaussian ditributions.
	*/
	class MultivariateNormalMixtureModelDistribution
	extends MixtureMultivariateRealDistribution<MultivariateNormalDistribution> {

	public MultivariateNormalMixtureModelDistribution(List<Pair<Double, MultivariateNormalDistribution>> components) {
	super(components);
	}
	}