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23 package org.hipparchus.distribution.multivariate;
24
25 import java.util.Random;
26
27 import org.hipparchus.UnitTestUtils;
28 import org.hipparchus.distribution.continuous.NormalDistribution;
29 import org.hipparchus.exception.LocalizedCoreFormats;
30 import org.hipparchus.exception.MathIllegalArgumentException;
31 import org.hipparchus.linear.Array2DRowRealMatrix;
32 import org.hipparchus.linear.RealMatrix;
33 import org.hipparchus.random.Well19937c;
34 import org.hipparchus.util.Precision;
35 import org.junit.Assert;
36 import org.junit.Test;
37
38
39
40
41 public class MultivariateNormalDistributionTest {
42
43
44
45 @Test
46 public void testGetMean() {
47 final double[] mu = { -1.5, 2 };
48 final double[][] sigma = { { 2, -1.1 },
49 { -1.1, 2 } };
50 final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
51
52 final double[] m = d.getMeans();
53 for (int i = 0; i < m.length; i++) {
54 Assert.assertEquals(mu[i], m[i], 0);
55 }
56 }
57
58
59
60
61 @Test
62 public void testGetCovarianceMatrix() {
63 final double[] mu = { -1.5, 2 };
64 final double[][] sigma = { { 2, -1.1 },
65 { -1.1, 2 } };
66 final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
67
68 final RealMatrix s = d.getCovariances();
69 final int dim = d.getDimension();
70 for (int i = 0; i < dim; i++) {
71 for (int j = 0; j < dim; j++) {
72 Assert.assertEquals(sigma[i][j], s.getEntry(i, j), 0);
73 }
74 }
75 }
76
77
78
79
80 @Test
81 public void testSampling() {
82 final double[] mu = { -1.5, 2 };
83 final double[][] sigma = { { 2, -1.1 },
84 { -1.1, 2 } };
85 final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
86 d.reseedRandomGenerator(50);
87
88 final int n = 500000;
89
90 final double[][] samples = d.sample(n);
91 final int dim = d.getDimension();
92 final double[] sampleMeans = new double[dim];
93
94 for (int i = 0; i < samples.length; i++) {
95 for (int j = 0; j < dim; j++) {
96 sampleMeans[j] += samples[i][j];
97 }
98 }
99
100 final double sampledValueTolerance = 1e-2;
101 for (int j = 0; j < dim; j++) {
102 sampleMeans[j] /= samples.length;
103 Assert.assertEquals(mu[j], sampleMeans[j], sampledValueTolerance);
104 }
105
106
107 final RealMatrix sampleSigma = UnitTestUtils.covarianceMatrix(new Array2DRowRealMatrix(samples));
108 for (int i = 0; i < dim; i++) {
109 for (int j = 0; j < dim; j++) {
110 Assert.assertEquals(sigma[i][j], sampleSigma.getEntry(i, j), sampledValueTolerance);
111 }
112 }
113 }
114
115
116
117
118 @Test
119 public void testDensities() {
120 final double[] mu = { -1.5, 2 };
121 final double[][] sigma = { { 2, -1.1 },
122 { -1.1, 2 } };
123 final MultivariateNormalDistribution d = new MultivariateNormalDistribution(mu, sigma);
124
125 final double[][] testValues = { { -1.5, 2 },
126 { 4, 4 },
127 { 1.5, -2 },
128 { 0, 0 } };
129 final double[] densities = new double[testValues.length];
130 for (int i = 0; i < densities.length; i++) {
131 densities[i] = d.density(testValues[i]);
132 }
133
134
135 final double[] correctDensities = { 0.09528357207691344,
136 5.80932710124009e-09,
137 0.001387448895173267,
138 0.03309922090210541 };
139
140 for (int i = 0; i < testValues.length; i++) {
141 Assert.assertEquals(correctDensities[i], densities[i], 1e-16);
142 }
143 }
144
145
146
147
148 @Test
149 public void testUnivariateDistribution() {
150 final double[] mu = { -1.5 };
151 final double[][] sigma = { { 1 } };
152
153 final MultivariateNormalDistribution multi = new MultivariateNormalDistribution(mu, sigma);
154
155 final NormalDistribution uni = new NormalDistribution(mu[0], sigma[0][0]);
156 final Random rng = new Random();
157 final int numCases = 100;
158 final double tol = Math.ulp(1d);
159 for (int i = 0; i < numCases; i++) {
160 final double v = rng.nextDouble() * 10 - 5;
161 Assert.assertEquals(uni.density(v), multi.density(new double[] { v }), tol);
162 }
163 }
164
165
166
167
168 @Test
169 public void testGetSingularMatrixTolerance() {
170 final double[] mu = { -1.5 };
171 final double[][] sigma = { { 1 } };
172
173 final double tolerance1 = 1e-2;
174 final MultivariateNormalDistribution mvd1 = new MultivariateNormalDistribution(mu, sigma, tolerance1);
175 Assert.assertEquals(tolerance1, mvd1.getSingularMatrixCheckTolerance(), Precision.EPSILON);
176
177 final double tolerance2 = 1e-3;
178 final MultivariateNormalDistribution mvd2 = new MultivariateNormalDistribution(mu, sigma, tolerance2);
179 Assert.assertEquals(tolerance2, mvd2.getSingularMatrixCheckTolerance(), Precision.EPSILON);
180 }
181
182 @Test
183 public void testNotPositiveDefinite() {
184 try {
185 new MultivariateNormalDistribution(new Well19937c(0x543l), new double[2],
186 new double[][] { { -1.0, 0.0 }, { 0.0, -2.0 } });
187 Assert.fail("an exception should have been thrown");
188 } catch (MathIllegalArgumentException miae) {
189 Assert.assertEquals(LocalizedCoreFormats.NOT_POSITIVE_DEFINITE_MATRIX, miae.getSpecifier());
190 }
191 }
192
193 @Test
194 public void testStd() {
195 MultivariateNormalDistribution d = new MultivariateNormalDistribution(new Well19937c(0x543l), new double[2],
196 new double[][] { { 4.0, 0.0 }, { 0.0, 9.0 } });
197 double[] s = d.getStandardDeviations();
198 Assert.assertEquals(2, s.length);
199 Assert.assertEquals(2.0, s[0], 1.0e-15);
200 Assert.assertEquals(3.0, s[1], 1.0e-15);
201 }
202
203 @Test
204 public void testWrongDensity() {
205 try {
206 MultivariateNormalDistribution d = new MultivariateNormalDistribution(new Well19937c(0x543l), new double[2],
207 new double[][] { { 4.0, 0.0 }, { 0.0, 4.0 } });
208 d.density(new double[3]);
209 Assert.fail("an exception should have been thrown");
210 } catch (MathIllegalArgumentException miae) {
211 Assert.assertEquals(LocalizedCoreFormats.DIMENSIONS_MISMATCH, miae.getSpecifier());
212 }
213 }
214
215 @Test
216 public void testWrongArguments() {
217 checkWrongArguments(new double[3], new double[6][6]);
218 checkWrongArguments(new double[3], new double[3][6]);
219 }
220
221 private void checkWrongArguments(double[] means, double[][] covariances) {
222 try {
223 new MultivariateNormalDistribution(new Well19937c(0x543l), means, covariances);
224 Assert.fail("an exception should have been thrown");
225 } catch (MathIllegalArgumentException miae) {
226 Assert.assertEquals(LocalizedCoreFormats.DIMENSIONS_MISMATCH, miae.getSpecifier());
227 }
228 }
229 }