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22 package org.hipparchus.stat.correlation;
23
24 import org.hipparchus.UnitTestUtils;
25 import org.hipparchus.exception.MathIllegalArgumentException;
26 import org.hipparchus.linear.Array2DRowRealMatrix;
27 import org.hipparchus.linear.RealMatrix;
28 import org.hipparchus.stat.descriptive.moment.Variance;
29 import org.junit.Assert;
30 import org.junit.Test;
31
32
33 public class CovarianceTest {
34
35 protected final double[] longleyData = new double[] {
36 60323,83.0,234289,2356,1590,107608,1947,
37 61122,88.5,259426,2325,1456,108632,1948,
38 60171,88.2,258054,3682,1616,109773,1949,
39 61187,89.5,284599,3351,1650,110929,1950,
40 63221,96.2,328975,2099,3099,112075,1951,
41 63639,98.1,346999,1932,3594,113270,1952,
42 64989,99.0,365385,1870,3547,115094,1953,
43 63761,100.0,363112,3578,3350,116219,1954,
44 66019,101.2,397469,2904,3048,117388,1955,
45 67857,104.6,419180,2822,2857,118734,1956,
46 68169,108.4,442769,2936,2798,120445,1957,
47 66513,110.8,444546,4681,2637,121950,1958,
48 68655,112.6,482704,3813,2552,123366,1959,
49 69564,114.2,502601,3931,2514,125368,1960,
50 69331,115.7,518173,4806,2572,127852,1961,
51 70551,116.9,554894,4007,2827,130081,1962
52 };
53
54 protected final double[] swissData = new double[] {
55 80.2,17.0,15,12,9.96,
56 83.1,45.1,6,9,84.84,
57 92.5,39.7,5,5,93.40,
58 85.8,36.5,12,7,33.77,
59 76.9,43.5,17,15,5.16,
60 76.1,35.3,9,7,90.57,
61 83.8,70.2,16,7,92.85,
62 92.4,67.8,14,8,97.16,
63 82.4,53.3,12,7,97.67,
64 82.9,45.2,16,13,91.38,
65 87.1,64.5,14,6,98.61,
66 64.1,62.0,21,12,8.52,
67 66.9,67.5,14,7,2.27,
68 68.9,60.7,19,12,4.43,
69 61.7,69.3,22,5,2.82,
70 68.3,72.6,18,2,24.20,
71 71.7,34.0,17,8,3.30,
72 55.7,19.4,26,28,12.11,
73 54.3,15.2,31,20,2.15,
74 65.1,73.0,19,9,2.84,
75 65.5,59.8,22,10,5.23,
76 65.0,55.1,14,3,4.52,
77 56.6,50.9,22,12,15.14,
78 57.4,54.1,20,6,4.20,
79 72.5,71.2,12,1,2.40,
80 74.2,58.1,14,8,5.23,
81 72.0,63.5,6,3,2.56,
82 60.5,60.8,16,10,7.72,
83 58.3,26.8,25,19,18.46,
84 65.4,49.5,15,8,6.10,
85 75.5,85.9,3,2,99.71,
86 69.3,84.9,7,6,99.68,
87 77.3,89.7,5,2,100.00,
88 70.5,78.2,12,6,98.96,
89 79.4,64.9,7,3,98.22,
90 65.0,75.9,9,9,99.06,
91 92.2,84.6,3,3,99.46,
92 79.3,63.1,13,13,96.83,
93 70.4,38.4,26,12,5.62,
94 65.7,7.7,29,11,13.79,
95 72.7,16.7,22,13,11.22,
96 64.4,17.6,35,32,16.92,
97 77.6,37.6,15,7,4.97,
98 67.6,18.7,25,7,8.65,
99 35.0,1.2,37,53,42.34,
100 44.7,46.6,16,29,50.43,
101 42.8,27.7,22,29,58.33
102 };
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115 @Test
116 public void testLongly() {
117 RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
118 RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
119 double[] rData = new double[] {
120 12333921.73333333246, 3.679666000000000e+04, 343330206.333333313,
121 1649102.666666666744, 1117681.066666666651, 23461965.733333334, 16240.93333333333248,
122 36796.66000000000, 1.164576250000000e+02, 1063604.115416667,
123 6258.666250000000, 3490.253750000000, 73503.000000000, 50.92333333333334,
124 343330206.33333331347, 1.063604115416667e+06, 9879353659.329166412,
125 56124369.854166664183, 30880428.345833335072, 685240944.600000024, 470977.90000000002328,
126 1649102.66666666674, 6.258666250000000e+03, 56124369.854166664,
127 873223.429166666698, -115378.762499999997, 4462741.533333333, 2973.03333333333330,
128 1117681.06666666665, 3.490253750000000e+03, 30880428.345833335,
129 -115378.762499999997, 484304.095833333326, 1764098.133333333, 1382.43333333333339,
130 23461965.73333333433, 7.350300000000000e+04, 685240944.600000024,
131 4462741.533333333209, 1764098.133333333302, 48387348.933333330, 32917.40000000000146,
132 16240.93333333333, 5.092333333333334e+01, 470977.900000000,
133 2973.033333333333, 1382.433333333333, 32917.40000000, 22.66666666666667
134 };
135
136 UnitTestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 7, 7), covarianceMatrix, 10E-9);
137
138 }
139
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143
144 @Test
145 public void testSwissFertility() {
146 RealMatrix matrix = createRealMatrix(swissData, 47, 5);
147 RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
148 double[] rData = new double[] {
149 156.0424976873265, 100.1691489361702, -64.36692876965772, -79.7295097132285, 241.5632030527289,
150 100.169148936170251, 515.7994172062905, -124.39283071230344, -139.6574005550416, 379.9043755781684,
151 -64.3669287696577, -124.3928307123034, 63.64662349676226, 53.5758556891767, -190.5606105457909,
152 -79.7295097132285, -139.6574005550416, 53.57585568917669, 92.4560592044403, -61.6988297872340,
153 241.5632030527289, 379.9043755781684, -190.56061054579092, -61.6988297872340, 1739.2945371877890
154 };
155
156 UnitTestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 5, 5), covarianceMatrix, 10E-13);
157 }
158
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161
162 @Test
163 public void testConstant() {
164 double[] noVariance = new double[] {1, 1, 1, 1};
165 double[] values = new double[] {1, 2, 3, 4};
166 Assert.assertEquals(0d, new Covariance().covariance(noVariance, values, true), Double.MIN_VALUE);
167 Assert.assertEquals(0d, new Covariance().covariance(noVariance, noVariance, true), Double.MIN_VALUE);
168 }
169
170
171
172
173 @Test
174 public void testOneColumn() {
175 RealMatrix cov = new Covariance(new double[][] {{1}, {2}}, false).getCovarianceMatrix();
176 Assert.assertEquals(1, cov.getRowDimension());
177 Assert.assertEquals(1, cov.getColumnDimension());
178 Assert.assertEquals(0.25, cov.getEntry(0, 0), 1.0e-15);
179 }
180
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183
184 @Test
185 public void testInsufficientData() {
186 double[] one = new double[] {1};
187 double[] two = new double[] {2};
188 try {
189 new Covariance().covariance(one, two, false);
190 Assert.fail("Expecting MathIllegalArgumentException");
191 } catch (MathIllegalArgumentException ex) {
192
193 }
194 try {
195 new Covariance(new double[][] {{},{}});
196 Assert.fail("Expecting MathIllegalArgumentException");
197 } catch (MathIllegalArgumentException ex) {
198
199 }
200 }
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206 @Test
207 public void testConsistency() {
208 final RealMatrix matrix = createRealMatrix(swissData, 47, 5);
209 final RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
210
211
212 Variance variance = new Variance();
213 for (int i = 0; i < 5; i++) {
214 Assert.assertEquals(variance.evaluate(matrix.getColumn(i)), covarianceMatrix.getEntry(i,i), 10E-14);
215 }
216
217
218 Assert.assertEquals(covarianceMatrix.getEntry(2, 3),
219 new Covariance().covariance(matrix.getColumn(2), matrix.getColumn(3), true), 10E-14);
220 Assert.assertEquals(covarianceMatrix.getEntry(2, 3), covarianceMatrix.getEntry(3, 2), Double.MIN_VALUE);
221
222
223 RealMatrix repeatedColumns = new Array2DRowRealMatrix(47, 3);
224 for (int i = 0; i < 3; i++) {
225 repeatedColumns.setColumnMatrix(i, matrix.getColumnMatrix(0));
226 }
227 RealMatrix repeatedCovarianceMatrix = new Covariance(repeatedColumns).getCovarianceMatrix();
228 double columnVariance = variance.evaluate(matrix.getColumn(0));
229 for (int i = 0; i < 3; i++) {
230 for (int j = 0; j < 3; j++) {
231 Assert.assertEquals(columnVariance, repeatedCovarianceMatrix.getEntry(i, j), 10E-14);
232 }
233 }
234
235
236 double[][] data = matrix.getData();
237 UnitTestUtils.assertEquals("Covariances",
238 covarianceMatrix, new Covariance().computeCovarianceMatrix(data),Double.MIN_VALUE);
239 UnitTestUtils.assertEquals("Covariances",
240 covarianceMatrix, new Covariance().computeCovarianceMatrix(data, true),Double.MIN_VALUE);
241
242 double[] x = data[0];
243 double[] y = data[1];
244 Assert.assertEquals(new Covariance().covariance(x, y),
245 new Covariance().covariance(x, y, true), Double.MIN_VALUE);
246 }
247
248 protected RealMatrix createRealMatrix(double[] data, int nRows, int nCols) {
249 double[][] matrixData = new double[nRows][nCols];
250 int ptr = 0;
251 for (int i = 0; i < nRows; i++) {
252 System.arraycopy(data, ptr, matrixData[i], 0, nCols);
253 ptr += nCols;
254 }
255 return new Array2DRowRealMatrix(matrixData);
256 }
257 }