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17 package org.apache.commons.math.stat.correlation;
18
19 import org.apache.commons.math.TestUtils;
20 import org.apache.commons.math.linear.RealMatrix;
21 import org.apache.commons.math.linear.Array2DRowRealMatrix;
22 import org.apache.commons.math.stat.descriptive.moment.Variance;
23
24 import junit.framework.TestCase;
25
26 public class CovarianceTest extends TestCase {
27
28 protected final double[] longleyData = new double[] {
29 60323,83.0,234289,2356,1590,107608,1947,
30 61122,88.5,259426,2325,1456,108632,1948,
31 60171,88.2,258054,3682,1616,109773,1949,
32 61187,89.5,284599,3351,1650,110929,1950,
33 63221,96.2,328975,2099,3099,112075,1951,
34 63639,98.1,346999,1932,3594,113270,1952,
35 64989,99.0,365385,1870,3547,115094,1953,
36 63761,100.0,363112,3578,3350,116219,1954,
37 66019,101.2,397469,2904,3048,117388,1955,
38 67857,104.6,419180,2822,2857,118734,1956,
39 68169,108.4,442769,2936,2798,120445,1957,
40 66513,110.8,444546,4681,2637,121950,1958,
41 68655,112.6,482704,3813,2552,123366,1959,
42 69564,114.2,502601,3931,2514,125368,1960,
43 69331,115.7,518173,4806,2572,127852,1961,
44 70551,116.9,554894,4007,2827,130081,1962
45 };
46
47 protected final double[] swissData = new double[] {
48 80.2,17.0,15,12,9.96,
49 83.1,45.1,6,9,84.84,
50 92.5,39.7,5,5,93.40,
51 85.8,36.5,12,7,33.77,
52 76.9,43.5,17,15,5.16,
53 76.1,35.3,9,7,90.57,
54 83.8,70.2,16,7,92.85,
55 92.4,67.8,14,8,97.16,
56 82.4,53.3,12,7,97.67,
57 82.9,45.2,16,13,91.38,
58 87.1,64.5,14,6,98.61,
59 64.1,62.0,21,12,8.52,
60 66.9,67.5,14,7,2.27,
61 68.9,60.7,19,12,4.43,
62 61.7,69.3,22,5,2.82,
63 68.3,72.6,18,2,24.20,
64 71.7,34.0,17,8,3.30,
65 55.7,19.4,26,28,12.11,
66 54.3,15.2,31,20,2.15,
67 65.1,73.0,19,9,2.84,
68 65.5,59.8,22,10,5.23,
69 65.0,55.1,14,3,4.52,
70 56.6,50.9,22,12,15.14,
71 57.4,54.1,20,6,4.20,
72 72.5,71.2,12,1,2.40,
73 74.2,58.1,14,8,5.23,
74 72.0,63.5,6,3,2.56,
75 60.5,60.8,16,10,7.72,
76 58.3,26.8,25,19,18.46,
77 65.4,49.5,15,8,6.10,
78 75.5,85.9,3,2,99.71,
79 69.3,84.9,7,6,99.68,
80 77.3,89.7,5,2,100.00,
81 70.5,78.2,12,6,98.96,
82 79.4,64.9,7,3,98.22,
83 65.0,75.9,9,9,99.06,
84 92.2,84.6,3,3,99.46,
85 79.3,63.1,13,13,96.83,
86 70.4,38.4,26,12,5.62,
87 65.7,7.7,29,11,13.79,
88 72.7,16.7,22,13,11.22,
89 64.4,17.6,35,32,16.92,
90 77.6,37.6,15,7,4.97,
91 67.6,18.7,25,7,8.65,
92 35.0,1.2,37,53,42.34,
93 44.7,46.6,16,29,50.43,
94 42.8,27.7,22,29,58.33
95 };
96
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107
108 public void testLongly() {
109 RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
110 RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
111 double[] rData = new double[] {
112 12333921.73333333246, 3.679666000000000e+04, 343330206.333333313,
113 1649102.666666666744, 1117681.066666666651, 23461965.733333334, 16240.93333333333248,
114 36796.66000000000, 1.164576250000000e+02, 1063604.115416667,
115 6258.666250000000, 3490.253750000000, 73503.000000000, 50.92333333333334,
116 343330206.33333331347, 1.063604115416667e+06, 9879353659.329166412,
117 56124369.854166664183, 30880428.345833335072, 685240944.600000024, 470977.90000000002328,
118 1649102.66666666674, 6.258666250000000e+03, 56124369.854166664,
119 873223.429166666698, -115378.762499999997, 4462741.533333333, 2973.03333333333330,
120 1117681.06666666665, 3.490253750000000e+03, 30880428.345833335,
121 -115378.762499999997, 484304.095833333326, 1764098.133333333, 1382.43333333333339,
122 23461965.73333333433, 7.350300000000000e+04, 685240944.600000024,
123 4462741.533333333209, 1764098.133333333302, 48387348.933333330, 32917.40000000000146,
124 16240.93333333333, 5.092333333333334e+01, 470977.900000000,
125 2973.033333333333, 1382.433333333333, 32917.40000000, 22.66666666666667
126 };
127
128 TestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 7, 7), covarianceMatrix, 10E-9);
129
130 }
131
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135
136 public void testSwissFertility() {
137 RealMatrix matrix = createRealMatrix(swissData, 47, 5);
138 RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
139 double[] rData = new double[] {
140 156.0424976873265, 100.1691489361702, -64.36692876965772, -79.7295097132285, 241.5632030527289,
141 100.169148936170251, 515.7994172062905, -124.39283071230344, -139.6574005550416, 379.9043755781684,
142 -64.3669287696577, -124.3928307123034, 63.64662349676226, 53.5758556891767, -190.5606105457909,
143 -79.7295097132285, -139.6574005550416, 53.57585568917669, 92.4560592044403, -61.6988297872340,
144 241.5632030527289, 379.9043755781684, -190.56061054579092, -61.6988297872340, 1739.2945371877890
145 };
146
147 TestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 5, 5), covarianceMatrix, 10E-13);
148 }
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152
153 public void testConstant() {
154 double[] noVariance = new double[] {1, 1, 1, 1};
155 double[] values = new double[] {1, 2, 3, 4};
156 assertEquals(0d, new Covariance().covariance(noVariance, values, true), Double.MIN_VALUE);
157 assertEquals(0d, new Covariance().covariance(noVariance, noVariance, true), Double.MIN_VALUE);
158 }
159
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161
162
163
164 public void testInsufficientData() {
165 double[] one = new double[] {1};
166 double[] two = new double[] {2};
167 try {
168 new Covariance().covariance(one, two, false);
169 fail("Expecting IllegalArgumentException");
170 } catch (IllegalArgumentException ex) {
171
172 }
173 RealMatrix matrix = new Array2DRowRealMatrix(new double[][] {{0},{1}});
174 try {
175 new Covariance(matrix);
176 fail("Expecting IllegalArgumentException");
177 } catch (IllegalArgumentException ex) {
178
179 }
180 }
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185
186 public void testConsistency() {
187 final RealMatrix matrix = createRealMatrix(swissData, 47, 5);
188 final RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
189
190
191 Variance variance = new Variance();
192 for (int i = 0; i < 5; i++) {
193 assertEquals(variance.evaluate(matrix.getColumn(i)), covarianceMatrix.getEntry(i,i), 10E-14);
194 }
195
196
197 assertEquals(covarianceMatrix.getEntry(2, 3),
198 new Covariance().covariance(matrix.getColumn(2), matrix.getColumn(3), true), 10E-14);
199 assertEquals(covarianceMatrix.getEntry(2, 3), covarianceMatrix.getEntry(3, 2), Double.MIN_VALUE);
200
201
202 RealMatrix repeatedColumns = new Array2DRowRealMatrix(47, 3);
203 for (int i = 0; i < 3; i++) {
204 repeatedColumns.setColumnMatrix(i, matrix.getColumnMatrix(0));
205 }
206 RealMatrix repeatedCovarianceMatrix = new Covariance(repeatedColumns).getCovarianceMatrix();
207 double columnVariance = variance.evaluate(matrix.getColumn(0));
208 for (int i = 0; i < 3; i++) {
209 for (int j = 0; j < 3; j++) {
210 assertEquals(columnVariance, repeatedCovarianceMatrix.getEntry(i, j), 10E-14);
211 }
212 }
213
214
215 double[][] data = matrix.getData();
216 TestUtils.assertEquals("Covariances",
217 covarianceMatrix, new Covariance().computeCovarianceMatrix(data),Double.MIN_VALUE);
218 TestUtils.assertEquals("Covariances",
219 covarianceMatrix, new Covariance().computeCovarianceMatrix(data, true),Double.MIN_VALUE);
220
221 double[] x = data[0];
222 double[] y = data[1];
223 assertEquals(new Covariance().covariance(x, y),
224 new Covariance().covariance(x, y, true), Double.MIN_VALUE);
225 }
226
227 protected RealMatrix createRealMatrix(double[] data, int nRows, int nCols) {
228 double[][] matrixData = new double[nRows][nCols];
229 int ptr = 0;
230 for (int i = 0; i < nRows; i++) {
231 System.arraycopy(data, ptr, matrixData[i], 0, nCols);
232 ptr += nCols;
233 }
234 return new Array2DRowRealMatrix(matrixData);
235 }
236 }