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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      https://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  /*
19   * This is not the original file distributed by the Apache Software Foundation
20   * It has been modified by the Hipparchus project
21   */
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         };
103 
104 
105     /**
106      * Test Longley dataset against R.
107      * Data Source: J. Longley (1967) "An Appraisal of Least Squares
108      * Programs for the Electronic Computer from the Point of View of the User"
109      * Journal of the American Statistical Association, vol. 62. September,
110      * pp. 819-841.
111      *
112      * Data are from NIST:
113      * <a href="https://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Longley.dat">Longley dataset</a>
114      */
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 
140     /**
141      * Test R Swiss fertility dataset against R.
142      * Data Source: R datasets package
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 
159     /**
160      * Constant column
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      * One column
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 
181     /**
182      * Insufficient data
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             // Expected
193         }
194         try {
195             new Covariance(new double[][] {{},{}});
196             Assert.fail("Expecting MathIllegalArgumentException");
197         } catch (MathIllegalArgumentException ex) {
198             // Expected
199         }
200     }
201 
202     /**
203      * Verify that diagonal entries are consistent with Variance computation and matrix matches
204      * column-by-column covariances
205      */
206     @Test
207     public void testConsistency() {
208         final RealMatrix matrix = createRealMatrix(swissData, 47, 5);
209         final RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
210 
211         // Variances on the diagonal
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         // Symmetry, column-consistency
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         // All columns same -> all entries = column variance
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         // Check bias-correction defaults
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 }