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Java example source code file (CovarianceTest.java)

This example Java source code file (CovarianceTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

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Java - Java tags/keywords

array2drowrealmatrix, covariance, covariances, covariancetest, expecting, illegalargumentexception, notstrictlypositiveexception, realmatrix, test

The CovarianceTest.java Java example source code

/*
 * 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.stat.correlation;

import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.Array2DRowRealMatrix;
import org.apache.commons.math3.stat.descriptive.moment.Variance;
import org.junit.Assert;
import org.junit.Test;


public class CovarianceTest {

    protected final double[] longleyData = new double[] {
            60323,83.0,234289,2356,1590,107608,1947,
            61122,88.5,259426,2325,1456,108632,1948,
            60171,88.2,258054,3682,1616,109773,1949,
            61187,89.5,284599,3351,1650,110929,1950,
            63221,96.2,328975,2099,3099,112075,1951,
            63639,98.1,346999,1932,3594,113270,1952,
            64989,99.0,365385,1870,3547,115094,1953,
            63761,100.0,363112,3578,3350,116219,1954,
            66019,101.2,397469,2904,3048,117388,1955,
            67857,104.6,419180,2822,2857,118734,1956,
            68169,108.4,442769,2936,2798,120445,1957,
            66513,110.8,444546,4681,2637,121950,1958,
            68655,112.6,482704,3813,2552,123366,1959,
            69564,114.2,502601,3931,2514,125368,1960,
            69331,115.7,518173,4806,2572,127852,1961,
            70551,116.9,554894,4007,2827,130081,1962
        };

    protected final double[] swissData = new double[] {
            80.2,17.0,15,12,9.96,
            83.1,45.1,6,9,84.84,
            92.5,39.7,5,5,93.40,
            85.8,36.5,12,7,33.77,
            76.9,43.5,17,15,5.16,
            76.1,35.3,9,7,90.57,
            83.8,70.2,16,7,92.85,
            92.4,67.8,14,8,97.16,
            82.4,53.3,12,7,97.67,
            82.9,45.2,16,13,91.38,
            87.1,64.5,14,6,98.61,
            64.1,62.0,21,12,8.52,
            66.9,67.5,14,7,2.27,
            68.9,60.7,19,12,4.43,
            61.7,69.3,22,5,2.82,
            68.3,72.6,18,2,24.20,
            71.7,34.0,17,8,3.30,
            55.7,19.4,26,28,12.11,
            54.3,15.2,31,20,2.15,
            65.1,73.0,19,9,2.84,
            65.5,59.8,22,10,5.23,
            65.0,55.1,14,3,4.52,
            56.6,50.9,22,12,15.14,
            57.4,54.1,20,6,4.20,
            72.5,71.2,12,1,2.40,
            74.2,58.1,14,8,5.23,
            72.0,63.5,6,3,2.56,
            60.5,60.8,16,10,7.72,
            58.3,26.8,25,19,18.46,
            65.4,49.5,15,8,6.10,
            75.5,85.9,3,2,99.71,
            69.3,84.9,7,6,99.68,
            77.3,89.7,5,2,100.00,
            70.5,78.2,12,6,98.96,
            79.4,64.9,7,3,98.22,
            65.0,75.9,9,9,99.06,
            92.2,84.6,3,3,99.46,
            79.3,63.1,13,13,96.83,
            70.4,38.4,26,12,5.62,
            65.7,7.7,29,11,13.79,
            72.7,16.7,22,13,11.22,
            64.4,17.6,35,32,16.92,
            77.6,37.6,15,7,4.97,
            67.6,18.7,25,7,8.65,
            35.0,1.2,37,53,42.34,
            44.7,46.6,16,29,50.43,
            42.8,27.7,22,29,58.33
        };


    /**
     * Test Longley dataset against R.
     * Data Source: J. Longley (1967) "An Appraisal of Least Squares
     * Programs for the Electronic Computer from the Point of View of the User"
     * Journal of the American Statistical Association, vol. 62. September,
     * pp. 819-841.
     *
     * Data are from NIST:
     * http://www.itl.nist.gov/div898/strd/lls/data/LINKS/DATA/Longley.dat
     */
    @Test
    public void testLongly() {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
        double[] rData = new double[] {
         12333921.73333333246, 3.679666000000000e+04, 343330206.333333313,
         1649102.666666666744, 1117681.066666666651, 23461965.733333334, 16240.93333333333248,
         36796.66000000000, 1.164576250000000e+02, 1063604.115416667,
         6258.666250000000, 3490.253750000000, 73503.000000000, 50.92333333333334,
         343330206.33333331347, 1.063604115416667e+06, 9879353659.329166412,
         56124369.854166664183, 30880428.345833335072, 685240944.600000024, 470977.90000000002328,
         1649102.66666666674, 6.258666250000000e+03, 56124369.854166664,
         873223.429166666698, -115378.762499999997, 4462741.533333333, 2973.03333333333330,
         1117681.06666666665, 3.490253750000000e+03, 30880428.345833335,
         -115378.762499999997, 484304.095833333326, 1764098.133333333, 1382.43333333333339,
         23461965.73333333433, 7.350300000000000e+04, 685240944.600000024,
         4462741.533333333209, 1764098.133333333302, 48387348.933333330, 32917.40000000000146,
         16240.93333333333, 5.092333333333334e+01, 470977.900000000,
         2973.033333333333, 1382.433333333333, 32917.40000000, 22.66666666666667
        };

        TestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 7, 7), covarianceMatrix, 10E-9);

    }

    /**
     * Test R Swiss fertility dataset against R.
     * Data Source: R datasets package
     */
    @Test
    public void testSwissFertility() {
         RealMatrix matrix = createRealMatrix(swissData, 47, 5);
         RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();
         double[] rData = new double[] {
           156.0424976873265, 100.1691489361702, -64.36692876965772, -79.7295097132285, 241.5632030527289,
           100.169148936170251, 515.7994172062905, -124.39283071230344, -139.6574005550416, 379.9043755781684,
           -64.3669287696577, -124.3928307123034, 63.64662349676226, 53.5758556891767, -190.5606105457909,
           -79.7295097132285, -139.6574005550416, 53.57585568917669, 92.4560592044403, -61.6988297872340,
            241.5632030527289, 379.9043755781684, -190.56061054579092, -61.6988297872340, 1739.2945371877890
         };

         TestUtils.assertEquals("covariance matrix", createRealMatrix(rData, 5, 5), covarianceMatrix, 10E-13);
    }

    /**
     * Constant column
     */
    @Test
    public void testConstant() {
        double[] noVariance = new double[] {1, 1, 1, 1};
        double[] values = new double[] {1, 2, 3, 4};
        Assert.assertEquals(0d, new Covariance().covariance(noVariance, values, true), Double.MIN_VALUE);
        Assert.assertEquals(0d, new Covariance().covariance(noVariance, noVariance, true), Double.MIN_VALUE);
    }

    /**
     * One column
     */
    @Test
    public void testOneColumn() {
        RealMatrix cov = new Covariance(new double[][] {{1}, {2}}, false).getCovarianceMatrix();
        Assert.assertEquals(1, cov.getRowDimension());
        Assert.assertEquals(1, cov.getColumnDimension());
        Assert.assertEquals(0.25, cov.getEntry(0, 0), 1.0e-15);
    }

    /**
     * Insufficient data
     */
    @Test
    public void testInsufficientData() {
        double[] one = new double[] {1};
        double[] two = new double[] {2};
        try {
            new Covariance().covariance(one, two, false);
            Assert.fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected
        }
        try {
            new Covariance(new double[][] {{},{}});
            Assert.fail("Expecting NotStrictlyPositiveException");
        } catch (NotStrictlyPositiveException ex) {
            // Expected
        }
    }

    /**
     * Verify that diagonal entries are consistent with Variance computation and matrix matches
     * column-by-column covariances
     */
    @Test
    public void testConsistency() {
        final RealMatrix matrix = createRealMatrix(swissData, 47, 5);
        final RealMatrix covarianceMatrix = new Covariance(matrix).getCovarianceMatrix();

        // Variances on the diagonal
        Variance variance = new Variance();
        for (int i = 0; i < 5; i++) {
            Assert.assertEquals(variance.evaluate(matrix.getColumn(i)), covarianceMatrix.getEntry(i,i), 10E-14);
        }

        // Symmetry, column-consistency
        Assert.assertEquals(covarianceMatrix.getEntry(2, 3),
                new Covariance().covariance(matrix.getColumn(2), matrix.getColumn(3), true), 10E-14);
        Assert.assertEquals(covarianceMatrix.getEntry(2, 3), covarianceMatrix.getEntry(3, 2), Double.MIN_VALUE);

        // All columns same -> all entries = column variance
        RealMatrix repeatedColumns = new Array2DRowRealMatrix(47, 3);
        for (int i = 0; i < 3; i++) {
            repeatedColumns.setColumnMatrix(i, matrix.getColumnMatrix(0));
        }
        RealMatrix repeatedCovarianceMatrix = new Covariance(repeatedColumns).getCovarianceMatrix();
        double columnVariance = variance.evaluate(matrix.getColumn(0));
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                Assert.assertEquals(columnVariance, repeatedCovarianceMatrix.getEntry(i, j), 10E-14);
            }
        }

        // Check bias-correction defaults
        double[][] data = matrix.getData();
        TestUtils.assertEquals("Covariances",
                covarianceMatrix, new Covariance().computeCovarianceMatrix(data),Double.MIN_VALUE);
        TestUtils.assertEquals("Covariances",
                covarianceMatrix, new Covariance().computeCovarianceMatrix(data, true),Double.MIN_VALUE);

        double[] x = data[0];
        double[] y = data[1];
        Assert.assertEquals(new Covariance().covariance(x, y),
                new Covariance().covariance(x, y, true), Double.MIN_VALUE);
    }

    protected RealMatrix createRealMatrix(double[] data, int nRows, int nCols) {
        double[][] matrixData = new double[nRows][nCols];
        int ptr = 0;
        for (int i = 0; i < nRows; i++) {
            System.arraycopy(data, ptr, matrixData[i], 0, nCols);
            ptr += nCols;
        }
        return new Array2DRowRealMatrix(matrixData);
    }
}

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