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Java example source code file (PearsonsCorrelationTest.java)

This example Java source code file (PearsonsCorrelationTest.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

blockrealmatrix, covariance, expecting, illegalargumentexception, pearsonscorrelation, pearsonscorrelationtest, realmatrix, tdistribution, test

The PearsonsCorrelationTest.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.distribution.TDistribution;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;


public class PearsonsCorrelationTest {

    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.
     */
    @Test
    public void testLongly() {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
        double[] rData = new double[] {
                1.000000000000000, 0.9708985250610560, 0.9835516111796693, 0.5024980838759942,
                0.4573073999764817, 0.960390571594376, 0.9713294591921188,
                0.970898525061056, 1.0000000000000000, 0.9915891780247822, 0.6206333925590966,
                0.4647441876006747, 0.979163432977498, 0.9911491900672053,
                0.983551611179669, 0.9915891780247822, 1.0000000000000000, 0.6042609398895580,
                0.4464367918926265, 0.991090069458478, 0.9952734837647849,
                0.502498083875994, 0.6206333925590966, 0.6042609398895580, 1.0000000000000000,
                -0.1774206295018783, 0.686551516365312, 0.6682566045621746,
                0.457307399976482, 0.4647441876006747, 0.4464367918926265, -0.1774206295018783,
                1.0000000000000000, 0.364416267189032, 0.4172451498349454,
                0.960390571594376, 0.9791634329774981, 0.9910900694584777, 0.6865515163653120,
                0.3644162671890320, 1.000000000000000, 0.9939528462329257,
                0.971329459192119, 0.9911491900672053, 0.9952734837647849, 0.6682566045621746,
                0.4172451498349454, 0.993952846232926, 1.0000000000000000
        };
        TestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 7, 7), correlationMatrix, 10E-15);

        double[] rPvalues = new double[] {
                4.38904690369668e-10,
                8.36353208910623e-12, 7.8159700933611e-14,
                0.0472894097790304, 0.01030636128354301, 0.01316878049026582,
                0.0749178049642416, 0.06971758330341182, 0.0830166169296545, 0.510948586323452,
                3.693245043123738e-09, 4.327782576751815e-11, 1.167954621905665e-13, 0.00331028281967516, 0.1652293725106684,
                3.95834476307755e-10, 1.114663916723657e-13, 1.332267629550188e-15, 0.00466039138541463, 0.1078477071581498, 7.771561172376096e-15
        };
        RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 7);
        fillUpper(rPMatrix, 0d);
        TestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
    }

    /**
     * Test R Swiss fertility dataset against R.
     */
    @Test
    public void testSwissFertility() {
         RealMatrix matrix = createRealMatrix(swissData, 47, 5);
         PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
         RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
         double[] rData = new double[] {
               1.0000000000000000, 0.3530791836199747, -0.6458827064572875, -0.6637888570350691,  0.4636847006517939,
                 0.3530791836199747, 1.0000000000000000,-0.6865422086171366, -0.6395225189483201, 0.4010950530487398,
                -0.6458827064572875, -0.6865422086171366, 1.0000000000000000, 0.6984152962884830, -0.5727418060641666,
                -0.6637888570350691, -0.6395225189483201, 0.6984152962884830, 1.0000000000000000, -0.1538589170909148,
                 0.4636847006517939, 0.4010950530487398, -0.5727418060641666, -0.1538589170909148, 1.0000000000000000
         };
         TestUtils.assertEquals("correlation matrix", createRealMatrix(rData, 5, 5), correlationMatrix, 10E-15);

         double[] rPvalues = new double[] {
                 0.01491720061472623,
                 9.45043734069043e-07, 9.95151527133974e-08,
                 3.658616965962355e-07, 1.304590105694471e-06, 4.811397236181847e-08,
                 0.001028523190118147, 0.005204433539191644, 2.588307925380906e-05, 0.301807756132683
         };
         RealMatrix rPMatrix = createLowerTriangularRealMatrix(rPvalues, 5);
         fillUpper(rPMatrix, 0d);
         TestUtils.assertEquals("correlation p values", rPMatrix, corrInstance.getCorrelationPValues(), 10E-15);
    }

    /**
     * Test p-value near 0. JIRA: MATH-371
     */
    @Test
    public void testPValueNearZero() {
        /*
         * Create a dataset that has r -> 1, p -> 0 as dimension increases.
         * Prior to the fix for MATH-371, p vanished for dimension >= 14.
         * Post fix, p-values diminish smoothly, vanishing at dimension = 127.
         * Tested value is ~1E-303.
         */
        int dimension = 120;
        double[][] data = new double[dimension][2];
        for (int i = 0; i < dimension; i++) {
            data[i][0] = i;
            data[i][1] = i + 1/((double)i + 1);
        }
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(data);
        Assert.assertTrue(corrInstance.getCorrelationPValues().getEntry(0, 1) > 0);
    }


    /**
     * Constant column
     */
    @Test
    public void testConstant() {
        double[] noVariance = new double[] {1, 1, 1, 1};
        double[] values = new double[] {1, 2, 3, 4};
        Assert.assertTrue(Double.isNaN(new PearsonsCorrelation().correlation(noVariance, values)));
        Assert.assertTrue(Double.isNaN(new PearsonsCorrelation().correlation(values, noVariance)));
    }


    /**
     * Insufficient data
     */

    @Test
    public void testInsufficientData() {
        double[] one = new double[] {1};
        double[] two = new double[] {2};
        try {
            new PearsonsCorrelation().correlation(one, two);
            Assert.fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected
        }
        RealMatrix matrix = new BlockRealMatrix(new double[][] {{0},{1}});
        try {
            new PearsonsCorrelation(matrix);
            Assert.fail("Expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // Expected
        }
    }

    /**
     * Verify that direct t-tests using standard error estimates are consistent
     * with reported p-values
     */
    @Test
    public void testStdErrorConsistency() {
        TDistribution tDistribution = new TDistribution(45);
        RealMatrix matrix = createRealMatrix(swissData, 47, 5);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        RealMatrix rValues = corrInstance.getCorrelationMatrix();
        RealMatrix pValues = corrInstance.getCorrelationPValues();
        RealMatrix stdErrors = corrInstance.getCorrelationStandardErrors();
        for (int i = 0; i < 5; i++) {
            for (int j = 0; j < i; j++) {
                double t = FastMath.abs(rValues.getEntry(i, j)) / stdErrors.getEntry(i, j);
                double p = 2 * (1 - tDistribution.cumulativeProbability(t));
                Assert.assertEquals(p, pValues.getEntry(i, j), 10E-15);
            }
        }
    }

    /**
     * Verify that creating correlation from covariance gives same results as
     * direct computation from the original matrix
     */
    @Test
    public void testCovarianceConsistency() {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        Covariance covInstance = new Covariance(matrix);
        PearsonsCorrelation corrFromCovInstance = new PearsonsCorrelation(covInstance);
        TestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
                corrFromCovInstance.getCorrelationMatrix(), 10E-15);
        TestUtils.assertEquals("p values", corrInstance.getCorrelationPValues(),
                corrFromCovInstance.getCorrelationPValues(), 10E-15);
        TestUtils.assertEquals("standard errors", corrInstance.getCorrelationStandardErrors(),
                corrFromCovInstance.getCorrelationStandardErrors(), 10E-15);

        PearsonsCorrelation corrFromCovInstance2 =
            new PearsonsCorrelation(covInstance.getCovarianceMatrix(), 16);
        TestUtils.assertEquals("correlation values", corrInstance.getCorrelationMatrix(),
                corrFromCovInstance2.getCorrelationMatrix(), 10E-15);
        TestUtils.assertEquals("p values", corrInstance.getCorrelationPValues(),
                corrFromCovInstance2.getCorrelationPValues(), 10E-15);
        TestUtils.assertEquals("standard errors", corrInstance.getCorrelationStandardErrors(),
                corrFromCovInstance2.getCorrelationStandardErrors(), 10E-15);
    }


    @Test
    public void testConsistency() {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        PearsonsCorrelation corrInstance = new PearsonsCorrelation(matrix);
        double[][] data = matrix.getData();
        double[] x = matrix.getColumn(0);
        double[] y = matrix.getColumn(1);
        Assert.assertEquals(new PearsonsCorrelation().correlation(x, y),
                corrInstance.getCorrelationMatrix().getEntry(0, 1), Double.MIN_VALUE);
        TestUtils.assertEquals("Correlation matrix", corrInstance.getCorrelationMatrix(),
                new PearsonsCorrelation().computeCorrelationMatrix(data), 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 BlockRealMatrix(matrixData);
    }

    protected RealMatrix createLowerTriangularRealMatrix(double[] data, int dimension) {
        int ptr = 0;
        RealMatrix result = new BlockRealMatrix(dimension, dimension);
        for (int i = 1; i < dimension; i++) {
            for (int j = 0; j < i; j++) {
                result.setEntry(i, j, data[ptr]);
                ptr++;
            }
        }
        return result;
    }

    protected void fillUpper(RealMatrix matrix, double diagonalValue) {
        int dimension = matrix.getColumnDimension();
        for (int i = 0; i < dimension; i++) {
            matrix.setEntry(i, i, diagonalValue);
            for (int j = i+1; j < dimension; j++) {
                matrix.setEntry(i, j, matrix.getEntry(j, i));
            }
        }
    }
}

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