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Java example source code file (KendallsCorrelationTest.java)

This example Java source code file (KendallsCorrelationTest.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.

Learn more about this Java project at its project page.

Java - Java tags/keywords

before, blockrealmatrix, kendall's, kendallscorrelation, kendallscorrelationtest, override, pearsonscorrelationtest, randomgenerator, realmatrix, test, util, well1024a

The KendallsCorrelationTest.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 java.util.Arrays;
import org.apache.commons.math3.TestUtils;
import org.apache.commons.math3.linear.BlockRealMatrix;
import org.apache.commons.math3.linear.RealMatrix;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well1024a;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;

/**
 * Test cases for Kendall's Tau rank correlation.
 */
public class KendallsCorrelationTest extends PearsonsCorrelationTest {

    private KendallsCorrelation correlation;

    @Before
    public void setUp() {
        correlation = new KendallsCorrelation();
    }

    /**
     * Test Longley dataset against R.
     */
    @Override
    @Test
    public void testLongly() {
        RealMatrix matrix = createRealMatrix(longleyData, 16, 7);
        KendallsCorrelation corrInstance = new KendallsCorrelation(matrix);
        RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
        double[] rData = new double[] {
                1, 0.9166666666666666, 0.9333333333333332, 0.3666666666666666, 0.05, 0.8999999999999999,
                0.8999999999999999, 0.9166666666666666, 1, 0.9833333333333333, 0.45, 0.03333333333333333,
                0.9833333333333333, 0.9833333333333333, 0.9333333333333332, 0.9833333333333333, 1,
                0.4333333333333333, 0.05, 0.9666666666666666, 0.9666666666666666, 0.3666666666666666,
                0.45, 0.4333333333333333, 1, -0.2166666666666666, 0.4666666666666666, 0.4666666666666666, 0.05,
                0.03333333333333333, 0.05, -0.2166666666666666, 1, 0.05, 0.05, 0.8999999999999999, 0.9833333333333333,
                0.9666666666666666, 0.4666666666666666, 0.05, 1, 0.9999999999999999, 0.8999999999999999,
                0.9833333333333333, 0.9666666666666666, 0.4666666666666666, 0.05, 0.9999999999999999, 1
        };
        TestUtils.assertEquals("Kendall's correlation matrix", createRealMatrix(rData, 7, 7), correlationMatrix, 10E-15);
    }

    /**
     * Test R swiss fertility dataset.
     */
    @Test
    public void testSwiss() {
        RealMatrix matrix = createRealMatrix(swissData, 47, 5);
        KendallsCorrelation corrInstance = new KendallsCorrelation(matrix);
        RealMatrix correlationMatrix = corrInstance.getCorrelationMatrix();
        double[] rData = new double[] {
                1, 0.1795465254708308, -0.4762437404200669, -0.3306111613580587, 0.2453703703703704,
                0.1795465254708308, 1, -0.4505221560842292, -0.4761645631778491, 0.2054604569820847,
                -0.4762437404200669, -0.4505221560842292, 1, 0.528943683925829, -0.3212755391722673,
                -0.3306111613580587, -0.4761645631778491, 0.528943683925829, 1, -0.08479652265379604,
                0.2453703703703704, 0.2054604569820847, -0.3212755391722673, -0.08479652265379604, 1
        };
        TestUtils.assertEquals("Kendall's correlation matrix", createRealMatrix(rData, 5, 5), correlationMatrix, 10E-15);
    }

    @Test
    public void testSimpleOrdered() {
        final int length = 10;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            xArray[i] = i;
            yArray[i] = i;
        }
        Assert.assertEquals(1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
    }

    @Test
    public void testSimpleReversed() {
        final int length = 10;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            xArray[length - i - 1] = i;
            yArray[i] = i;
        }
        Assert.assertEquals(-1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
    }

    @Test
    public void testSimpleOrderedPowerOf2() {
        final int length = 16;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            xArray[i] = i;
            yArray[i] = i;
        }
        Assert.assertEquals(1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
    }

    @Test
    public void testSimpleReversedPowerOf2() {
        final int length = 16;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            xArray[length - i - 1] = i;
            yArray[i] = i;
        }
        Assert.assertEquals(-1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
    }

    @Test
    public void testSimpleJumble() {
        //                                     A    B    C    D
        final double[] xArray = new double[] {1.0, 2.0, 3.0, 4.0};
        final double[] yArray = new double[] {1.0, 3.0, 2.0, 4.0};

        // 6 pairs: (A,B) (A,C) (A,D) (B,C) (B,D) (C,D)
        // (B,C) is discordant, the other 5 are concordant

        Assert.assertEquals((5 - 1) / (double) 6,
                correlation.correlation(xArray, yArray),
                Double.MIN_VALUE);
    }

    @Test
    public void testBalancedJumble() {
        //                                     A    B    C    D
        final double[] xArray = new double[] {1.0, 2.0, 3.0, 4.0};
        final double[] yArray = new double[] {1.0, 4.0, 3.0, 2.0};

        // 6 pairs: (A,B) (A,C) (A,D) (B,C) (B,D) (C,D)
        // (A,B) (A,C), (A,D) are concordant, the other 3 are discordant

        Assert.assertEquals(0.0,
                correlation.correlation(xArray, yArray),
                Double.MIN_VALUE);
    }

    @Test
    public void testOrderedTies() {
        final int length = 10;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            xArray[i] = i / 2;
            yArray[i] = i / 2;
        }
        // 5 pairs of points that are tied in both values.
        // 16 + 12 + 8 + 4 = 40 concordant
        // (40 - 0) / Math.sqrt((45 - 5) * (45 - 5)) = 1
        Assert.assertEquals(1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
    }


    @Test
    public void testAllTiesInBoth() {
        final int length = 10;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
    }

    @Test
    public void testAllTiesInX() {
        final int length = 10;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            xArray[i] = i;
        }
        Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
    }

    @Test
    public void testAllTiesInY() {
        final int length = 10;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        for (int i = 0; i < length; i++) {
            yArray[i] = i;
        }
        Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
    }

    @Test
    public void testSingleElement() {
        final int length = 1;
        final double[] xArray = new double[length];
        final double[] yArray = new double[length];
        Assert.assertEquals(Double.NaN, correlation.correlation(xArray, yArray), 0);
    }

    @Test
    public void testTwoElements() {
        final double[] xArray = new double[] {2.0, 1.0};
        final double[] yArray = new double[] {1.0, 2.0};
        Assert.assertEquals(-1.0, correlation.correlation(xArray, yArray), Double.MIN_VALUE);
    }

    @Test
    public void test2dDoubleArray() {
        final double[][] input = new double[][] {
                new double[] {2.0, 1.0, 2.0},
                new double[] {1.0, 2.0, 1.0},
                new double[] {0.0, 0.0, 0.0}
        };

        final double[][] expected = new double[][] {
                new double[] {1.0, 1.0 / 3.0, 1.0},
                new double[] {1.0 / 3.0, 1.0, 1.0 / 3.0},
                new double[] {1.0, 1.0 / 3.0, 1.0}};

        Assert.assertEquals(correlation.computeCorrelationMatrix(input),
                new BlockRealMatrix(expected));

    }

    @Test
    public void testBlockMatrix() {
        final double[][] input = new double[][] {
                new double[] {2.0, 1.0, 2.0},
                new double[] {1.0, 2.0, 1.0},
                new double[] {0.0, 0.0, 0.0}
        };

        final double[][] expected = new double[][] {
                new double[] {1.0, 1.0 / 3.0, 1.0},
                new double[] {1.0 / 3.0, 1.0, 1.0 / 3.0},
                new double[] {1.0, 1.0 / 3.0, 1.0}};

        Assert.assertEquals(
                correlation.computeCorrelationMatrix(new BlockRealMatrix(input)),
                new BlockRealMatrix(expected));
    }

    @Test
    public void testLargeArray() {
        // test integer overflow detected in MATH-1068
        double[] xArray = new double[100000];
        Arrays.fill(xArray, 0, 2500, 1.0);

        Assert.assertEquals(1.0, correlation.correlation(xArray, xArray), 1e-6);
    }

    @Test
    public void testMath1277() {
        // example that led to a correlation coefficient outside of [-1, 1]
        // due to the bug reported in MATH-1277
        RandomGenerator rng = new Well1024a(0);
        double[] xArray = new double[120000];
        double[] yArray = new double[120000];
        for (int i = 0; i < xArray.length; ++i) {
            xArray[i] =  rng.nextDouble();
        }
        for (int i = 0; i < yArray.length; ++i) {
            yArray[i] =  rng.nextDouble();
        }
        double coefficient = correlation.correlation(xArray, yArray);
        Assert.assertTrue(1.0 >= coefficient && -1.0 <= coefficient);
    }
}

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