ContinuousDistributionAbstractTest.java

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 * 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
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package org.apache.commons.statistics.distribution;

import java.util.ArrayList;
import java.util.Collections;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.integration.BaseAbstractUnivariateIntegrator;
import org.apache.commons.math3.analysis.integration.IterativeLegendreGaussIntegrator;
import org.apache.commons.rng.simple.RandomSource;
import org.junit.jupiter.api.Test;
import org.junit.jupiter.api.AfterEach;
import org.junit.jupiter.api.Assertions;
import org.junit.jupiter.api.BeforeEach;

/**
 * Abstract base class for {@link ContinuousDistribution} tests.
 * <p>
 * To create a concrete test class for a continuous distribution
 * implementation, first implement makeDistribution() to return a distribution
 * instance to use in tests. Then implement each of the test data generation
 * methods below.  In each case, the test points and test values arrays
 * returned represent parallel arrays of inputs and expected values for the
 * distribution returned by makeDistribution().  Default implementations
 * are provided for the makeInverseXxx methods that just invert the mapping
 * defined by the arrays returned by the makeCumulativeXxx methods.
 * <p>
 * makeCumulativeTestPoints() -- arguments used to test cumulative probabilities
 * makeCumulativeTestValues() -- expected cumulative probabilities
 * makeDensityTestValues() -- expected density values at cumulativeTestPoints
 * makeInverseCumulativeTestPoints() -- arguments used to test inverse cdf
 * makeInverseCumulativeTestValues() -- expected inverse cdf values
 * <p>
 * To implement additional test cases with different distribution instances and
 * test data, use the setXxx methods for the instance data in test cases and
 * call the verifyXxx methods to verify results.
 * <p>
 * Error tolerance can be overridden by implementing getTolerance().
 * <p>
 * Test data should be validated against reference tables or other packages
 * where possible, and the source of the reference data and/or validation
 * should be documented in the test cases.  A framework for validating
 * distribution data against R is included in the /src/test/R source tree.
 * <p>
 * See {@link NormalDistributionTest} and {@link ChiSquaredDistributionTest}
 * for examples.
 */
abstract class ContinuousDistributionAbstractTest {

//-------------------- Private test instance data -------------------------
    /**  Distribution instance used to perform tests */
    private ContinuousDistribution distribution;

    /** Tolerance used in comparing expected and returned values */
    private double tolerance = 1e-4;

    /** Arguments used to test cumulative probability density calculations */
    private double[] cumulativeTestPoints;

    /** Values used to test cumulative probability density calculations */
    private double[] cumulativeTestValues;

    /** Arguments used to test inverse cumulative probability density calculations */
    private double[] inverseCumulativeTestPoints;

    /** Values used to test inverse cumulative probability density calculations */
    private double[] inverseCumulativeTestValues;

    /** Values used to test density calculations */
    private double[] densityTestValues;

    /** Values used to test logarithmic density calculations */
    private double[] logDensityTestValues;

    //-------------------- Abstract methods -----------------------------------

    /** Creates the default continuous distribution instance to use in tests. */
    public abstract ContinuousDistribution makeDistribution();

    /** Creates the default cumulative probability test input values */
    public abstract double[] makeCumulativeTestPoints();

    /** Creates the default cumulative probability test expected values */
    public abstract double[] makeCumulativeTestValues();

    /** Creates the default density test expected values */
    public abstract double[] makeDensityTestValues();

    /** Creates the default logarithmic density test expected values.
     * The default implementation simply computes the logarithm
     * of each value returned by {@link #makeDensityTestValues()}.*/
    public double[] makeLogDensityTestValues() {
        final double[] density = makeDensityTestValues();
        final double[] logDensity = new double[density.length];
        for (int i = 0; i < density.length; i++) {
            logDensity[i] = Math.log(density[i]);
        }
        return logDensity;
    }

    //---- Default implementations of inverse test data generation methods ----

    /** Creates the default inverse cumulative probability test input values */
    public double[] makeInverseCumulativeTestPoints() {
        return makeCumulativeTestValues();
    }

    /** Creates the default inverse cumulative probability density test expected values */
    public double[] makeInverseCumulativeTestValues() {
        return makeCumulativeTestPoints();
    }

    //-------------------- Setup / tear down ----------------------------------

    /**
     * Setup sets all test instance data to default values.
     * <p>
     * This method is @BeforeEach (created for each test) as certain test methods may wish
     * to alter the defaults.
     */
    @BeforeEach
    void setUp() {
        distribution = makeDistribution();
        cumulativeTestPoints = makeCumulativeTestPoints();
        cumulativeTestValues = makeCumulativeTestValues();
        inverseCumulativeTestPoints = makeInverseCumulativeTestPoints();
        inverseCumulativeTestValues = makeInverseCumulativeTestValues();
        densityTestValues = makeDensityTestValues();
        logDensityTestValues = makeLogDensityTestValues();
    }

    /**
     * Cleans up test instance data
     */
    @AfterEach
    void tearDown() {
        distribution = null;
        cumulativeTestPoints = null;
        cumulativeTestValues = null;
        inverseCumulativeTestPoints = null;
        inverseCumulativeTestValues = null;
        densityTestValues = null;
        logDensityTestValues = null;
    }

    //-------------------- Verification methods -------------------------------

    /**
     * Verifies that cumulative probability density calculations match expected values
     * using current test instance data
     */
    protected void verifyCumulativeProbabilities() {
        // verify cumulativeProbability(double)
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            TestUtils.assertEquals("Incorrect cumulative probability value returned for " +
                                   cumulativeTestPoints[i], cumulativeTestValues[i],
                                   distribution.cumulativeProbability(cumulativeTestPoints[i]),
                                   getTolerance());
        }
        // verify probability(double, double)
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            for (int j = 0; j < cumulativeTestPoints.length; j++) {
                if (cumulativeTestPoints[i] <= cumulativeTestPoints[j]) {
                    TestUtils.assertEquals(cumulativeTestValues[j] - cumulativeTestValues[i],
                                           distribution.probability(cumulativeTestPoints[i], cumulativeTestPoints[j]),
                                           getTolerance());
                } else {
                    try {
                        distribution.probability(cumulativeTestPoints[i], cumulativeTestPoints[j]);
                    } catch (final IllegalArgumentException e) {
                        continue;
                    }
                    Assertions.fail("distribution.probability(double, double) should have thrown an exception that second argument is too large");
                }
            }
        }
    }

    /**
     * Verifies that inverse cumulative probability density calculations match expected values
     * using current test instance data
     */
    protected void verifyInverseCumulativeProbabilities() {
        for (int i = 0; i < inverseCumulativeTestPoints.length; i++) {
            TestUtils.assertEquals("Incorrect inverse cumulative probability value returned for " +
                                   inverseCumulativeTestPoints[i], inverseCumulativeTestValues[i],
                                   distribution.inverseCumulativeProbability(inverseCumulativeTestPoints[i]),
                                   getTolerance());
        }
    }

    /**
     * Verifies that density calculations match expected values
     */
    protected void verifyDensities() {
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            TestUtils.assertEquals("Incorrect probability density value returned for " +
                                   cumulativeTestPoints[i], densityTestValues[i],
                                   distribution.density(cumulativeTestPoints[i]),
                                   getTolerance());
        }
    }

    /**
     * Verifies that logarithmic density calculations match expected values
     */
    protected void verifyLogDensities() {
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            TestUtils.assertEquals("Incorrect probability density value returned for " +
                                   cumulativeTestPoints[i], logDensityTestValues[i],
                                   distribution.logDensity(cumulativeTestPoints[i]),
                                   getTolerance());
        }
    }

    //------------------------ Default test cases -----------------------------

    /**
     * Verifies that cumulative probability density calculations match expected values
     * using default test instance data
     */
    @Test
    void testCumulativeProbabilities() {
        verifyCumulativeProbabilities();
    }

    /**
     * Verifies that inverse cumulative probability density calculations match expected values
     * using default test instance data
     */
    @Test
    void testInverseCumulativeProbabilities() {
        verifyInverseCumulativeProbabilities();
    }

    /**
     * Verifies that density calculations return expected values
     * for default test instance data
     */
    @Test
    void testDensities() {
        verifyDensities();
    }

    /**
     * Verifies that logarithmic density calculations return expected values
     * for default test instance data
     */
    @Test
    void testLogDensities() {
        verifyLogDensities();
    }

    /**
     * Verifies that probability computations are consistent
     */
    @Test
    void testConsistency() {
        for (int i = 1; i < cumulativeTestPoints.length; i++) {

            // check that cdf(x, x) = 0
            TestUtils.assertEquals(0d,
                                   distribution.probability(cumulativeTestPoints[i], cumulativeTestPoints[i]),
                                   tolerance);

            // check that P(a < X <= b) = P(X <= b) - P(X <= a)
            final double upper = Math.max(cumulativeTestPoints[i], cumulativeTestPoints[i - 1]);
            final double lower = Math.min(cumulativeTestPoints[i], cumulativeTestPoints[i - 1]);
            final double diff = distribution.cumulativeProbability(upper) -
                distribution.cumulativeProbability(lower);
            final double direct = distribution.probability(lower, upper);
            TestUtils.assertEquals("Inconsistent probability for (" +
                                   lower + "," + upper + ")", diff, direct, tolerance);
        }
    }

    /**
     * Verifies that illegal arguments are correctly handled
     */
    @Test
    void testPrecondition1() {
        Assertions.assertThrows(DistributionException.class, () -> distribution.probability(1, 0));
    }
    @Test
    void testPrecondition2() {
        Assertions.assertThrows(DistributionException.class, () -> distribution.inverseCumulativeProbability(-1));
    }
    @Test
    void testPrecondition3() {
        Assertions.assertThrows(DistributionException.class, () -> distribution.inverseCumulativeProbability(2));
    }

    @Test
    void testOutsideSupport() {
        // Test various quantities when the variable is outside the support.
        final double lo = distribution.getSupportLowerBound();
        final double hi = distribution.getSupportUpperBound();
        final double below = lo - Math.ulp(lo);
        final double above = hi + Math.ulp(hi);

        Assertions.assertEquals(0d, distribution.density(below));
        Assertions.assertEquals(0d, distribution.density(above));
        Assertions.assertEquals(Double.NEGATIVE_INFINITY, distribution.logDensity(below));
        Assertions.assertEquals(Double.NEGATIVE_INFINITY, distribution.logDensity(above));
        Assertions.assertEquals(0d, distribution.cumulativeProbability(below));
        Assertions.assertEquals(1d, distribution.cumulativeProbability(above));
    }

    /**
     * Test sampling
     */
    @Test
    void testSampler() {
        final int sampleSize = 1000;
        final ContinuousDistribution.Sampler sampler =
            distribution.createSampler(RandomSource.create(RandomSource.WELL_19937_C, 123456789L));
        final double[] sample = AbstractContinuousDistribution.sample(sampleSize, sampler);
        final double[] quartiles = TestUtils.getDistributionQuartiles(distribution);
        final double[] expected = {250, 250, 250, 250};
        final long[] counts = new long[4];

        for (int i = 0; i < sampleSize; i++) {
            TestUtils.updateCounts(sample[i], counts, quartiles);
        }
        TestUtils.assertChiSquareAccept(expected, counts, 0.001);
    }

    /**
     * Verify that density integrals match the distribution.
     * The (filtered, sorted) cumulativeTestPoints array is used to source
     * integration limits. The integral of the density (estimated using a
     * Legendre-Gauss integrator) is compared with the cdf over the same
     * interval. Test points outside of the domain of the density function
     * are discarded.
     */
    @Test
    void testDensityIntegrals() {
        final double tol = 1e-9;
        final BaseAbstractUnivariateIntegrator integrator =
            new IterativeLegendreGaussIntegrator(5, 1e-12, 1e-10);
        final UnivariateFunction d = new UnivariateFunction() {
                @Override
                public double value(double x) {
                    return distribution.density(x);
                }
            };
        final ArrayList<Double> integrationTestPoints = new ArrayList<>();
        for (int i = 0; i < cumulativeTestPoints.length; i++) {
            if (Double.isNaN(cumulativeTestValues[i]) ||
                cumulativeTestValues[i] < 1e-5 ||
                cumulativeTestValues[i] > 1 - 1e-5) {
                continue; // exclude integrals outside domain.
            }
            integrationTestPoints.add(cumulativeTestPoints[i]);
        }
        Collections.sort(integrationTestPoints);
        for (int i = 1; i < integrationTestPoints.size(); i++) {
            Assertions.assertEquals(distribution.probability(integrationTestPoints.get(0), integrationTestPoints.get(i)),
                                integrator.integrate(1000000, // Triangle integrals are very slow to converge
                                                     d, integrationTestPoints.get(0),
                                                     integrationTestPoints.get(i)), tol);
        }
    }

    /**
     * Test if the distribution is support connected. This test exists to ensure the support
     * connected property is tested. This may be evaluated in the default implementation
     * of {@link AbstractContinuousDistribution#inverseCumulativeProbability(double)}
     * depending on the data points used to test the distribution (see
     * {@link #makeInverseCumulativeTestPoints()}). If this default method has been overridden
     * then the support connected property is not used elsewhere in the standard tests.
     */
    @Test
    void testIsSupportConnected() {
        Assertions.assertEquals(isSupportConnected(), distribution.isSupportConnected());
    }

    //------------------ Getters / Setters for test instance data -----------
    /**
     * @return Returns the cumulativeTestPoints.
     */
    protected double[] getCumulativeTestPoints() {
        return cumulativeTestPoints;
    }

    /**
     * @param cumulativeTestPoints The cumulativeTestPoints to set.
     */
    protected void setCumulativeTestPoints(double[] cumulativeTestPoints) {
        this.cumulativeTestPoints = cumulativeTestPoints;
    }

    /**
     * @return Returns the cumulativeTestValues.
     */
    protected double[] getCumulativeTestValues() {
        return cumulativeTestValues;
    }

    /**
     * @param cumulativeTestValues The cumulativeTestValues to set.
     */
    protected void setCumulativeTestValues(double[] cumulativeTestValues) {
        this.cumulativeTestValues = cumulativeTestValues;
    }

    /**
     * @return Returns the densityTestValues.
     */
    protected double[] getDensityTestValues() {
        return densityTestValues;
    }

    /**
     * @param densityTestValues The densityTestValues to set.
     */
    protected void setDensityTestValues(double[] densityTestValues) {
        this.densityTestValues = densityTestValues;
    }

    /**
     * @return Returns the distribution.
     */
    protected ContinuousDistribution getDistribution() {
        return distribution;
    }

    /**
     * @param distribution The distribution to set.
     */
    protected void setDistribution(ContinuousDistribution distribution) {
        this.distribution = distribution;
    }

    /**
     * @return Returns the inverseCumulativeTestPoints.
     */
    protected double[] getInverseCumulativeTestPoints() {
        return inverseCumulativeTestPoints;
    }

    /**
     * @param inverseCumulativeTestPoints The inverseCumulativeTestPoints to set.
     */
    protected void setInverseCumulativeTestPoints(double[] inverseCumulativeTestPoints) {
        this.inverseCumulativeTestPoints = inverseCumulativeTestPoints;
    }

    /**
     * @return Returns the inverseCumulativeTestValues.
     */
    protected double[] getInverseCumulativeTestValues() {
        return inverseCumulativeTestValues;
    }

    /**
     * @param inverseCumulativeTestValues The inverseCumulativeTestValues to set.
     */
    protected void setInverseCumulativeTestValues(double[] inverseCumulativeTestValues) {
        this.inverseCumulativeTestValues = inverseCumulativeTestValues;
    }

    /**
     * @return Returns the tolerance.
     */
    protected double getTolerance() {
        return tolerance;
    }

    /**
     * @param tolerance The tolerance to set.
     */
    protected void setTolerance(double tolerance) {
        this.tolerance = tolerance;
    }

    /**
     * The expected value for {@link ContinuousDistribution#isSupportConnected()}.
     * The default is {@code true}. Test class should override this when the distribution
     * is not support connected.
     *
     * @return Returns true if the distribution is support connected
     */
    protected boolean isSupportConnected() {
        return true;
    }
}