Commons Math example source code file (RandomDataTest.java)

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Java - Commons Math tags/keywords

chisquaretestimpl, decimalformat, exception, frequency, frequency, hashset, hashset, illegalargumentexception, illegalargumentexception, object, randomdataimpl, randomdataimpl, randomdatatest, string, text, util

The Commons Math RandomDataTest.java 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.math.random;

import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;

import junit.framework.AssertionFailedError;

import org.apache.commons.math.RetryTestCase;
import org.apache.commons.math.distribution.PoissonDistribution;
import org.apache.commons.math.distribution.PoissonDistributionImpl;
import org.apache.commons.math.stat.Frequency;
import org.apache.commons.math.stat.descriptive.SummaryStatistics;
import org.apache.commons.math.stat.inference.ChiSquareTest;
import org.apache.commons.math.stat.inference.ChiSquareTestImpl;

/**
 * Test cases for the RandomData class.
 *
 * @version $Revision: 924362 $ $Date: 2009-04-05 11:55:59 -0500 (Sun, 05 Apr
 *          2009) $
 */

public class RandomDataTest extends RetryTestCase {

    public RandomDataTest(String name) {
        super(name);
        randomData = new RandomDataImpl();
    }

    protected long smallSampleSize = 1000;
    protected double[] expected = { 250, 250, 250, 250 };
    protected int largeSampleSize = 10000;
    private String[] hex = { "0", "1", "2", "3", "4", "5", "6", "7", "8", "9",
            "a", "b", "c", "d", "e", "f" };
    protected RandomDataImpl randomData = null;
    protected ChiSquareTestImpl testStatistic = new ChiSquareTestImpl();

    public void testNextIntExtremeValues() {
        int x = randomData.nextInt(Integer.MIN_VALUE, Integer.MAX_VALUE);
        int y = randomData.nextInt(Integer.MIN_VALUE, Integer.MAX_VALUE);
        assertFalse(x == y);
    }

    public void testNextLongExtremeValues() {
        long x = randomData.nextLong(Long.MIN_VALUE, Long.MAX_VALUE);
        long y = randomData.nextLong(Long.MIN_VALUE, Long.MAX_VALUE);
        assertFalse(x == y);
    }

    /** test dispersion and failure modes for nextInt() */
    public void testNextInt() {
        try {
            randomData.nextInt(4, 3);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        Frequency freq = new Frequency();
        int value = 0;
        for (int i = 0; i < smallSampleSize; i++) {
            value = randomData.nextInt(0, 3);
            assertTrue("nextInt range", (value >= 0) && (value <= 3));
            freq.addValue(value);
        }
        long[] observed = new long[4];
        for (int i = 0; i < 4; i++) {
            observed[i] = freq.getCount(i);
        }

        /*
         * Use ChiSquare dist with df = 4-1 = 3, alpha = .001 Change to 11.34
         * for alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 16.27);
    }

    /** test dispersion and failure modes for nextLong() */
    public void testNextLong() {
        try {
            randomData.nextLong(4, 3);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        Frequency freq = new Frequency();
        long value = 0;
        for (int i = 0; i < smallSampleSize; i++) {
            value = randomData.nextLong(0, 3);
            assertTrue("nextInt range", (value >= 0) && (value <= 3));
            freq.addValue(value);
        }
        long[] observed = new long[4];
        for (int i = 0; i < 4; i++) {
            observed[i] = freq.getCount(i);
        }

        /*
         * Use ChiSquare dist with df = 4-1 = 3, alpha = .001 Change to 11.34
         * for alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 16.27);
    }

    /** test dispersion and failure modes for nextSecureLong() */
    public void testNextSecureLong() {
        try {
            randomData.nextSecureLong(4, 3);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        Frequency freq = new Frequency();
        long value = 0;
        for (int i = 0; i < smallSampleSize; i++) {
            value = randomData.nextSecureLong(0, 3);
            assertTrue("nextInt range", (value >= 0) && (value <= 3));
            freq.addValue(value);
        }
        long[] observed = new long[4];
        for (int i = 0; i < 4; i++) {
            observed[i] = freq.getCount(i);
        }

        /*
         * Use ChiSquare dist with df = 4-1 = 3, alpha = .001 Change to 11.34
         * for alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 16.27);
    }

    /** test dispersion and failure modes for nextSecureInt() */
    public void testNextSecureInt() {
        try {
            randomData.nextSecureInt(4, 3);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        Frequency freq = new Frequency();
        int value = 0;
        for (int i = 0; i < smallSampleSize; i++) {
            value = randomData.nextSecureInt(0, 3);
            assertTrue("nextInt range", (value >= 0) && (value <= 3));
            freq.addValue(value);
        }
        long[] observed = new long[4];
        for (int i = 0; i < 4; i++) {
            observed[i] = freq.getCount(i);
        }

        /*
         * Use ChiSquare dist with df = 4-1 = 3, alpha = .001 Change to 11.34
         * for alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 16.27);
    }

    /**
     * Make sure that empirical distribution of random Poisson(4)'s has P(X <=
     * 5) close to actual cumulative Poisson probablity and that nextPoisson
     * fails when mean is non-positive TODO: replace with statistical test,
     * adding test stat to TestStatistic
     */
    public void testNextPoisson() {
        try {
            randomData.nextPoisson(0);
            fail("zero mean -- expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        Frequency f = new Frequency();
        for (int i = 0; i < largeSampleSize; i++) {
            try {
                f.addValue(randomData.nextPoisson(4.0d));
            } catch (Exception ex) {
                fail(ex.getMessage());
            }
        }
        long cumFreq = f.getCount(0) + f.getCount(1) + f.getCount(2)
                + f.getCount(3) + f.getCount(4) + f.getCount(5);
        long sumFreq = f.getSumFreq();
        double cumPct = Double.valueOf(cumFreq).doubleValue()
                / Double.valueOf(sumFreq).doubleValue();
        assertEquals("cum Poisson(4)", cumPct, 0.7851, 0.2);
        try {
            randomData.nextPoisson(-1);
            fail("negative mean supplied -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        try {
            randomData.nextPoisson(0);
            fail("0 mean supplied -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }

    }

    public void testNextPoissonConsistency() throws Exception {
        // Small integral means
        for (int i = 1; i < 100; i++) {
            checkNextPoissonConsistency(i);
        }
        // non-integer means
        RandomData randomData = new RandomDataImpl();
        for (int i = 1; i < 10; i++) {
            checkNextPoissonConsistency(randomData.nextUniform(1, 1000));
        }
        // large means
        // TODO: When MATH-282 is resolved, s/3000/10000 below
        for (int i = 1; i < 10; i++) {
            checkNextPoissonConsistency(randomData.nextUniform(1000, 3000));
        }
    }

    /**
     * Verifies that nextPoisson(mean) generates an empirical distribution of values
     * consistent with PoissonDistributionImpl by generating 1000 values, computing a
     * grouped frequency distribution of the observed values and comparing this distribution
     * to the corresponding expected distribution computed using PoissonDistributionImpl.
     * Uses ChiSquare test of goodness of fit to evaluate the null hypothesis that the
     * distributions are the same. If the null hypothesis can be rejected with confidence
     * 1 - alpha, the check fails.  This check will fail randomly with probability alpha.
     */
    public void checkNextPoissonConsistency(double mean) throws Exception {
        // Generate sample values
        int sampleSize = 1000;        // Number of deviates to generate
        int minExpectedCount = 7;     // Minimum size of expected bin count
        long maxObservedValue = 0;
        double alpha = 0.001;         // Probability of false failure
        Frequency frequency = new Frequency();
        for (int i = 0; i < sampleSize; i++) {
            long value = randomData.nextPoisson(mean);
            if (value > maxObservedValue) {
                maxObservedValue = value;
            }
            frequency.addValue(value);
        }

        /*
         *  Set up bins for chi-square test.
         *  Ensure expected counts are all at least minExpectedCount.
         *  Start with upper and lower tail bins.
         *  Lower bin = [0, lower); Upper bin = [upper, +inf).
         */
        PoissonDistribution poissonDistribution = new PoissonDistributionImpl(mean);
        int lower = 1;
        while (poissonDistribution.cumulativeProbability(lower - 1) * sampleSize < minExpectedCount) {
            lower++;
        }
        int upper = (int) (5 * mean);  // Even for mean = 1, not much mass beyond 5
        while ((1 - poissonDistribution.cumulativeProbability(upper - 1)) * sampleSize < minExpectedCount) {
            upper--;
        }

        // Set bin width for interior bins.  For poisson, only need to look at end bins.
        int binWidth = 1;
        boolean widthSufficient = false;
        double lowerBinMass = 0;
        double upperBinMass = 0;
        while (!widthSufficient) {
            lowerBinMass = poissonDistribution.cumulativeProbability(lower, lower + binWidth - 1);
            upperBinMass = poissonDistribution.cumulativeProbability(upper - binWidth + 1, upper);
            widthSufficient = Math.min(lowerBinMass, upperBinMass) * sampleSize >= minExpectedCount;
            binWidth++;
        }

        /*
         *  Determine interior bin bounds.  Bins are
         *  [1, lower = binBounds[0]), [lower, binBounds[1]), [binBounds[1], binBounds[2]), ... ,
         *    [binBounds[binCount - 2], upper = binBounds[binCount - 1]), [upper, +inf)
         *
         */
        List<Integer> binBounds = new ArrayList();
        binBounds.add(lower);
        int bound = lower + binWidth;
        while (bound < upper - binWidth) {
            binBounds.add(bound);
            bound += binWidth;
        }
        binBounds.add(bound);
        binBounds.add(upper);

        // Compute observed and expected bin counts
        final int binCount = binBounds.size() + 1;
        long[] observed = new long[binCount];
        double[] expected = new double[binCount];

        // Bottom bin
        observed[0] = 0;
        for (int i = 0; i < lower; i++) {
            observed[0] += frequency.getCount(i);
        }
        expected[0] = poissonDistribution.cumulativeProbability(lower - 1) * sampleSize;

        // Top bin
        observed[binCount - 1] = 0;
        for (int i = upper; i <= maxObservedValue; i++) {
            observed[binCount - 1] += frequency.getCount(i);
        }
        expected[binCount - 1] = (1 - poissonDistribution.cumulativeProbability(upper - 1)) * sampleSize;

        // Interior bins
        for (int i = 1; i < binCount - 1; i++) {
            observed[i] = 0;
            for (int j = binBounds.get(i - 1); j < binBounds.get(i); j++) {
                observed[i] += frequency.getCount(j);
            } // Expected count is (mass in [binBounds[i], binBounds[i+1])) * sampleSize
            expected[i] = (poissonDistribution.cumulativeProbability(binBounds.get(i) - 1) -
                poissonDistribution.cumulativeProbability(binBounds.get(i - 1) -1)) * sampleSize;
        }

        // Use chisquare test to verify that generated values are poisson(mean)-distributed
        ChiSquareTest chiSquareTest = new ChiSquareTestImpl();
        try {
            // Fail if we can reject null hypothesis that distributions are the same
            assertFalse(chiSquareTest.chiSquareTest(expected, observed, alpha));
        } catch (AssertionFailedError ex) {
            StringBuffer msgBuffer = new StringBuffer();
            DecimalFormat df = new DecimalFormat("#.##");
            msgBuffer.append("Chisquare test failed for mean = ");
            msgBuffer.append(mean);
            msgBuffer.append(" p-value = ");
            msgBuffer.append(chiSquareTest.chiSquareTest(expected, observed));
            msgBuffer.append(" chisquare statistic = ");
            msgBuffer.append(chiSquareTest.chiSquare(expected, observed));
            msgBuffer.append(". \n");
            msgBuffer.append("bin\t\texpected\tobserved\n");
            for (int i = 0; i < expected.length; i++) {
                msgBuffer.append("[");
                msgBuffer.append(i == 0 ? 1: binBounds.get(i - 1));
                msgBuffer.append(",");
                msgBuffer.append(i == binBounds.size() ? "inf": binBounds.get(i));
                msgBuffer.append(")");
                msgBuffer.append("\t\t");
                msgBuffer.append(df.format(expected[i]));
                msgBuffer.append("\t\t");
                msgBuffer.append(observed[i]);
                msgBuffer.append("\n");
            }
            msgBuffer.append("This test can fail randomly due to sampling error with probability ");
            msgBuffer.append(alpha);
            msgBuffer.append(".");
            fail(msgBuffer.toString());
        }
    }

    /** test dispersion and failute modes for nextHex() */
    public void testNextHex() {
        try {
            randomData.nextHexString(-1);
            fail("negative length supplied -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        try {
            randomData.nextHexString(0);
            fail("zero length supplied -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        String hexString = randomData.nextHexString(3);
        if (hexString.length() != 3) {
            fail("incorrect length for generated string");
        }
        hexString = randomData.nextHexString(1);
        if (hexString.length() != 1) {
            fail("incorrect length for generated string");
        }
        try {
            hexString = randomData.nextHexString(0);
            fail("zero length requested -- expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        if (hexString.length() != 1) {
            fail("incorrect length for generated string");
        }
        Frequency f = new Frequency();
        for (int i = 0; i < smallSampleSize; i++) {
            hexString = randomData.nextHexString(100);
            if (hexString.length() != 100) {
                fail("incorrect length for generated string");
            }
            for (int j = 0; j < hexString.length(); j++) {
                f.addValue(hexString.substring(j, j + 1));
            }
        }
        double[] expected = new double[16];
        long[] observed = new long[16];
        for (int i = 0; i < 16; i++) {
            expected[i] = (double) smallSampleSize * 100 / 16;
            observed[i] = f.getCount(hex[i]);
        }
        /*
         * Use ChiSquare dist with df = 16-1 = 15, alpha = .001 Change to 30.58
         * for alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 37.70);
    }

    /** test dispersion and failute modes for nextHex() */
    public void testNextSecureHex() {
        try {
            randomData.nextSecureHexString(-1);
            fail("negative length -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        try {
            randomData.nextSecureHexString(0);
            fail("zero length -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        String hexString = randomData.nextSecureHexString(3);
        if (hexString.length() != 3) {
            fail("incorrect length for generated string");
        }
        hexString = randomData.nextSecureHexString(1);
        if (hexString.length() != 1) {
            fail("incorrect length for generated string");
        }
        try {
            hexString = randomData.nextSecureHexString(0);
            fail("zero length requested -- expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        if (hexString.length() != 1) {
            fail("incorrect length for generated string");
        }
        Frequency f = new Frequency();
        for (int i = 0; i < smallSampleSize; i++) {
            hexString = randomData.nextSecureHexString(100);
            if (hexString.length() != 100) {
                fail("incorrect length for generated string");
            }
            for (int j = 0; j < hexString.length(); j++) {
                f.addValue(hexString.substring(j, j + 1));
            }
        }
        double[] expected = new double[16];
        long[] observed = new long[16];
        for (int i = 0; i < 16; i++) {
            expected[i] = (double) smallSampleSize * 100 / 16;
            observed[i] = f.getCount(hex[i]);
        }
        /*
         * Use ChiSquare dist with df = 16-1 = 15, alpha = .001 Change to 30.58
         * for alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 37.70);
    }

    /** test failure modes and dispersion of nextUniform() */
    public void testNextUniform() {
        try {
            randomData.nextUniform(4, 3);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        try {
            randomData.nextUniform(3, 3);
            fail("IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        double[] expected = { 500, 500 };
        long[] observed = { 0, 0 };
        double lower = -1d;
        double upper = 20d;
        double midpoint = (lower + upper) / 2d;
        double result = 0;
        for (int i = 0; i < 1000; i++) {
            result = randomData.nextUniform(lower, upper);
            if ((result == lower) || (result == upper)) {
                fail("generated value equal to an endpoint: " + result);
            }
            if (result < midpoint) {
                observed[0]++;
            } else {
                observed[1]++;
            }
        }
        /*
         * Use ChiSquare dist with df = 2-1 = 1, alpha = .001 Change to 6.64 for
         * alpha = .01
         */
        assertTrue("chi-square test -- will fail about 1 in 1000 times",
                testStatistic.chiSquare(expected, observed) < 10.83);
    }

    /** test exclusive endpoints of nextUniform **/
    public void testNextUniformExclusiveEndpoints() {
        for (int i = 0; i < 1000; i++) {
            double u = randomData.nextUniform(0.99, 1);
            assertTrue(u > 0.99 && u < 1);
        }
    }

    /** test failure modes and distribution of nextGaussian() */
    public void testNextGaussian() {
        try {
            randomData.nextGaussian(0, 0);
            fail("zero sigma -- IllegalArgumentException expected");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        SummaryStatistics u = new SummaryStatistics();
        for (int i = 0; i < largeSampleSize; i++) {
            u.addValue(randomData.nextGaussian(0, 1));
        }
        double xbar = u.getMean();
        double s = u.getStandardDeviation();
        double n = u.getN();
        /*
         * t-test at .001-level TODO: replace with externalized t-test, with
         * test statistic defined in TestStatistic
         */
        assertTrue(Math.abs(xbar) / (s / Math.sqrt(n)) < 3.29);
    }

    /** test failure modes and distribution of nextExponential() */
    public void testNextExponential() {
        try {
            randomData.nextExponential(-1);
            fail("negative mean -- expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        try {
            randomData.nextExponential(0);
            fail("zero mean -- expecting IllegalArgumentException");
        } catch (IllegalArgumentException ex) {
            // ignored
        }
        long cumFreq = 0;
        double v = 0;
        for (int i = 0; i < largeSampleSize; i++) {
            v = randomData.nextExponential(1);
            assertTrue("exponential deviate postive", v > 0);
            if (v < 2)
                cumFreq++;
        }
        /*
         * TODO: Replace with a statistical test, with statistic added to
         * TestStatistic. Check below compares observed cumulative distribution
         * evaluated at 2 with exponential CDF
         */
        assertEquals("exponential cumulative distribution", (double) cumFreq
                / (double) largeSampleSize, 0.8646647167633873, .2);
    }

    /** test reseeding, algorithm/provider games */
    public void testConfig() {
        randomData.reSeed(1000);
        double v = randomData.nextUniform(0, 1);
        randomData.reSeed();
        assertTrue("different seeds", Math
                .abs(v - randomData.nextUniform(0, 1)) > 10E-12);
        randomData.reSeed(1000);
        assertEquals("same seeds", v, randomData.nextUniform(0, 1), 10E-12);
        randomData.reSeedSecure(1000);
        String hex = randomData.nextSecureHexString(40);
        randomData.reSeedSecure();
        assertTrue("different seeds", !hex.equals(randomData
                .nextSecureHexString(40)));
        randomData.reSeedSecure(1000);
        assertTrue("same seeds", !hex
                .equals(randomData.nextSecureHexString(40)));

        /*
         * remove this test back soon, since it takes about 4 seconds
         *
         * try { randomData.setSecureAlgorithm("SHA1PRNG","SUN"); } catch
         * (NoSuchProviderException ex) { ; } assertTrue("different seeds",
         * !hex.equals(randomData.nextSecureHexString(40))); try {
         * randomData.setSecureAlgorithm("NOSUCHTHING","SUN");
         * fail("expecting NoSuchAlgorithmException"); } catch
         * (NoSuchProviderException ex) { ; } catch (NoSuchAlgorithmException
         * ex) { ; }
         *
         * try { randomData.setSecureAlgorithm("SHA1PRNG","NOSUCHPROVIDER");
         * fail("expecting NoSuchProviderException"); } catch
         * (NoSuchProviderException ex) { ; }
         */

        // test reseeding without first using the generators
        RandomDataImpl rd = new RandomDataImpl();
        rd.reSeed(100);
        rd.nextLong(1, 2);
        RandomDataImpl rd2 = new RandomDataImpl();
        rd2.reSeedSecure(2000);
        rd2.nextSecureLong(1, 2);
        rd = new RandomDataImpl();
        rd.reSeed();
        rd.nextLong(1, 2);
        rd2 = new RandomDataImpl();
        rd2.reSeedSecure();
        rd2.nextSecureLong(1, 2);
    }

    /** tests for nextSample() sampling from Collection */
    public void testNextSample() {
        Object[][] c = { { "0", "1" }, { "0", "2" }, { "0", "3" },
                { "0", "4" }, { "1", "2" }, { "1", "3" }, { "1", "4" },
                { "2", "3" }, { "2", "4" }, { "3", "4" } };
        long[] observed = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
        double[] expected = { 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 };

        HashSet<Object> cPop = new HashSet