gatk-3.8/public/java/test/org/broadinstitute/sting/utils/MathUtilsUnitTest.java

/*
* Copyright (c) 2012 The Broad Institute
* 
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package org.broadinstitute.sting.utils;

import org.broadinstitute.sting.BaseTest;
import org.testng.Assert;
import org.testng.annotations.BeforeClass;
import org.testng.annotations.Test;

import java.util.*;

/**
 * Basic unit test for MathUtils
 */
public class MathUtilsUnitTest extends BaseTest {
    @BeforeClass
    public void init() {
    }

    /**
     * Tests that we get the right values from the binomial distribution
     */
    @Test
    public void testBinomialProbability() {
        logger.warn("Executing testBinomialProbability");

        Assert.assertEquals(MathUtils.binomialProbability(3, 2, 0.5), 0.375, 0.0001);
        Assert.assertEquals(MathUtils.binomialProbability(100, 10, 0.5), 1.365543e-17, 1e-18);
        Assert.assertEquals(MathUtils.binomialProbability(217, 73, 0.02), 4.521904e-67, 1e-68);
        Assert.assertEquals(MathUtils.binomialProbability(300, 100, 0.02), 9.27097e-91, 1e-92);
        Assert.assertEquals(MathUtils.binomialProbability(300, 150, 0.98), 6.462892e-168, 1e-169);
        Assert.assertEquals(MathUtils.binomialProbability(300, 120, 0.98), 3.090054e-221, 1e-222);
        Assert.assertEquals(MathUtils.binomialProbability(300, 112, 0.98), 2.34763e-236, 1e-237);
    }

    /**
     * Tests that we get the right values from the multinomial distribution
     */
    @Test
    public void testMultinomialProbability() {
        logger.warn("Executing testMultinomialProbability");

        int[] counts0 = {2, 0, 1};
        double[] probs0 = {0.33, 0.33, 0.34};
        Assert.assertEquals(MathUtils.multinomialProbability(counts0, probs0), 0.111078, 1e-6);

        int[] counts1 = {10, 20, 30};
        double[] probs1 = {0.25, 0.25, 0.50};
        Assert.assertEquals(MathUtils.multinomialProbability(counts1, probs1), 0.002870301, 1e-9);

        int[] counts2 = {38, 82, 50, 36};
        double[] probs2 = {0.25, 0.25, 0.25, 0.25};
        Assert.assertEquals(MathUtils.multinomialProbability(counts2, probs2), 1.88221e-09, 1e-10);

        int[] counts3 = {1, 600, 1};
        double[] probs3 = {0.33, 0.33, 0.34};
        Assert.assertEquals(MathUtils.multinomialProbability(counts3, probs3), 5.20988e-285, 1e-286);
    }

    /**
     * Tests that the random index selection is working correctly
     */
    @Test
    public void testRandomIndicesWithReplacement() {
        logger.warn("Executing testRandomIndicesWithReplacement");

        // Check that the size of the list returned is correct
        Assert.assertTrue(MathUtils.sampleIndicesWithReplacement(5, 0).size() == 0);
        Assert.assertTrue(MathUtils.sampleIndicesWithReplacement(5, 1).size() == 1);
        Assert.assertTrue(MathUtils.sampleIndicesWithReplacement(5, 5).size() == 5);
        Assert.assertTrue(MathUtils.sampleIndicesWithReplacement(5, 1000).size() == 1000);

        // Check that the list contains only the k element range that as asked for - no more, no less
        List<Integer> Five = new ArrayList<Integer>();
        Collections.addAll(Five, 0, 1, 2, 3, 4);
        List<Integer> BigFive = MathUtils.sampleIndicesWithReplacement(5, 10000);
        Assert.assertTrue(BigFive.containsAll(Five));
        Assert.assertTrue(Five.containsAll(BigFive));
    }

    /**
     * Tests that we get the right values from the multinomial distribution
     */
    @Test
    public void testSliceListByIndices() {
        logger.warn("Executing testSliceListByIndices");

        // Check that the list contains only the k element range that as asked for - no more, no less but now
        // use the index list to pull elements from another list using sliceListByIndices
        List<Integer> Five = new ArrayList<Integer>();
        Collections.addAll(Five, 0, 1, 2, 3, 4);
        List<Character> FiveAlpha = new ArrayList<Character>();
        Collections.addAll(FiveAlpha, 'a', 'b', 'c', 'd', 'e');
        List<Integer> BigFive = MathUtils.sampleIndicesWithReplacement(5, 10000);
        List<Character> BigFiveAlpha = MathUtils.sliceListByIndices(BigFive, FiveAlpha);
        Assert.assertTrue(BigFiveAlpha.containsAll(FiveAlpha));
        Assert.assertTrue(FiveAlpha.containsAll(BigFiveAlpha));
    }

    /**
     * Tests that we correctly compute mean and standard deviation from a stream of numbers
     */
    @Test
    public void testRunningAverage() {
        logger.warn("Executing testRunningAverage");

        int[] numbers = {1, 2, 4, 5, 3, 128, 25678, -24};
        MathUtils.RunningAverage r = new MathUtils.RunningAverage();

        for (int i = 0; i < numbers.length; i++)
            r.add((double) numbers[i]);

        Assert.assertEquals((long) numbers.length, r.observationCount());
        Assert.assertTrue(r.mean() - 3224.625 < 2e-10);
        Assert.assertTrue(r.stddev() - 9072.6515881128 < 2e-10);
    }

    @Test
    public void testLog10Gamma() {
        logger.warn("Executing testLog10Gamma");

        Assert.assertEquals(MathUtils.log10Gamma(4.0), 0.7781513, 1e-6);
        Assert.assertEquals(MathUtils.log10Gamma(10), 5.559763, 1e-6);
        Assert.assertEquals(MathUtils.log10Gamma(10654), 38280.53, 1e-2);
    }

    @Test
    public void testLog10BinomialCoefficient() {
        logger.warn("Executing testLog10BinomialCoefficient");

        Assert.assertEquals(MathUtils.log10BinomialCoefficient(4, 2), 0.7781513, 1e-6);
        Assert.assertEquals(MathUtils.log10BinomialCoefficient(10, 3), 2.079181, 1e-6);
        Assert.assertEquals(MathUtils.log10BinomialCoefficient(103928, 119), 400.2156, 1e-4);
    }

    @Test
    public void testFactorial() {
        logger.warn("Executing testFactorial");
        Assert.assertEquals((int) MathUtils.factorial(4), 24);
        Assert.assertEquals((int) MathUtils.factorial(10), 3628800);
        Assert.assertEquals((int) MathUtils.factorial(12), 479001600);
    }

    @Test
    public void testLog10Factorial() {
        logger.warn("Executing testLog10Factorial");
        Assert.assertEquals(MathUtils.log10Factorial(4), 1.380211, 1e-6);
        Assert.assertEquals(MathUtils.log10Factorial(10), 6.559763, 1e-6);
        Assert.assertEquals(MathUtils.log10Factorial(12), 8.680337, 1e-6);
        Assert.assertEquals(MathUtils.log10Factorial(200), 374.8969, 1e-3);
        Assert.assertEquals(MathUtils.log10Factorial(12342), 45138.26, 1e-1);
    }

    @Test(enabled = true)
    public void testRandomSubset() {
        Integer[] x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
        Assert.assertEquals(MathUtils.randomSubset(x, 0).length, 0);
        Assert.assertEquals(MathUtils.randomSubset(x, 1).length, 1);
        Assert.assertEquals(MathUtils.randomSubset(x, 2).length, 2);
        Assert.assertEquals(MathUtils.randomSubset(x, 3).length, 3);
        Assert.assertEquals(MathUtils.randomSubset(x, 4).length, 4);
        Assert.assertEquals(MathUtils.randomSubset(x, 5).length, 5);
        Assert.assertEquals(MathUtils.randomSubset(x, 6).length, 6);
        Assert.assertEquals(MathUtils.randomSubset(x, 7).length, 7);
        Assert.assertEquals(MathUtils.randomSubset(x, 8).length, 8);
        Assert.assertEquals(MathUtils.randomSubset(x, 9).length, 9);
        Assert.assertEquals(MathUtils.randomSubset(x, 10).length, 10);
        Assert.assertEquals(MathUtils.randomSubset(x, 11).length, 10);

        for (int i = 0; i < 25; i++)
            Assert.assertTrue(hasUniqueElements(MathUtils.randomSubset(x, 5)));

    }

    @Test(enabled = true)
    public void testArrayShuffle() {
        Integer[] x = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
        for (int i = 0; i < 25; i++) {
            Object[] t = MathUtils.arrayShuffle(x);
            Assert.assertTrue(hasUniqueElements(t));
            Assert.assertTrue(hasAllElements(x, t));
        }
    }

    /**
     * Private functions used by testArrayShuffle()
     */
    private boolean hasUniqueElements(Object[] x) {
        for (int i = 0; i < x.length; i++)
            for (int j = i + 1; j < x.length; j++)
                if (x[i].equals(x[j]) || x[i] == x[j])
                    return false;
        return true;
    }

    private boolean hasAllElements(final Object[] expected, final Object[] actual) {
        HashSet<Object> set = new HashSet<Object>();
        set.addAll(Arrays.asList(expected));
        set.removeAll(Arrays.asList(actual));
        return set.isEmpty();
    }

    @Test
    public void testApproximateLog10SumLog10() {
        
        final double requiredPrecision = 1E-4;

        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {0.0}), 0.0, requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-5.15}), -5.15, requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {130.0}), 130.0, requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-0.145}), -0.145, requiredPrecision);

        Assert.assertEquals(MathUtils.approximateLog10SumLog10(0.0, 0.0), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-1.0, 0.0), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(0.0, -1.0), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, -1.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-2.2, -3.5), Math.log10(Math.pow(10.0, -2.2) + Math.pow(10.0, -3.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-1.0, -7.1), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, -7.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(5.0, 6.2), Math.log10(Math.pow(10.0, 5.0) + Math.pow(10.0, 6.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(38.1, 16.2), Math.log10(Math.pow(10.0, 38.1) + Math.pow(10.0, 16.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-38.1, 6.2), Math.log10(Math.pow(10.0, -38.1) + Math.pow(10.0, 6.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-19.1, -37.1), Math.log10(Math.pow(10.0, -19.1) + Math.pow(10.0, -37.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-29.1, -27.6), Math.log10(Math.pow(10.0, -29.1) + Math.pow(10.0, -27.6)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-0.12345, -0.23456), Math.log10(Math.pow(10.0, -0.12345) + Math.pow(10.0, -0.23456)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-15.7654, -17.0101), Math.log10(Math.pow(10.0, -15.7654) + Math.pow(10.0, -17.0101)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-0.12345, Double.NEGATIVE_INFINITY), -0.12345, requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-15.7654, Double.NEGATIVE_INFINITY), -15.7654, requiredPrecision);

        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {0.0, 0.0}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-1.0, 0.0}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {0.0, -1.0}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, -1.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-2.2, -3.5}), Math.log10(Math.pow(10.0, -2.2) + Math.pow(10.0, -3.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-1.0, -7.1}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, -7.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {5.0, 6.2}), Math.log10(Math.pow(10.0, 5.0) + Math.pow(10.0, 6.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {38.1, 16.2}), Math.log10(Math.pow(10.0, 38.1) + Math.pow(10.0, 16.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-38.1, 6.2}), Math.log10(Math.pow(10.0, -38.1) + Math.pow(10.0, 6.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-19.1, -37.1}), Math.log10(Math.pow(10.0, -19.1) + Math.pow(10.0, -37.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-29.1, -27.6}), Math.log10(Math.pow(10.0, -29.1) + Math.pow(10.0, -27.6)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-0.12345, -0.23456}), Math.log10(Math.pow(10.0, -0.12345) + Math.pow(10.0, -0.23456)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-15.7654, -17.0101}), Math.log10(Math.pow(10.0, -15.7654) + Math.pow(10.0, -17.0101)), requiredPrecision);

        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {0.0, 0.0, 0.0}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-1.0, 0.0, 0.0}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {0.0, -1.0, -2.5}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, -1.0) + Math.pow(10.0, -2.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-2.2, -3.5, -1.1}), Math.log10(Math.pow(10.0, -2.2) + Math.pow(10.0, -3.5) + Math.pow(10.0, -1.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-1.0, -7.1, 0.5}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, -7.1) + Math.pow(10.0, 0.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {5.0, 6.2, 1.3}), Math.log10(Math.pow(10.0, 5.0) + Math.pow(10.0, 6.2) + Math.pow(10.0, 1.3)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {38.1, 16.2, 18.1}), Math.log10(Math.pow(10.0, 38.1) + Math.pow(10.0, 16.2) + Math.pow(10.0, 18.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-38.1, 6.2, 26.6}), Math.log10(Math.pow(10.0, -38.1) + Math.pow(10.0, 6.2) + Math.pow(10.0, 26.6)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-19.1, -37.1, -45.1}), Math.log10(Math.pow(10.0, -19.1) + Math.pow(10.0, -37.1) + Math.pow(10.0, -45.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-29.1, -27.6, -26.2}), Math.log10(Math.pow(10.0, -29.1) + Math.pow(10.0, -27.6) + Math.pow(10.0, -26.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-0.12345, -0.23456, -0.34567}), Math.log10(Math.pow(10.0, -0.12345) + Math.pow(10.0, -0.23456) + Math.pow(10.0, -0.34567)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(new double[] {-15.7654, -17.0101, -17.9341}), Math.log10(Math.pow(10.0, -15.7654) + Math.pow(10.0, -17.0101) + Math.pow(10.0, -17.9341)), requiredPrecision);

        Assert.assertEquals(MathUtils.approximateLog10SumLog10(0.0, 0.0, 0.0), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-1.0, 0.0, 0.0), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(0.0, -1.0, -2.5), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, -1.0) + Math.pow(10.0, -2.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-2.2, -3.5, -1.1), Math.log10(Math.pow(10.0, -2.2) + Math.pow(10.0, -3.5) + Math.pow(10.0, -1.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-1.0, -7.1, 0.5), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, -7.1) + Math.pow(10.0, 0.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(5.0, 6.2, 1.3), Math.log10(Math.pow(10.0, 5.0) + Math.pow(10.0, 6.2) + Math.pow(10.0, 1.3)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(38.1, 16.2, 18.1), Math.log10(Math.pow(10.0, 38.1) + Math.pow(10.0, 16.2) + Math.pow(10.0, 18.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-38.1, 6.2, 26.6), Math.log10(Math.pow(10.0, -38.1) + Math.pow(10.0, 6.2) + Math.pow(10.0, 26.6)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-19.1, -37.1, -45.1), Math.log10(Math.pow(10.0, -19.1) + Math.pow(10.0, -37.1) + Math.pow(10.0, -45.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-29.1, -27.6, -26.2), Math.log10(Math.pow(10.0, -29.1) + Math.pow(10.0, -27.6) + Math.pow(10.0, -26.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-0.12345, -0.23456, -0.34567), Math.log10(Math.pow(10.0, -0.12345) + Math.pow(10.0, -0.23456) + Math.pow(10.0, -0.34567)), requiredPrecision);
        Assert.assertEquals(MathUtils.approximateLog10SumLog10(-15.7654, -17.0101, -17.9341), Math.log10(Math.pow(10.0, -15.7654) + Math.pow(10.0, -17.0101) + Math.pow(10.0, -17.9341)), requiredPrecision);
    }

    @Test
    public void testNormalizeFromLog10() {
        Assert.assertTrue(compareDoubleArrays(MathUtils.normalizeFromLog10(new double[] {0.0, 0.0, -1.0, -1.1, -7.8}, false, true), new double[] {0.0, 0.0, -1.0, -1.1, -7.8}));
        Assert.assertTrue(compareDoubleArrays(MathUtils.normalizeFromLog10(new double[] {-1.0, -1.0, -1.0, -1.1, -7.8}, false, true), new double[] {0.0, 0.0, 0.0, -0.1, -6.8}));
        Assert.assertTrue(compareDoubleArrays(MathUtils.normalizeFromLog10(new double[] {-10.0, -7.8, -10.5, -1.1, -10.0}, false, true), new double[] {-8.9, -6.7, -9.4, 0.0, -8.9}));

        Assert.assertTrue(compareDoubleArrays(MathUtils.normalizeFromLog10(new double[] {-1.0, -1.0, -1.0, -1.0}), new double[] {0.25, 0.25, 0.25, 0.25}));
        Assert.assertTrue(compareDoubleArrays(MathUtils.normalizeFromLog10(new double[] {-1.0, -3.0, -1.0, -1.0}), new double[] {0.1 * 1.0 / 0.301, 0.001 * 1.0 / 0.301, 0.1 * 1.0 / 0.301, 0.1 * 1.0 / 0.301}));
        Assert.assertTrue(compareDoubleArrays(MathUtils.normalizeFromLog10(new double[] {-1.0, -3.0, -1.0, -2.0}), new double[] {0.1 * 1.0 / 0.211, 0.001 * 1.0 / 0.211, 0.1 * 1.0 / 0.211, 0.01 * 1.0 / 0.211}));
    }

    @Test
    public void testLog10sumLog10() {
        final double requiredPrecision = 1E-14;

        final double log3 = 0.477121254719662;
        Assert.assertEquals(MathUtils.log10sumLog10(new double[]{0.0, 0.0, 0.0}), log3, requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, 0.0, 0.0}, 0), log3, requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[]{0.0, 0.0, 0.0}, 0, 3), log3, requiredPrecision);

        final double log2 = 0.301029995663981;
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, 0.0, 0.0}, 0, 2), log2, requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, 0.0, 0.0}, 0, 1), 0.0, requiredPrecision);

        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0}), 0.0, requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-5.15}), -5.15, requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {130.0}), 130.0, requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-0.145}), -0.145, requiredPrecision);

        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, 0.0}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-1.0, 0.0}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, -1.0}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, -1.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-2.2, -3.5}), Math.log10(Math.pow(10.0, -2.2) + Math.pow(10.0, -3.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-1.0, -7.1}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, -7.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {5.0, 6.2}), Math.log10(Math.pow(10.0, 5.0) + Math.pow(10.0, 6.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {38.1, 16.2}), Math.log10(Math.pow(10.0, 38.1) + Math.pow(10.0, 16.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-38.1, 6.2}), Math.log10(Math.pow(10.0, -38.1) + Math.pow(10.0, 6.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-19.1, -37.1}), Math.log10(Math.pow(10.0, -19.1) + Math.pow(10.0, -37.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-29.1, -27.6}), Math.log10(Math.pow(10.0, -29.1) + Math.pow(10.0, -27.6)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-0.12345, -0.23456}), Math.log10(Math.pow(10.0, -0.12345) + Math.pow(10.0, -0.23456)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-15.7654, -17.0101}), Math.log10(Math.pow(10.0, -15.7654) + Math.pow(10.0, -17.0101)), requiredPrecision);

        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, 0.0, 0.0}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-1.0, 0.0, 0.0}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, 0.0) + Math.pow(10.0, 0.0)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {0.0, -1.0, -2.5}), Math.log10(Math.pow(10.0, 0.0) + Math.pow(10.0, -1.0) + Math.pow(10.0, -2.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-2.2, -3.5, -1.1}), Math.log10(Math.pow(10.0, -2.2) + Math.pow(10.0, -3.5) + Math.pow(10.0, -1.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-1.0, -7.1, 0.5}), Math.log10(Math.pow(10.0, -1.0) + Math.pow(10.0, -7.1) + Math.pow(10.0, 0.5)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {5.0, 6.2, 1.3}), Math.log10(Math.pow(10.0, 5.0) + Math.pow(10.0, 6.2) + Math.pow(10.0, 1.3)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {38.1, 16.2, 18.1}), Math.log10(Math.pow(10.0, 38.1) + Math.pow(10.0, 16.2) + Math.pow(10.0, 18.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-38.1, 6.2, 26.6}), Math.log10(Math.pow(10.0, -38.1) + Math.pow(10.0, 6.2) + Math.pow(10.0, 26.6)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-19.1, -37.1, -45.1}), Math.log10(Math.pow(10.0, -19.1) + Math.pow(10.0, -37.1) + Math.pow(10.0, -45.1)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-29.1, -27.6, -26.2}), Math.log10(Math.pow(10.0, -29.1) + Math.pow(10.0, -27.6) + Math.pow(10.0, -26.2)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-0.12345, -0.23456, -0.34567}), Math.log10(Math.pow(10.0, -0.12345) + Math.pow(10.0, -0.23456) + Math.pow(10.0, -0.34567)), requiredPrecision);
        Assert.assertEquals(MathUtils.log10sumLog10(new double[] {-15.7654, -17.0101, -17.9341}), Math.log10(Math.pow(10.0, -15.7654) + Math.pow(10.0, -17.0101) + Math.pow(10.0, -17.9341)), requiredPrecision);
    }

    @Test
    public void testDotProduct() {
        Assert.assertEquals(MathUtils.dotProduct(new Double[]{-5.0,-3.0,2.0}, new Double[]{6.0,7.0,8.0}),-35.0,1e-3);
        Assert.assertEquals(MathUtils.dotProduct(new Double[]{-5.0}, new Double[]{6.0}),-30.0,1e-3);
    }

    @Test
    public void testLogDotProduct() {
        Assert.assertEquals(MathUtils.logDotProduct(new double[]{-5.0,-3.0,2.0}, new double[]{6.0,7.0,8.0}),10.0,1e-3);
        Assert.assertEquals(MathUtils.logDotProduct(new double[]{-5.0}, new double[]{6.0}),1.0,1e-3);
    }

    /**
     * Private function used by testNormalizeFromLog10()
     */
    private boolean compareDoubleArrays(double[] b1, double[] b2) {
        if (b1.length != b2.length) {
            return false; // sanity check
        }

        for (int i = 0; i < b1.length; i++) {
            if (MathUtils.compareDoubles(b1[i], b2[i]) != 0)
                return false;
        }
        return true;
    }
}