org.apache.commons.math3.distribution.UniformRealDistribution Java Examples

@Test
public void testPolynomialFit() {
    final Random randomizer = new Random(53882150042L);
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    final WeightedObservedPoints obs = new WeightedObservedPoints();
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        obs.add(x, f.value(x) + 0.1 * randomizer.nextGaussian());
    }

    final ParametricUnivariateFunction function = new PolynomialFunction.Parametric(); 
    // Start fit from initial guesses that are far from the optimal values.
    final SimpleCurveFitter fitter
        = SimpleCurveFitter.create(function,
                                   new double[] { -1e20, 3e15, -5e25 });
    final double[] best = fitter.fit(obs.toList());

    TestUtils.assertEquals("best != coeff", coeff, best, 2e-2);
}
 

@Test
public void testFit() {
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
    final PolynomialFitter fitter = new PolynomialFitter(optim);
    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        fitter.addObservedPoint(x, f.value(x));
    }

    // Start fit from initial guesses that are far from the optimal values.
    final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });

    TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
}
 

@Test
public void testRealDistributionDeserializerWithUniformDistribution() throws Exception {
  String syntheticOptions =
      "{\"seed\":12345,"
          + "\"delayDistribution\":{\"type\":\"uniform\",\"lower\":0,\"upper\":100}}";
  SyntheticOptions sourceOptions = optionsFromString(syntheticOptions, SyntheticOptions.class);
  assertEquals(
      0,
      (long)
          ((UniformRealDistribution) (sourceOptions.delayDistribution.getDistribution()))
              .getSupportLowerBound());
  assertEquals(
      100,
      (long)
          ((UniformRealDistribution) (sourceOptions.delayDistribution.getDistribution()))
              .getSupportUpperBound());
}
 

/**
 * Creates the features' initializers: an approximate circle around the
 * barycentre of the cities.
 *
 * @return an array containing the two initializers.
 */
private FeatureInitializer[] makeInitializers() {
    // Barycentre.
    final double[] centre = barycentre(cities);
    // Largest distance from centre.
    final double radius = 0.5 * largestDistance(centre[0], centre[1], cities);

    final double omega = 2 * Math.PI / numberOfNeurons;
    final UnivariateFunction h1 = new HarmonicOscillator(radius, omega, 0);
    final UnivariateFunction h2 = new HarmonicOscillator(radius, omega, 0.5 * Math.PI);

    final UnivariateFunction f1 = FunctionUtils.add(h1, new Constant(centre[0]));
    final UnivariateFunction f2 = FunctionUtils.add(h2, new Constant(centre[1]));

    final RealDistribution u
        = new UniformRealDistribution(random, -0.05 * radius, 0.05 * radius);

    return new FeatureInitializer[] {
        FeatureInitializerFactory.randomize(u, FeatureInitializerFactory.function(f1, 0, 1)),
        FeatureInitializerFactory.randomize(u, FeatureInitializerFactory.function(f2, 0, 1))
    };
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

@Test
public void testFit() {
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    final WeightedObservedPoints obs = new WeightedObservedPoints();
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        obs.add(x, f.value(x));
    }

    // Start fit from initial guesses that are far from the optimal values.
    final PolynomialCurveFitter fitter
        = PolynomialCurveFitter.create(0).withStartPoint(new double[] { -1e-20, 3e15, -5e25 });
    final double[] best = fitter.fit(obs.toList());

    TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

@Test
public void testFit() {
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
    final PolynomialFitter fitter = new PolynomialFitter(optim);
    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        fitter.addObservedPoint(x, f.value(x));
    }

    // Start fit from initial guesses that are far from the optimal values.
    final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });

    TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

@Test
public void testFit() {
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
    final PolynomialFitter fitter = new PolynomialFitter(optim);
    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        fitter.addObservedPoint(x, f.value(x));
    }

    // Start fit from initial guesses that are far from the optimal values.
    final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });

    TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

/**
 * Creates the features' initializers: an approximate circle around the
 * barycentre of the cities.
 *
 * @return an array containing the two initializers.
 */
private FeatureInitializer[] makeInitializers() {
    // Barycentre.
    final double[] centre = barycentre(cities);
    // Largest distance from centre.
    final double radius = 0.5 * largestDistance(centre[0], centre[1], cities);

    final double omega = 2 * Math.PI / numberOfNeurons;
    final UnivariateFunction h1 = new HarmonicOscillator(radius, omega, 0);
    final UnivariateFunction h2 = new HarmonicOscillator(radius, omega, 0.5 * Math.PI);

    final UnivariateFunction f1 = FunctionUtils.add(h1, new Constant(centre[0]));
    final UnivariateFunction f2 = FunctionUtils.add(h2, new Constant(centre[1]));

    final RealDistribution u
        = new UniformRealDistribution(random, -0.05 * radius, 0.05 * radius);

    return new FeatureInitializer[] {
        FeatureInitializerFactory.randomize(u, FeatureInitializerFactory.function(f1, 0, 1)),
        FeatureInitializerFactory.randomize(u, FeatureInitializerFactory.function(f2, 0, 1))
    };
}
 

/**
 * @param x Abscissa of the circle center.
 * @param y Ordinate of the circle center.
 * @param radius Radius of the circle.
 * @param xSigma Error on the x-coordinate of the circumference points.
 * @param ySigma Error on the y-coordinate of the circumference points.
 * @param seed RNG seed.
 */
public RandomCirclePointGenerator(double x,
                                  double y,
                                  double radius,
                                  double xSigma,
                                  double ySigma,
                                  long seed) {
    final RandomGenerator rng = new Well44497b(seed);
    this.radius = radius;
    cX = new NormalDistribution(rng, x, xSigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    cY = new NormalDistribution(rng, y, ySigma,
                                NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
    tP = new UniformRealDistribution(rng, 0, MathUtils.TWO_PI,
                                     UniformRealDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
 

@Test
public void testFit() {
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
    final PolynomialFitter fitter = new PolynomialFitter(optim);
    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        fitter.addObservedPoint(x, f.value(x));
    }

    // Start fit from initial guesses that are far from the optimal values.
    final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });

    TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
}
 

@Test
public void testFit() {
    final RealDistribution rng = new UniformRealDistribution(-100, 100);
    rng.reseedRandomGenerator(64925784252L);

    final LevenbergMarquardtOptimizer optim = new LevenbergMarquardtOptimizer();
    final PolynomialFitter fitter = new PolynomialFitter(optim);
    final double[] coeff = { 12.9, -3.4, 2.1 }; // 12.9 - 3.4 x + 2.1 x^2
    final PolynomialFunction f = new PolynomialFunction(coeff);

    // Collect data from a known polynomial.
    for (int i = 0; i < 100; i++) {
        final double x = rng.sample();
        fitter.addObservedPoint(x, f.value(x));
    }

    // Start fit from initial guesses that are far from the optimal values.
    final double[] best = fitter.fit(new double[] { -1e-20, 3e15, -5e25 });

    TestUtils.assertEquals("best != coeff", coeff, best, 1e-12);
}
 

/**
 * Make sure that permuted arrays do not hash to the same value.
 */
@Test
public void testPermutedArrayHash() {
    double[] original = new double[10];
    double[] permuted = new double[10];
    RandomDataGenerator random = new RandomDataGenerator();

    // Generate 10 distinct random values
    for (int i = 0; i < 10; i++) {
        final RealDistribution u = new UniformRealDistribution(i + 0.5, i + 0.75);
        original[i] = u.sample();
    }

    // Generate a random permutation, making sure it is not the identity
    boolean isIdentity = true;
    do {
        int[] permutation = random.nextPermutation(10, 10);
        for (int i = 0; i < 10; i++) {
            if (i != permutation[i]) {
                isIdentity = false;
            }
            permuted[i] = original[permutation[i]];
        }
    } while (isIdentity);

    // Verify that permuted array has different hash
    Assert.assertFalse(MathUtils.hash(original) == MathUtils.hash(permuted));
}
 

/**
 * Make sure that permuted arrays do not hash to the same value.
 */
@Test
public void testPermutedArrayHash() {
    double[] original = new double[10];
    double[] permuted = new double[10];
    RandomDataGenerator random = new RandomDataGenerator();

    // Generate 10 distinct random values
    for (int i = 0; i < 10; i++) {
        final RealDistribution u = new UniformRealDistribution(i + 0.5, i + 0.75);
        original[i] = u.sample();
    }

    // Generate a random permutation, making sure it is not the identity
    boolean isIdentity = true;
    do {
        int[] permutation = random.nextPermutation(10, 10);
        for (int i = 0; i < 10; i++) {
            if (i != permutation[i]) {
                isIdentity = false;
            }
            permuted[i] = original[permutation[i]];
        }
    } while (isIdentity);

    // Verify that permuted array has different hash
    Assert.assertFalse(MathUtils.hash(original) == MathUtils.hash(permuted));
}
 

/** Uniform distribution, unit normal dataset */
@Test
public void testOneSampleUniformGaussian() {
    final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
    final UniformRealDistribution unif = new UniformRealDistribution(-0.5, 0.5);
    // Value was obtained via exact test, validated against R. Running exact test takes a long
    // time.
    Assert.assertEquals(4.9405812774239166E-11, test.kolmogorovSmirnovTest(unif, gaussian, false), TOLERANCE);
    Assert.assertTrue(test.kolmogorovSmirnovTest(unif, gaussian, 0.05));
    Assert.assertEquals(0.3401058049019608, test.kolmogorovSmirnovStatistic(unif, gaussian), TOLERANCE);
}
 

private Object[][] getUnivariateGaussianTargetsWithDropout(final double sigma, final double dropoutRate) {
    Random rng = new Random(337);
    final RandomGenerator randomGenerator = RandomGeneratorFactory.createRandomGenerator(rng);
    NormalDistribution n = new NormalDistribution(randomGenerator, 1, sigma);
    final int numDataPoints = 10000;
    final int numEventPoints = 2000;

    // Randomly select dropoutRate of targets and reduce by 25%-75% (uniformly distributed)
    UniformRealDistribution uniformRealDistribution = new UniformRealDistribution(randomGenerator, 0, 1.0);
    final List<ReadCountRecord.SingleSampleRecord> targetList = new ArrayList<>();
    for (int i = 0; i < numDataPoints; i++){
        double coverage = n.sample() + (i < (numDataPoints - numEventPoints) ? 0.0 : 0.5);
        if (uniformRealDistribution.sample() < dropoutRate) {
            double multiplier = .25 + uniformRealDistribution.sample()/2;
            coverage = coverage * multiplier;
        }
        targetList.add(new ReadCountRecord.SingleSampleRecord(new Target("arbitrary_name", new SimpleInterval("chr1", 100 + 2*i, 101 + 2 * i)), coverage));
    }

    HashedListTargetCollection<ReadCountRecord.SingleSampleRecord> targets = new HashedListTargetCollection<>(targetList);

    List<ModeledSegment> segments = new ArrayList<>();
    segments.add(new ModeledSegment(new SimpleInterval("chr1", 100, 16050), 8000, 1));
    segments.add(new ModeledSegment(new SimpleInterval("chr1", 16100, 20200), 2000, 1.5));

    return new Object [] []{ {targets, segments}};
}
 

/**
 * Make sure that permuted arrays do not hash to the same value.
 */
@Test
public void testPermutedArrayHash() {
    double[] original = new double[10];
    double[] permuted = new double[10];
    RandomDataImpl random = new RandomDataImpl();

    // Generate 10 distinct random values
    for (int i = 0; i < 10; i++) {
        final RealDistribution u = new UniformRealDistribution(i + 0.5, i + 0.75);
        original[i] = u.sample();
    }

    // Generate a random permutation, making sure it is not the identity
    boolean isIdentity = true;
    do {
        int[] permutation = random.nextPermutation(10, 10);
        for (int i = 0; i < 10; i++) {
            if (i != permutation[i]) {
                isIdentity = false;
            }
            permuted[i] = original[permutation[i]];
        }
    } while (isIdentity);

    // Verify that permuted array has different hash
    Assert.assertFalse(MathUtils.hash(original) == MathUtils.hash(permuted));
}
 

/**
 * Generates a random sample of double values.
 * Sample size is random, between 10 and 100 and values are
 * uniformly distributed over [-100, 100].
 *
 * @return array of random double values
 */
private double[] generateSample() {
    final IntegerDistribution size = new UniformIntegerDistribution(10, 100);
    final RealDistribution randomData = new UniformRealDistribution(-100, 100);
    final int sampleSize = size.sample();
    final double[] out = randomData.sample(sampleSize);
    return out;
}
 

/**
 * Make sure that permuted arrays do not hash to the same value.
 */
@Test
public void testPermutedArrayHash() {
    double[] original = new double[10];
    double[] permuted = new double[10];
    RandomDataImpl random = new RandomDataImpl();

    // Generate 10 distinct random values
    for (int i = 0; i < 10; i++) {
        final RealDistribution u = new UniformRealDistribution(i + 0.5, i + 0.75);
        original[i] = u.sample();
    }

    // Generate a random permutation, making sure it is not the identity
    boolean isIdentity = true;
    do {
        int[] permutation = random.nextPermutation(10, 10);
        for (int i = 0; i < 10; i++) {
            if (i != permutation[i]) {
                isIdentity = false;
            }
            permuted[i] = original[permutation[i]];
        }
    } while (isIdentity);

    // Verify that permuted array has different hash
    Assert.assertFalse(MathUtils.hash(original) == MathUtils.hash(permuted));
}
 

/** Uniform distribution, unit normal dataset */
@Test
public void testOneSampleUniformGaussian() {
    final KolmogorovSmirnovTest test = new KolmogorovSmirnovTest();
    final UniformRealDistribution unif = new UniformRealDistribution(-0.5, 0.5);
    // Value was obtained via exact test, validated against R. Running exact test takes a long
    // time.
    Assert.assertEquals(4.9405812774239166E-11, test.kolmogorovSmirnovTest(unif, gaussian, false), TOLERANCE);
    Assert.assertTrue(test.kolmogorovSmirnovTest(unif, gaussian, 0.05));
    Assert.assertEquals(0.3401058049019608, test.kolmogorovSmirnovStatistic(unif, gaussian), TOLERANCE);
}