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Java example source code file (GaussianTest.java)

This example Java source code file (GaussianTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

derivativestructure, eps, gaussian, gaussiantest, test, univariatedifferentiablefunction, univariatefunction

The GaussianTest.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.commons.math3.analysis.function;

import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test for class {@link Gaussian}.
 */
public class GaussianTest {
    private final double EPS = Math.ulp(1d);

    @Test(expected=NotStrictlyPositiveException.class)
    public void testPreconditions() {
        new Gaussian(1, 2, -1);
    }

    @Test
    public void testSomeValues() {
        final UnivariateFunction f = new Gaussian();

        Assert.assertEquals(1 / FastMath.sqrt(2 * Math.PI), f.value(0), EPS);
    }

    @Test
    public void testLargeArguments() {
        final UnivariateFunction f = new Gaussian();

        Assert.assertEquals(0, f.value(Double.NEGATIVE_INFINITY), 0);
        Assert.assertEquals(0, f.value(-Double.MAX_VALUE), 0);
        Assert.assertEquals(0, f.value(-1e2), 0);
        Assert.assertEquals(0, f.value(1e2), 0);
        Assert.assertEquals(0, f.value(Double.MAX_VALUE), 0);
        Assert.assertEquals(0, f.value(Double.POSITIVE_INFINITY), 0);
    }

    @Test
    public void testDerivatives() {
        final UnivariateDifferentiableFunction gaussian = new Gaussian(2.0, 0.9, 3.0);
        final DerivativeStructure dsX = new DerivativeStructure(1, 4, 0, 1.1);
        final DerivativeStructure dsY = gaussian.value(dsX);
        Assert.assertEquals( 1.9955604901712128349,   dsY.getValue(),              EPS);
        Assert.assertEquals(-0.044345788670471396332, dsY.getPartialDerivative(1), EPS);
        Assert.assertEquals(-0.22074348138190206174,  dsY.getPartialDerivative(2), EPS);
        Assert.assertEquals( 0.014760030401924800557, dsY.getPartialDerivative(3), EPS);
        Assert.assertEquals( 0.073253159785035691678, dsY.getPartialDerivative(4), EPS);
    }

    @Test
    public void testDerivativeLargeArguments() {
        final Gaussian f = new Gaussian(0, 1e-50);

        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, Double.NEGATIVE_INFINITY)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, -Double.MAX_VALUE)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, -1e50)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, -1e2)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, 1e2)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, 1e50)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, Double.MAX_VALUE)).getPartialDerivative(1), 0);
        Assert.assertEquals(0, f.value(new DerivativeStructure(1, 1, 0, Double.POSITIVE_INFINITY)).getPartialDerivative(1), 0);
    }

    @Test
    public void testDerivativesNaN() {
        final Gaussian f = new Gaussian(0, 1e-50);
        final DerivativeStructure fx = f.value(new DerivativeStructure(1, 5, 0, Double.NaN));
        for (int i = 0; i <= fx.getOrder(); ++i) {
            Assert.assertTrue(Double.isNaN(fx.getPartialDerivative(i)));
        }
    }

    @Test(expected=NullArgumentException.class)
    public void testParametricUsage1() {
        final Gaussian.Parametric g = new Gaussian.Parametric();
        g.value(0, null);
    }

    @Test(expected=DimensionMismatchException.class)
    public void testParametricUsage2() {
        final Gaussian.Parametric g = new Gaussian.Parametric();
        g.value(0, new double[] {0});
    }

    @Test(expected=NotStrictlyPositiveException.class)
    public void testParametricUsage3() {
        final Gaussian.Parametric g = new Gaussian.Parametric();
        g.value(0, new double[] {0, 1, 0});
    }

    @Test(expected=NullArgumentException.class)
    public void testParametricUsage4() {
        final Gaussian.Parametric g = new Gaussian.Parametric();
        g.gradient(0, null);
    }

    @Test(expected=DimensionMismatchException.class)
    public void testParametricUsage5() {
        final Gaussian.Parametric g = new Gaussian.Parametric();
        g.gradient(0, new double[] {0});
    }

    @Test(expected=NotStrictlyPositiveException.class)
    public void testParametricUsage6() {
        final Gaussian.Parametric g = new Gaussian.Parametric();
        g.gradient(0, new double[] {0, 1, 0});
    }

    @Test
    public void testParametricValue() {
        final double norm = 2;
        final double mean = 3;
        final double sigma = 4;
        final Gaussian f = new Gaussian(norm, mean, sigma);

        final Gaussian.Parametric g = new Gaussian.Parametric();
        Assert.assertEquals(f.value(-1), g.value(-1, new double[] {norm, mean, sigma}), 0);
        Assert.assertEquals(f.value(0), g.value(0, new double[] {norm, mean, sigma}), 0);
        Assert.assertEquals(f.value(2), g.value(2, new double[] {norm, mean, sigma}), 0);
    }

    @Test
    public void testParametricGradient() {
        final double norm = 2;
        final double mean = 3;
        final double sigma = 4;
        final Gaussian.Parametric f = new Gaussian.Parametric();

        final double x = 1;
        final double[] grad = f.gradient(1, new double[] {norm, mean, sigma});
        final double diff = x - mean;
        final double n = FastMath.exp(-diff * diff / (2 * sigma * sigma));
        Assert.assertEquals(n, grad[0], EPS);
        final double m = norm * n * diff / (sigma * sigma);
        Assert.assertEquals(m, grad[1], EPS);
        final double s = m * diff / sigma;
        Assert.assertEquals(s, grad[2], EPS);
    }
}

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