/*
* 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.integration.gauss;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.util.FastMath;
import org.junit.Test;
import org.junit.Assert;
/**
* Test of the {@link HermiteRuleFactory}.
*
*/
public class HermiteTest {
private static final GaussIntegratorFactory factory = new GaussIntegratorFactory();
@Test
public void testNormalDistribution() {
final double oneOverSqrtPi = 1 / FastMath.sqrt(Math.PI);
// By defintion, Gauss-Hermite quadrature readily provides the
// integral of the normal distribution density.
final int numPoints = 1;
// Change of variable:
// y = (x - mu) / (sqrt(2) * sigma)
// such that the integrand
// N(x, mu, sigma)
// is transformed to
// f(y) * exp(-y^2)
final UnivariateFunction f = new UnivariateFunction() {
public double value(double y) {
return oneOverSqrtPi; // Constant function.
}
};
final GaussIntegrator integrator = factory.hermite(numPoints);
final double result = integrator.integrate(f);
final double expected = 1;
Assert.assertEquals(expected, result, Math.ulp(expected));
}
@Test
public void testNormalMean() {
final double sqrtTwo = FastMath.sqrt(2);
final double oneOverSqrtPi = 1 / FastMath.sqrt(Math.PI);
final double mu = 12345.6789;
final double sigma = 987.654321;
final int numPoints = 5;
// Change of variable:
// y = (x - mu) / (sqrt(2) * sigma)
// such that the integrand
// x * N(x, mu, sigma)
// is transformed to
// f(y) * exp(-y^2)
final UnivariateFunction f = new UnivariateFunction() {
public double value(double y) {
return oneOverSqrtPi * (sqrtTwo * sigma * y + mu);
}
};
final GaussIntegrator integrator = factory.hermite(numPoints);
final double result = integrator.integrate(f);
final double expected = mu;
Assert.assertEquals(expected, result, Math.ulp(expected));
}
@Test
public void testNormalVariance() {
final double twoOverSqrtPi = 2 / FastMath.sqrt(Math.PI);
final double sigma = 987.654321;
final double sigma2 = sigma * sigma;
final int numPoints = 5;
// Change of variable:
// y = (x - mu) / (sqrt(2) * sigma)
// such that the integrand
// (x - mu)^2 * N(x, mu, sigma)
// is transformed to
// f(y) * exp(-y^2)
final UnivariateFunction f = new UnivariateFunction() {
public double value(double y) {
return twoOverSqrtPi * sigma2 * y * y;
}
};
final GaussIntegrator integrator = factory.hermite(numPoints);
final double result = integrator.integrate(f);
final double expected = sigma2;
Assert.assertEquals(expected, result, 10 * Math.ulp(expected));
}
}