| /* |
| * 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.math4.legacy.analysis.integration.gauss; |
| |
| import org.apache.commons.math4.legacy.analysis.UnivariateFunction; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| 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 / AccurateMath.sqrt(Math.PI); |
| |
| // By definition, 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() { |
| @Override |
| 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 = AccurateMath.sqrt(2); |
| final double oneOverSqrtPi = 1 / AccurateMath.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() { |
| @Override |
| 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 / AccurateMath.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() { |
| @Override |
| 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)); |
| } |
| } |