1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * https://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17
18 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.analysis.integration.gauss;
23
24 import org.hipparchus.analysis.UnivariateFunction;
25 import org.hipparchus.util.FastMath;
26 import org.junit.Assert;
27 import org.junit.Test;
28
29 /**
30 * Test of the {@link HermiteRuleFactory}.
31 *
32 */
33 public class HermiteTest {
34 private static final GaussIntegratorFactory factory = new GaussIntegratorFactory();
35
36 @Test
37 public void testNormalDistribution() {
38 final double oneOverSqrtPi = 1 / FastMath.sqrt(Math.PI);
39
40 // By defintion, Gauss-Hermite quadrature readily provides the
41 // integral of the normal distribution density.
42 final int numPoints = 1;
43
44 // Change of variable:
45 // y = (x - mu) / (sqrt(2) * sigma)
46 // such that the integrand
47 // N(x, mu, sigma)
48 // is transformed to
49 // f(y) * exp(-y^2)
50 final UnivariateFunction f = new UnivariateFunction() {
51 public double value(double y) {
52 return oneOverSqrtPi; // Constant function.
53 }
54 };
55
56 final GaussIntegrator integrator = factory.hermite(numPoints);
57 final double result = integrator.integrate(f);
58 final double expected = 1;
59 Assert.assertEquals(expected, result, FastMath.ulp(expected));
60 }
61
62 @Test
63 public void testNormalMean() {
64 final double sqrtTwo = FastMath.sqrt(2);
65 final double oneOverSqrtPi = 1 / FastMath.sqrt(Math.PI);
66
67 final double mu = 12345.6789;
68 final double sigma = 987.654321;
69 final int numPoints = 6;
70
71 // Change of variable:
72 // y = (x - mu) / (sqrt(2) * sigma)
73 // such that the integrand
74 // x * N(x, mu, sigma)
75 // is transformed to
76 // f(y) * exp(-y^2)
77 final UnivariateFunction f = new UnivariateFunction() {
78 public double value(double y) {
79 return oneOverSqrtPi * (sqrtTwo * sigma * y + mu);
80 }
81 };
82
83 final GaussIntegrator integrator = factory.hermite(numPoints);
84 final double result = integrator.integrate(f);
85 final double expected = mu;
86 Assert.assertEquals(expected, result, 5 * FastMath.ulp(expected));
87 }
88
89 @Test
90 public void testNormalVariance() {
91 final double twoOverSqrtPi = 2 / FastMath.sqrt(Math.PI);
92
93 final double sigma = 987.654321;
94 final double sigma2 = sigma * sigma;
95 final int numPoints = 5;
96
97 // Change of variable:
98 // y = (x - mu) / (sqrt(2) * sigma)
99 // such that the integrand
100 // (x - mu)^2 * N(x, mu, sigma)
101 // is transformed to
102 // f(y) * exp(-y^2)
103 final UnivariateFunction f = new UnivariateFunction() {
104 public double value(double y) {
105 return twoOverSqrtPi * sigma2 * y * y;
106 }
107 };
108
109 final GaussIntegrator integrator = factory.hermite(numPoints);
110 final double result = integrator.integrate(f);
111 final double expected = sigma2;
112 Assert.assertEquals(expected, result, 10 * FastMath.ulp(expected));
113 }
114 }