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.jupiter.api.Test;
27
28 import static org.junit.jupiter.api.Assertions.assertEquals;
29
30 /**
31 * Test of the {@link HermiteRuleFactory}.
32 *
33 */
34 class HermiteTest {
35 private static final GaussIntegratorFactory factory = new GaussIntegratorFactory();
36
37 @Test
38 void testNormalDistribution() {
39 final double oneOverSqrtPi = 1 / FastMath.sqrt(Math.PI);
40
41 // By defintion, Gauss-Hermite quadrature readily provides the
42 // integral of the normal distribution density.
43 final int numPoints = 1;
44
45 // Change of variable:
46 // y = (x - mu) / (sqrt(2) * sigma)
47 // such that the integrand
48 // N(x, mu, sigma)
49 // is transformed to
50 // f(y) * exp(-y^2)
51 final UnivariateFunction f = new UnivariateFunction() {
52 public double value(double y) {
53 return oneOverSqrtPi; // Constant function.
54 }
55 };
56
57 final GaussIntegrator integrator = factory.hermite(numPoints);
58 final double result = integrator.integrate(f);
59 final double expected = 1;
60 assertEquals(expected, result, FastMath.ulp(expected));
61 }
62
63 @Test
64 void testNormalMean() {
65 final double sqrtTwo = FastMath.sqrt(2);
66 final double oneOverSqrtPi = 1 / FastMath.sqrt(Math.PI);
67
68 final double mu = 12345.6789;
69 final double sigma = 987.654321;
70 final int numPoints = 6;
71
72 // Change of variable:
73 // y = (x - mu) / (sqrt(2) * sigma)
74 // such that the integrand
75 // x * N(x, mu, sigma)
76 // is transformed to
77 // f(y) * exp(-y^2)
78 final UnivariateFunction f = new UnivariateFunction() {
79 public double value(double y) {
80 return oneOverSqrtPi * (sqrtTwo * sigma * y + mu);
81 }
82 };
83
84 final GaussIntegrator integrator = factory.hermite(numPoints);
85 final double result = integrator.integrate(f);
86 final double expected = mu;
87 assertEquals(expected, result, 5 * FastMath.ulp(expected));
88 }
89
90 @Test
91 void testNormalVariance() {
92 final double twoOverSqrtPi = 2 / FastMath.sqrt(Math.PI);
93
94 final double sigma = 987.654321;
95 final double sigma2 = sigma * sigma;
96 final int numPoints = 5;
97
98 // Change of variable:
99 // y = (x - mu) / (sqrt(2) * sigma)
100 // such that the integrand
101 // (x - mu)^2 * N(x, mu, sigma)
102 // is transformed to
103 // f(y) * exp(-y^2)
104 final UnivariateFunction f = new UnivariateFunction() {
105 public double value(double y) {
106 return twoOverSqrtPi * sigma2 * y * y;
107 }
108 };
109
110 final GaussIntegrator integrator = factory.hermite(numPoints);
111 final double result = integrator.integrate(f);
112 final double expected = sigma2;
113 assertEquals(expected, result, 10 * FastMath.ulp(expected));
114 }
115 }