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.function.Power;
25 import org.hipparchus.util.FastMath;
26
27 import static org.junit.jupiter.api.Assertions.assertEquals;
28
29
30 /**
31 * Base class for standard testing of Gaussian quadrature rules,
32 * which are exact for polynomials up to a certain degree. In this test, each
33 * monomial in turn is tested against the specified quadrature rule.
34 *
35 */
36 public abstract class GaussianQuadratureAbstractTest {
37
38 /**
39 * Returns the expected value of the integral of the specified monomial.
40 * The integration is carried out on the natural interval of the quadrature
41 * rule under test.
42 *
43 * @param n Degree of the monomial.
44 * @return the expected value of the integral of x<sup>n</sup>.
45 */
46 public abstract double getExpectedValue(final int n);
47
48 /**
49 * Checks that the value of the integral of each monomial
50 * <code>x<sup>0</sup>, ... , x<sup>p</sup></code>
51 * returned by the quadrature rule under test conforms with the expected
52 * value.
53 * Here {@code p} denotes the degree of the highest polynomial for which
54 * exactness is to be expected.
55 */
56 public void testAllMonomials(GaussIntegrator integrator,
57 int maxDegree,
58 double eps,
59 double numUlps) {
60 for (int n = 0; n <= maxDegree; n++) {
61 final double expected = getExpectedValue(n);
62
63 final Power monomial = new Power(n);
64 final double actual = integrator.integrate(monomial);
65
66 // System.out.println(n + "/" + maxDegree + " " + integrator.getNumberOfPoints()
67 // + " " + expected + " " + actual + " " + Math.ulp(expected));
68 if (expected == 0) {
69 assertEquals(expected, actual, eps, "while integrating monomial x**" + n +
70 " with a " +
71 integrator.getNumberOfPoints() + "-point quadrature rule");
72 } else {
73 double err = FastMath.abs(actual - expected) / Math.ulp(expected);
74 assertEquals(expected, actual, Math.ulp(expected) * numUlps, "while integrating monomial x**" + n + " with a " +
75 + integrator.getNumberOfPoints() + "-point quadrature rule, " +
76 " error was " + err + " ulps");
77 }
78 }
79 }
80 }