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.util.Binary64;
25 import org.hipparchus.util.FastMath;
26
27 import static org.junit.jupiter.api.Assertions.assertEquals;
28
29 /**
30 * Base class for standard testing of Gaussian quadrature rules,
31 * which are exact for polynomials up to a certain degree. In this test, each
32 * monomial in turn is tested against the specified quadrature rule.
33 *
34 */
35 public abstract class FieldGaussianQuadratureAbstractTest {
36
37 /**
38 * Returns the expected value of the integral of the specified monomial.
39 * The integration is carried out on the natural interval of the quadrature
40 * rule under test.
41 *
42 * @param n Degree of the monomial.
43 * @return the expected value of the integral of x<sup>n</sup>.
44 */
45 public abstract double getExpectedValue(final int n);
46
47 /**
48 * Checks that the value of the integral of each monomial
49 * <code>x<sup>0</sup>, ... , x<sup>p</sup></code>
50 * returned by the quadrature rule under test conforms with the expected
51 * value. Here {@code p} denotes the degree of the highest polynomial for
52 * which exactness is to be expected.
53 */
54 public void testAllMonomials(FieldGaussIntegrator<Binary64> integrator,
55 int maxDegree, double eps, double numUlps) {
56 for (int n = 0; n <= maxDegree; n++) {
57 final double expected = getExpectedValue(n);
58
59 final int p = n;
60 final double actual = integrator.integrate(x -> FastMath.pow(x, p))
61 .getReal();
62
63 // System.out.println(n + "/" + maxDegree + " " + integrator.getNumberOfPoints()
64 // + " " + expected + " " + actual + " " + Math.ulp(expected));
65 if (expected == 0) {
66 assertEquals(expected, actual, eps,
67 "while integrating monomial x**" + n + " with a " + integrator.getNumberOfPoints() + "-point quadrature rule");
68 } else {
69 double err = FastMath.abs(actual - expected) / Math.ulp(
70 expected);
71 assertEquals(expected, actual,
72 Math.ulp(expected) * numUlps,
73 "while integrating monomial x**" + n + " with a " + +integrator.getNumberOfPoints() + "-point quadrature rule, " + " error was " + err + " ulps");
74 }
75 }
76 }
77 }