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Java example source code file (GaussianQuadratureAbstractTest.java)

This example Java source code file (GaussianQuadratureAbstractTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

gaussianquadratureabstracttest, gaussintegrator, power, test

The GaussianQuadratureAbstractTest.java Java example source code

/*
 * 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.math3.analysis.integration.gauss;

import org.apache.commons.math3.analysis.function.Power;
import org.apache.commons.math3.util.FastMath;
import org.junit.Test;
import org.junit.Assert;

/**
 * Base class for standard testing of Gaussian quadrature rules,
 * which are exact for polynomials up to a certain degree. In this test, each
 * monomial in turn is tested against the specified quadrature rule.
 *
 */
public abstract class GaussianQuadratureAbstractTest {
    /**
     * The maximum absolute error (for zero testing).
     */
    private final double eps;
    /**
     * The maximum relative error (in ulps).
     */
    private final double numUlps;
    /**
     * The quadrature rule under test.
     */
    private final GaussIntegrator integrator;
    /**
     * Maximum degree of monomials to be tested.
     */
    private final int maxDegree;

    /**
     * Creates a new instance of this abstract test with the specified
     * quadrature rule.
     * If the expected value is non-zero, equality of actual and expected values
     * is checked in the relative sense <center>
     * |x<sub>act - xexp| ≤  n 
     * <code>Math.ulp(xexp),  where n is
     * the maximum relative error (in ulps). If the expected value is zero, the
     * test checks that <center> |xact| ≤ ε,
     * </center> where ε is the maximum absolute error.
     *
     * @param integrator Quadrature rule under test.
     * @param maxDegree Maximum degree of monomials to be tested.
     * @param eps ε.
     * @param numUlps Value of the maximum relative error (in ulps).
     */
    public GaussianQuadratureAbstractTest(GaussIntegrator integrator,
                                          int maxDegree,
                                          double eps,
                                          double numUlps) {
        this.integrator = integrator;
        this.maxDegree = maxDegree;
        this.eps = eps;
        this.numUlps = numUlps;
    }

    /**
     * Returns the expected value of the integral of the specified monomial.
     * The integration is carried out on the natural interval of the quadrature
     * rule under test.
     *
     * @param n Degree of the monomial.
     * @return the expected value of the integral of x<sup>n.
     */
    public abstract double getExpectedValue(final int n);

    /**
     * Checks that the value of the integral of each monomial
     *   <code>x0, ... , xp
     * returned by the quadrature rule under test conforms with the expected
     * value.
     * Here {@code p} denotes the degree of the highest polynomial for which
     * exactness is to be expected.
     */
    @Test
    public void testAllMonomials() {
        for (int n = 0; n <= maxDegree; n++) {
            final double expected = getExpectedValue(n);

            final Power monomial = new Power(n);
            final double actual = integrator.integrate(monomial);

            // System.out.println(n + "/" + maxDegree + " " + integrator.getNumberOfPoints()
            //                    + " " + expected + " " + actual + " " + Math.ulp(expected));
            if (expected == 0) {
                Assert.assertEquals("while integrating monomial x**" + n +
                                    " with a " +
                                    integrator.getNumberOfPoints() + "-point quadrature rule",
                                    expected, actual, eps);
            } else {
                double err = FastMath.abs(actual - expected) / Math.ulp(expected);
                Assert.assertEquals("while integrating monomial x**" + n + " with a " +
                                    + integrator.getNumberOfPoints() + "-point quadrature rule, " +
                                    " error was " + err + " ulps",
                                    expected, actual, Math.ulp(expected) * numUlps);
            }
        }
    }
}

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