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Java example source code file (BaseSecantSolverAbstractTest.java)

This example Java source code file (BaseSecantSolverAbstractTest.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.

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Java - Java tags/keywords

basesecantsolverabstracttest, bracketedunivariatesolver, classcastexception, expecting, nobracketingexception, numberistoolargeexception, pegasussolver, quinticfunction, sin, suppresswarnings, test, univariatefunction, univariatesolver, xminus5function

The BaseSecantSolverAbstractTest.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.solvers;

import org.apache.commons.math3.analysis.QuinticFunction;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.XMinus5Function;
import org.apache.commons.math3.analysis.function.Sin;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.util.FastMath;
import org.junit.Assert;
import org.junit.Test;

/**
 * Base class for root-finding algorithms tests derived from
 * {@link BaseSecantSolver}.
 *
 */
public abstract class BaseSecantSolverAbstractTest {
    /** Returns the solver to use to perform the tests.
     * @return the solver to use to perform the tests
     */
    protected abstract UnivariateSolver getSolver();

    /** Returns the expected number of evaluations for the
     * {@link #testQuinticZero} unit test. A value of {@code -1} indicates that
     * the test should be skipped for that solver.
     * @return the expected number of evaluations for the
     * {@link #testQuinticZero} unit test
     */
    protected abstract int[] getQuinticEvalCounts();

    @Test
    public void testSinZero() {
        // The sinus function is behaved well around the root at pi. The second
        // order derivative is zero, which means linear approximating methods
        // still converge quadratically.
        UnivariateFunction f = new Sin();
        double result;
        UnivariateSolver solver = getSolver();

        result = solver.solve(100, f, 3, 4);
        //System.out.println(
        //    "Root: " + result + " Evaluations: " + solver.getEvaluations());
        Assert.assertEquals(result, FastMath.PI, solver.getAbsoluteAccuracy());
        Assert.assertTrue(solver.getEvaluations() <= 6);
        result = solver.solve(100, f, 1, 4);
        //System.out.println(
        //    "Root: " + result + " Evaluations: " + solver.getEvaluations());
        Assert.assertEquals(result, FastMath.PI, solver.getAbsoluteAccuracy());
        Assert.assertTrue(solver.getEvaluations() <= 7);
    }

    @Test
    public void testQuinticZero() {
        // The quintic function has zeros at 0, +-0.5 and +-1.
        // Around the root of 0 the function is well behaved, with a second
        // derivative of zero a 0.
        // The other roots are less well to find, in particular the root at 1,
        // because the function grows fast for x>1.
        // The function has extrema (first derivative is zero) at 0.27195613
        // and 0.82221643, intervals containing these values are harder for
        // the solvers.
        UnivariateFunction f = new QuinticFunction();
        double result;
        UnivariateSolver solver = getSolver();
        double atol = solver.getAbsoluteAccuracy();
        int[] counts = getQuinticEvalCounts();

        // Tests data: initial bounds, and expected solution, per test case.
        double[][] testsData = {{-0.2,  0.2,  0.0},
                                {-0.1,  0.3,  0.0},
                                {-0.3,  0.45, 0.0},
                                { 0.3,  0.7,  0.5},
                                { 0.2,  0.6,  0.5},
                                { 0.05, 0.95, 0.5},
                                { 0.85, 1.25, 1.0},
                                { 0.8,  1.2,  1.0},
                                { 0.85, 1.75, 1.0},
                                { 0.55, 1.45, 1.0},
                                { 0.85, 5.0,  1.0},
                               };
        int maxIter = 500;

        for(int i = 0; i < testsData.length; i++) {
            // Skip test, if needed.
            if (counts[i] == -1) continue;

            // Compute solution.
            double[] testData = testsData[i];
            result = solver.solve(maxIter, f, testData[0], testData[1]);
            //System.out.println(
            //    "Root: " + result + " Evaluations: " + solver.getEvaluations());

            // Check solution.
            Assert.assertEquals(result, testData[2], atol);
            Assert.assertTrue(solver.getEvaluations() <= counts[i] + 1);
        }
    }

    @Test
    public void testRootEndpoints() {
        UnivariateFunction f = new XMinus5Function();
        UnivariateSolver solver = getSolver();

        // End-point is root. This should be a special case in the solver, and
        // the initial end-point should be returned exactly.
        double result = solver.solve(100, f, 5.0, 6.0);
        Assert.assertEquals(5.0, result, 0.0);

        result = solver.solve(100, f, 4.0, 5.0);
        Assert.assertEquals(5.0, result, 0.0);

        result = solver.solve(100, f, 5.0, 6.0, 5.5);
        Assert.assertEquals(5.0, result, 0.0);

        result = solver.solve(100, f, 4.0, 5.0, 4.5);
        Assert.assertEquals(5.0, result, 0.0);
    }

    @Test
    public void testBadEndpoints() {
        UnivariateFunction f = new Sin();
        UnivariateSolver solver = getSolver();
        try {  // bad interval
            solver.solve(100, f, 1, -1);
            Assert.fail("Expecting NumberIsTooLargeException - bad interval");
        } catch (NumberIsTooLargeException ex) {
            // expected
        }
        try {  // no bracket
            solver.solve(100, f, 1, 1.5);
            Assert.fail("Expecting NoBracketingException - non-bracketing");
        } catch (NoBracketingException ex) {
            // expected
        }
        try {  // no bracket
            solver.solve(100, f, 1, 1.5, 1.2);
            Assert.fail("Expecting NoBracketingException - non-bracketing");
        } catch (NoBracketingException ex) {
            // expected
        }
    }

    @Test
    public void testSolutionLeftSide() {
        UnivariateFunction f = new Sin();
        UnivariateSolver solver = getSolver();
        double left = -1.5;
        double right = 0.05;
        for(int i = 0; i < 10; i++) {
            // Test whether the allowed solutions are taken into account.
            double solution = getSolution(solver, 100, f, left, right, AllowedSolution.LEFT_SIDE);
            if (!Double.isNaN(solution)) {
                Assert.assertTrue(solution <= 0.0);
            }

            // Prepare for next test.
            left -= 0.1;
            right += 0.3;
        }
    }

    @Test
    public void testSolutionRightSide() {
        UnivariateFunction f = new Sin();
        UnivariateSolver solver = getSolver();
        double left = -1.5;
        double right = 0.05;
        for(int i = 0; i < 10; i++) {
            // Test whether the allowed solutions are taken into account.
            double solution = getSolution(solver, 100, f, left, right, AllowedSolution.RIGHT_SIDE);
            if (!Double.isNaN(solution)) {
                Assert.assertTrue(solution >= 0.0);
            }

            // Prepare for next test.
            left -= 0.1;
            right += 0.3;
        }
    }
    @Test
    public void testSolutionBelowSide() {
        UnivariateFunction f = new Sin();
        UnivariateSolver solver = getSolver();
        double left = -1.5;
        double right = 0.05;
        for(int i = 0; i < 10; i++) {
            // Test whether the allowed solutions are taken into account.
            double solution = getSolution(solver, 100, f, left, right, AllowedSolution.BELOW_SIDE);
            if (!Double.isNaN(solution)) {
                Assert.assertTrue(f.value(solution) <= 0.0);
            }

            // Prepare for next test.
            left -= 0.1;
            right += 0.3;
        }
    }

    @Test
    public void testSolutionAboveSide() {
        UnivariateFunction f = new Sin();
        UnivariateSolver solver = getSolver();
        double left = -1.5;
        double right = 0.05;
        for(int i = 0; i < 10; i++) {
            // Test whether the allowed solutions are taken into account.
            double solution = getSolution(solver, 100, f, left, right, AllowedSolution.ABOVE_SIDE);
            if (!Double.isNaN(solution)) {
                Assert.assertTrue(f.value(solution) >= 0.0);
            }

            // Prepare for next test.
            left -= 0.1;
            right += 0.3;
        }
    }

    private double getSolution(UnivariateSolver solver, int maxEval, UnivariateFunction f,
                               double left, double right, AllowedSolution allowedSolution) {
        try {
            @SuppressWarnings("unchecked")
            BracketedUnivariateSolver<UnivariateFunction> bracketing =
            (BracketedUnivariateSolver<UnivariateFunction>) solver;
            return bracketing.solve(100, f, left, right, allowedSolution);
        } catch (ClassCastException cce) {
            double baseRoot = solver.solve(maxEval, f, left, right);
            if ((baseRoot <= left) || (baseRoot >= right)) {
                // the solution slipped out of interval
                return Double.NaN;
            }
            PegasusSolver bracketing =
                    new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy(),
                                      solver.getFunctionValueAccuracy());
            return UnivariateSolverUtils.forceSide(maxEval - solver.getEvaluations(),
                                                       f, bracketing, baseRoot, left, right,
                                                       allowedSolution);
        }
    }

}

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