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Java example source code file (BracketingNthOrderBrentSolverTest.java)

This example Java source code file (BracketingNthOrderBrentSolverTest.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, bracketingnthorderbrentsolver, bracketingnthorderbrentsolvertest, derivativestructure, newtonraphsonsolver, override, quinticfunction, test, testfunction, toomanyevaluationsexception, univariatedifferentiablefunction, univariatefunction, univariatesolver

The BracketingNthOrderBrentSolverTest.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.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
import org.apache.commons.math3.exception.NumberIsTooSmallException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.junit.Assert;
import org.junit.Test;

/**
 * Test case for {@link BracketingNthOrderBrentSolver bracketing n<sup>th order Brent} solver.
 *
 */
public final class BracketingNthOrderBrentSolverTest extends BaseSecantSolverAbstractTest {
    /** {@inheritDoc} */
    @Override
    protected UnivariateSolver getSolver() {
        return new BracketingNthOrderBrentSolver();
    }

    /** {@inheritDoc} */
    @Override
    protected int[] getQuinticEvalCounts() {
        return new int[] {1, 3, 8, 1, 9, 4, 8, 1, 12, 1, 16};
    }

    @Test(expected=NumberIsTooSmallException.class)
    public void testInsufficientOrder1() {
        new BracketingNthOrderBrentSolver(1.0e-10, 1);
    }

    @Test(expected=NumberIsTooSmallException.class)
    public void testInsufficientOrder2() {
        new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 1);
    }

    @Test(expected=NumberIsTooSmallException.class)
    public void testInsufficientOrder3() {
        new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 1.0e-10, 1);
    }

    @Test
    public void testConstructorsOK() {
        Assert.assertEquals(2, new BracketingNthOrderBrentSolver(1.0e-10, 2).getMaximalOrder());
        Assert.assertEquals(2, new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 2).getMaximalOrder());
        Assert.assertEquals(2, new BracketingNthOrderBrentSolver(1.0e-10, 1.0e-10, 1.0e-10, 2).getMaximalOrder());
    }

    @Test
    public void testConvergenceOnFunctionAccuracy() {
        BracketingNthOrderBrentSolver solver =
                new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-10, 0.001, 3);
        QuinticFunction f = new QuinticFunction();
        double result = solver.solve(20, f, 0.2, 0.9, 0.4, AllowedSolution.BELOW_SIDE);
        Assert.assertEquals(0, f.value(result), solver.getFunctionValueAccuracy());
        Assert.assertTrue(f.value(result) <= 0);
        Assert.assertTrue(result - 0.5 > solver.getAbsoluteAccuracy());
        result = solver.solve(20, f, -0.9, -0.2,  -0.4, AllowedSolution.ABOVE_SIDE);
        Assert.assertEquals(0, f.value(result), solver.getFunctionValueAccuracy());
        Assert.assertTrue(f.value(result) >= 0);
        Assert.assertTrue(result + 0.5 < -solver.getAbsoluteAccuracy());
    }

    @Test
    public void testIssue716() {
        BracketingNthOrderBrentSolver solver =
                new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-10, 1.0e-22, 5);
        UnivariateFunction sharpTurn = new UnivariateFunction() {
            public double value(double x) {
                return (2 * x + 1) / (1.0e9 * (x + 1));
            }
        };
        double result = solver.solve(100, sharpTurn, -0.9999999, 30, 15, AllowedSolution.RIGHT_SIDE);
        Assert.assertEquals(0, sharpTurn.value(result), solver.getFunctionValueAccuracy());
        Assert.assertTrue(sharpTurn.value(result) >= 0);
        Assert.assertEquals(-0.5, result, 1.0e-10);
    }

    @Test
    public void testFasterThanNewton() {
        // the following test functions come from Beny Neta's paper:
        // "Several New Methods for solving Equations"
        // intern J. Computer Math Vol 23 pp 265-282
        // available here: http://www.math.nps.navy.mil/~bneta/SeveralNewMethods.PDF
        // the reference roots have been computed by the Dfp solver to more than
        // 80 digits and checked with emacs (only the first 20 digits are reproduced here)
        compare(new TestFunction(0.0, -2, 2) {
            @Override
            public DerivativeStructure value(DerivativeStructure x) {
                return x.sin().subtract(x.multiply(0.5));
            }
        });
        compare(new TestFunction(6.3087771299726890947, -5, 10) {
            @Override
            public DerivativeStructure value(DerivativeStructure x) {
                return x.pow(5).add(x).subtract(10000);
            }
        });
        compare(new TestFunction(9.6335955628326951924, 0.001, 10) {
            @Override
            public DerivativeStructure value(DerivativeStructure x) {
                return x.sqrt().subtract(x.reciprocal()).subtract(3);
            }
        });
        compare(new TestFunction(2.8424389537844470678, -5, 5) {
            @Override
            public DerivativeStructure value(DerivativeStructure x) {
                return x.exp().add(x).subtract(20);
            }
        });
        compare(new TestFunction(8.3094326942315717953, 0.001, 10) {
            @Override
            public DerivativeStructure value(DerivativeStructure x) {
                return x.log().add(x.sqrt()).subtract(5);
            }
        });
        compare(new TestFunction(1.4655712318767680266, -0.5, 1.5) {
            @Override
            public DerivativeStructure value(DerivativeStructure x) {
                return x.subtract(1).multiply(x).multiply(x).subtract(1);
            }
        });

    }

    private void compare(TestFunction f) {
        compare(f, f.getRoot(), f.getMin(), f.getMax());
    }

    private void compare(final UnivariateDifferentiableFunction f,
                         double root, double min, double max) {
        NewtonRaphsonSolver newton = new NewtonRaphsonSolver(1.0e-12);
        BracketingNthOrderBrentSolver bracketing =
                new BracketingNthOrderBrentSolver(1.0e-12, 1.0e-12, 1.0e-18, 5);
        double resultN;
        try {
            resultN = newton.solve(100, f, min, max);
        } catch (TooManyEvaluationsException tmee) {
            resultN = Double.NaN;
        }
        double resultB;
        try {
            resultB = bracketing.solve(100, f, min, max);
        } catch (TooManyEvaluationsException tmee) {
            resultB = Double.NaN;
        }
        Assert.assertEquals(root, resultN, newton.getAbsoluteAccuracy());
        Assert.assertEquals(root, resultB, bracketing.getAbsoluteAccuracy());

        // bracketing solver evaluates only function value, we set the weight to 1
        final int weightedBracketingEvaluations = bracketing.getEvaluations();

        // Newton-Raphson solver evaluates both function value and derivative, we set the weight to 2
        final int weightedNewtonEvaluations = 2 * newton.getEvaluations();

        Assert.assertTrue(weightedBracketingEvaluations < weightedNewtonEvaluations);

    }

    private static abstract class TestFunction implements UnivariateDifferentiableFunction {

        private final double root;
        private final double min;
        private final double max;

        protected TestFunction(final double root, final double min, final double max) {
            this.root = root;
            this.min  = min;
            this.max  = max;
        }

        public double getRoot() {
            return root;
        }

        public double getMin() {
            return min;
        }

        public double getMax() {
            return max;
        }

        public double value(final double x) {
            return value(new DerivativeStructure(0, 0, x)).getValue();
        }

        public abstract DerivativeStructure value(final DerivativeStructure t);

    }

}

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