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Java example source code file (BaseSecantSolver.java)

This example Java source code file (BaseSecantSolver.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

above_side, allowedsolution, any_side, basesecantsolver, below_side, convergenceexception, illinois, left_side, mathinternalerror, method, override, pegasus, right_side, univariatefunction

The BaseSecantSolver.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.util.FastMath;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.MathInternalError;

/**
 * Base class for all bracketing <em>Secant-based methods for root-finding
 * (approximating a zero of a univariate real function).
 *
 * <p>Implementation of the {@link RegulaFalsiSolver Regula Falsi} and
 * {@link IllinoisSolver <em>Illinois} methods is based on the
 * following article: M. Dowell and P. Jarratt,
 * <em>A modified regula falsi method for computing the root of an
 * equation</em>, BIT Numerical Mathematics, volume 11, number 2,
 * pages 168-174, Springer, 1971.</p>
 *
 * <p>Implementation of the {@link PegasusSolver Pegasus} method is
 * based on the following article: M. Dowell and P. Jarratt,
 * <em>The "Pegasus" method for computing the root of an equation,
 * BIT Numerical Mathematics, volume 12, number 4, pages 503-508, Springer,
 * 1972.</p>
 *
 * <p>The {@link SecantSolver Secant} method is not a
 * bracketing method, so it is not implemented here. It has a separate
 * implementation.</p>
 *
 * @since 3.0
 */
public abstract class BaseSecantSolver
    extends AbstractUnivariateSolver
    implements BracketedUnivariateSolver<UnivariateFunction> {

    /** Default absolute accuracy. */
    protected static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;

    /** The kinds of solutions that the algorithm may accept. */
    private AllowedSolution allowed;

    /** The <em>Secant-based root-finding method to use. */
    private final Method method;

    /**
     * Construct a solver.
     *
     * @param absoluteAccuracy Absolute accuracy.
     * @param method <em>Secant-based root-finding method to use.
     */
    protected BaseSecantSolver(final double absoluteAccuracy, final Method method) {
        super(absoluteAccuracy);
        this.allowed = AllowedSolution.ANY_SIDE;
        this.method = method;
    }

    /**
     * Construct a solver.
     *
     * @param relativeAccuracy Relative accuracy.
     * @param absoluteAccuracy Absolute accuracy.
     * @param method <em>Secant-based root-finding method to use.
     */
    protected BaseSecantSolver(final double relativeAccuracy,
                               final double absoluteAccuracy,
                               final Method method) {
        super(relativeAccuracy, absoluteAccuracy);
        this.allowed = AllowedSolution.ANY_SIDE;
        this.method = method;
    }

    /**
     * Construct a solver.
     *
     * @param relativeAccuracy Maximum relative error.
     * @param absoluteAccuracy Maximum absolute error.
     * @param functionValueAccuracy Maximum function value error.
     * @param method <em>Secant-based root-finding method to use
     */
    protected BaseSecantSolver(final double relativeAccuracy,
                               final double absoluteAccuracy,
                               final double functionValueAccuracy,
                               final Method method) {
        super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy);
        this.allowed = AllowedSolution.ANY_SIDE;
        this.method = method;
    }

    /** {@inheritDoc} */
    public double solve(final int maxEval, final UnivariateFunction f,
                        final double min, final double max,
                        final AllowedSolution allowedSolution) {
        return solve(maxEval, f, min, max, min + 0.5 * (max - min), allowedSolution);
    }

    /** {@inheritDoc} */
    public double solve(final int maxEval, final UnivariateFunction f,
                        final double min, final double max, final double startValue,
                        final AllowedSolution allowedSolution) {
        this.allowed = allowedSolution;
        return super.solve(maxEval, f, min, max, startValue);
    }

    /** {@inheritDoc} */
    @Override
    public double solve(final int maxEval, final UnivariateFunction f,
                        final double min, final double max, final double startValue) {
        return solve(maxEval, f, min, max, startValue, AllowedSolution.ANY_SIDE);
    }

    /**
     * {@inheritDoc}
     *
     * @throws ConvergenceException if the algorithm failed due to finite
     * precision.
     */
    @Override
    protected final double doSolve()
        throws ConvergenceException {
        // Get initial solution
        double x0 = getMin();
        double x1 = getMax();
        double f0 = computeObjectiveValue(x0);
        double f1 = computeObjectiveValue(x1);

        // If one of the bounds is the exact root, return it. Since these are
        // not under-approximations or over-approximations, we can return them
        // regardless of the allowed solutions.
        if (f0 == 0.0) {
            return x0;
        }
        if (f1 == 0.0) {
            return x1;
        }

        // Verify bracketing of initial solution.
        verifyBracketing(x0, x1);

        // Get accuracies.
        final double ftol = getFunctionValueAccuracy();
        final double atol = getAbsoluteAccuracy();
        final double rtol = getRelativeAccuracy();

        // Keep track of inverted intervals, meaning that the left bound is
        // larger than the right bound.
        boolean inverted = false;

        // Keep finding better approximations.
        while (true) {
            // Calculate the next approximation.
            final double x = x1 - ((f1 * (x1 - x0)) / (f1 - f0));
            final double fx = computeObjectiveValue(x);

            // If the new approximation is the exact root, return it. Since
            // this is not an under-approximation or an over-approximation,
            // we can return it regardless of the allowed solutions.
            if (fx == 0.0) {
                return x;
            }

            // Update the bounds with the new approximation.
            if (f1 * fx < 0) {
                // The value of x1 has switched to the other bound, thus inverting
                // the interval.
                x0 = x1;
                f0 = f1;
                inverted = !inverted;
            } else {
                switch (method) {
                case ILLINOIS:
                    f0 *= 0.5;
                    break;
                case PEGASUS:
                    f0 *= f1 / (f1 + fx);
                    break;
                case REGULA_FALSI:
                    // Detect early that algorithm is stuck, instead of waiting
                    // for the maximum number of iterations to be exceeded.
                    if (x == x1) {
                        throw new ConvergenceException();
                    }
                    break;
                default:
                    // Should never happen.
                    throw new MathInternalError();
                }
            }
            // Update from [x0, x1] to [x0, x].
            x1 = x;
            f1 = fx;

            // If the function value of the last approximation is too small,
            // given the function value accuracy, then we can't get closer to
            // the root than we already are.
            if (FastMath.abs(f1) <= ftol) {
                switch (allowed) {
                case ANY_SIDE:
                    return x1;
                case LEFT_SIDE:
                    if (inverted) {
                        return x1;
                    }
                    break;
                case RIGHT_SIDE:
                    if (!inverted) {
                        return x1;
                    }
                    break;
                case BELOW_SIDE:
                    if (f1 <= 0) {
                        return x1;
                    }
                    break;
                case ABOVE_SIDE:
                    if (f1 >= 0) {
                        return x1;
                    }
                    break;
                default:
                    throw new MathInternalError();
                }
            }

            // If the current interval is within the given accuracies, we
            // are satisfied with the current approximation.
            if (FastMath.abs(x1 - x0) < FastMath.max(rtol * FastMath.abs(x1),
                                                     atol)) {
                switch (allowed) {
                case ANY_SIDE:
                    return x1;
                case LEFT_SIDE:
                    return inverted ? x1 : x0;
                case RIGHT_SIDE:
                    return inverted ? x0 : x1;
                case BELOW_SIDE:
                    return (f1 <= 0) ? x1 : x0;
                case ABOVE_SIDE:
                    return (f1 >= 0) ? x1 : x0;
                default:
                    throw new MathInternalError();
                }
            }
        }
    }

    /** <em>Secant-based root-finding methods. */
    protected enum Method {

        /**
         * The {@link RegulaFalsiSolver <em>Regula Falsi} or
         * <em>False Position method.
         */
        REGULA_FALSI,

        /** The {@link IllinoisSolver <em>Illinois} method. */
        ILLINOIS,

        /** The {@link PegasusSolver <em>Pegasus} method. */
        PEGASUS;

    }
}

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