001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math3.analysis.solvers;
018
019import org.apache.commons.math3.util.FastMath;
020import org.apache.commons.math3.exception.TooManyEvaluationsException;
021
022/**
023 * Implements the <a href="http://mathworld.wolfram.com/Bisection.html">
024 * bisection algorithm</a> for finding zeros of univariate real functions.
025 * <p>
026 * The function should be continuous but not necessarily smooth.</p>
027 *
028 * @version $Id: BisectionSolver.java 1391927 2012-09-30 00:03:30Z erans $
029 */
030public class BisectionSolver extends AbstractUnivariateSolver {
031    /** Default absolute accuracy. */
032    private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
033
034    /**
035     * Construct a solver with default accuracy (1e-6).
036     */
037    public BisectionSolver() {
038        this(DEFAULT_ABSOLUTE_ACCURACY);
039    }
040    /**
041     * Construct a solver.
042     *
043     * @param absoluteAccuracy Absolute accuracy.
044     */
045    public BisectionSolver(double absoluteAccuracy) {
046        super(absoluteAccuracy);
047    }
048    /**
049     * Construct a solver.
050     *
051     * @param relativeAccuracy Relative accuracy.
052     * @param absoluteAccuracy Absolute accuracy.
053     */
054    public BisectionSolver(double relativeAccuracy,
055                           double absoluteAccuracy) {
056        super(relativeAccuracy, absoluteAccuracy);
057    }
058
059    /**
060     * {@inheritDoc}
061     */
062    @Override
063    protected double doSolve()
064        throws TooManyEvaluationsException {
065        double min = getMin();
066        double max = getMax();
067        verifyInterval(min, max);
068        final double absoluteAccuracy = getAbsoluteAccuracy();
069        double m;
070        double fm;
071        double fmin;
072
073        while (true) {
074            m = UnivariateSolverUtils.midpoint(min, max);
075            fmin = computeObjectiveValue(min);
076            fm = computeObjectiveValue(m);
077
078            if (fm * fmin > 0) {
079                // max and m bracket the root.
080                min = m;
081            } else {
082                // min and m bracket the root.
083                max = m;
084            }
085
086            if (FastMath.abs(max - min) <= absoluteAccuracy) {
087                m = UnivariateSolverUtils.midpoint(min, max);
088                return m;
089            }
090        }
091    }
092}