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 */
017
018package org.apache.commons.math3.analysis.solvers;
019
020import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
021import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
022import org.apache.commons.math3.util.FastMath;
023import org.apache.commons.math3.exception.TooManyEvaluationsException;
024
025/**
026 * Implements <a href="http://mathworld.wolfram.com/NewtonsMethod.html">
027 * Newton's Method</a> for finding zeros of real univariate differentiable
028 * functions.
029 *
030 * @since 3.1
031 * @version $Id: NewtonRaphsonSolver.java 1383441 2012-09-11 14:56:39Z luc $
032 */
033public class NewtonRaphsonSolver extends AbstractUnivariateDifferentiableSolver {
034    /** Default absolute accuracy. */
035    private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
036
037    /**
038     * Construct a solver.
039     */
040    public NewtonRaphsonSolver() {
041        this(DEFAULT_ABSOLUTE_ACCURACY);
042    }
043    /**
044     * Construct a solver.
045     *
046     * @param absoluteAccuracy Absolute accuracy.
047     */
048    public NewtonRaphsonSolver(double absoluteAccuracy) {
049        super(absoluteAccuracy);
050    }
051
052    /**
053     * Find a zero near the midpoint of {@code min} and {@code max}.
054     *
055     * @param f Function to solve.
056     * @param min Lower bound for the interval.
057     * @param max Upper bound for the interval.
058     * @param maxEval Maximum number of evaluations.
059     * @return the value where the function is zero.
060     * @throws org.apache.commons.math3.exception.TooManyEvaluationsException
061     * if the maximum evaluation count is exceeded.
062     * @throws org.apache.commons.math3.exception.NumberIsTooLargeException
063     * if {@code min >= max}.
064     */
065    @Override
066    public double solve(int maxEval, final UnivariateDifferentiableFunction f,
067                        final double min, final double max)
068        throws TooManyEvaluationsException {
069        return super.solve(maxEval, f, UnivariateSolverUtils.midpoint(min, max));
070    }
071
072    /**
073     * {@inheritDoc}
074     */
075    @Override
076    protected double doSolve()
077        throws TooManyEvaluationsException {
078        final double startValue = getStartValue();
079        final double absoluteAccuracy = getAbsoluteAccuracy();
080
081        double x0 = startValue;
082        double x1;
083        while (true) {
084            final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0);
085            x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1));
086            if (FastMath.abs(x1 - x0) <= absoluteAccuracy) {
087                return x1;
088            }
089
090            x0 = x1;
091        }
092    }
093}