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/* * Copyright 2004 The Apache Software Foundation. * * Licensed 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.math.analysis; import org.apache.commons.math.ConvergenceException; import org.apache.commons.math.FunctionEvaluationException; /** * Implements <a href="http://mathworld.wolfram.com/NewtonsMethod.html"> * Newton's Method</a> for finding zeros of real univariate functions. * <p> * The function should be continuous but not necessarily smooth. * * @version $Revision: 1.6 $ $Date: 2004/07/17 21:19:39 $ */ public class NewtonSolver extends UnivariateRealSolverImpl { /** Serializable version identifier */ static final long serialVersionUID = 2606474895443431607L; /** The first derivative of the target function. */ private UnivariateRealFunction derivative; /** * Construct a solver for the given function. * @param f function to solve. */ public NewtonSolver(DifferentiableUnivariateRealFunction f) { super(f, 100, 1E-6); derivative = f.derivative(); } /** * Find a zero near the midpoint of <code>min</code> and <code>max</code>. * * @param min the lower bound for the interval * @param max the upper bound for the interval * @return the value where the function is zero * @throws ConvergenceException if the maximum iteration count is exceeded * @throws FunctionEvaluationException if an error occurs evaluating the * function or derivative * @throws IllegalArgumentException if min is not less than max */ public double solve(double min, double max) throws ConvergenceException, FunctionEvaluationException { return solve(min, max, UnivariateRealSolverUtils.midpoint(min, max)); } /** * Find a zero near the value <code>startValue</code>. * * @param min the lower bound for the interval (ignored). * @param max the upper bound for the interval (ignored). * @param startValue the start value to use. * @return the value where the function is zero * @throws ConvergenceException if the maximum iteration count is exceeded * @throws FunctionEvaluationException if an error occurs evaluating the * function or derivative * @throws IllegalArgumentException if startValue is not between min and max */ public double solve(double min, double max, double startValue) throws ConvergenceException, FunctionEvaluationException { clearResult(); verifySequence(min, startValue, max); double x0 = startValue; double x1; int i = 0; while (i < maximalIterationCount) { x1 = x0 - (f.value(x0) / derivative.value(x0)); if (Math.abs(x1 - x0) <= absoluteAccuracy) { setResult(x1, i); return x1; } x0 = x1; ++i; } throw new ConvergenceException("Maximum number of iterations exceeded " + i); } }