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.math4.legacy.analysis.solvers; 019 020import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure; 021import org.apache.commons.math4.legacy.analysis.differentiation.UnivariateDifferentiableFunction; 022import org.apache.commons.math4.legacy.exception.TooManyEvaluationsException; 023import org.apache.commons.math4.core.jdkmath.JdkMath; 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 */ 032public class NewtonRaphsonSolver extends AbstractUnivariateDifferentiableSolver { 033 /** Default absolute accuracy. */ 034 private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6; 035 036 /** 037 * Construct a solver. 038 */ 039 public NewtonRaphsonSolver() { 040 this(DEFAULT_ABSOLUTE_ACCURACY); 041 } 042 /** 043 * Construct a solver. 044 * 045 * @param absoluteAccuracy Absolute accuracy. 046 */ 047 public NewtonRaphsonSolver(double absoluteAccuracy) { 048 super(absoluteAccuracy); 049 } 050 051 /** 052 * Find a zero near the midpoint of {@code min} and {@code max}. 053 * 054 * @param f Function to solve. 055 * @param min Lower bound for the interval. 056 * @param max Upper bound for the interval. 057 * @param maxEval Maximum number of evaluations. 058 * @return the value where the function is zero. 059 * @throws org.apache.commons.math4.legacy.exception.TooManyEvaluationsException 060 * if the maximum evaluation count is exceeded. 061 * @throws org.apache.commons.math4.legacy.exception.NumberIsTooLargeException 062 * if {@code min >= max}. 063 */ 064 @Override 065 public double solve(int maxEval, final UnivariateDifferentiableFunction f, 066 final double min, final double max) 067 throws TooManyEvaluationsException { 068 return super.solve(maxEval, f, UnivariateSolverUtils.midpoint(min, max)); 069 } 070 071 /** 072 * {@inheritDoc} 073 */ 074 @Override 075 protected double doSolve() 076 throws TooManyEvaluationsException { 077 final double startValue = getStartValue(); 078 final double absoluteAccuracy = getAbsoluteAccuracy(); 079 080 double x0 = startValue; 081 double x1; 082 while (true) { 083 final DerivativeStructure y0 = computeObjectiveValueAndDerivative(x0); 084 x1 = x0 - (y0.getValue() / y0.getPartialDerivative(1)); 085 if (JdkMath.abs(x1 - x0) <= absoluteAccuracy) { 086 return x1; 087 } 088 089 x0 = x1; 090 } 091 } 092}