| /* |
| * 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.numbers.rootfinder; |
| |
| import java.util.function.DoubleUnaryOperator; |
| import org.apache.commons.numbers.core.Precision; |
| |
| /** |
| * This class implements the <a href="http://mathworld.wolfram.com/BrentsMethod.html"> |
| * Brent algorithm</a> for finding zeros of real univariate functions. |
| * The function should be continuous but not necessarily smooth. |
| * The {@code solve} method returns a zero {@code x} of the function {@code f} |
| * in the given interval {@code [a, b]} to within a tolerance |
| * {@code 2 eps abs(x) + t} where {@code eps} is the relative accuracy and |
| * {@code t} is the absolute accuracy. |
| * <p>The given interval must bracket the root.</p> |
| * <p> |
| * The reference implementation is given in chapter 4 of |
| * <blockquote> |
| * <b>Algorithms for Minimization Without Derivatives</b>, |
| * <em>Richard P. Brent</em>, |
| * Dover, 2002 |
| * </blockquote> |
| */ |
| public class BrentSolver { |
| /** Relative accuracy. */ |
| private final double relativeAccuracy; |
| /** Absolute accuracy. */ |
| private final double absoluteAccuracy; |
| /** Function accuracy. */ |
| private final double functionValueAccuracy; |
| |
| /** |
| * Construct a solver. |
| * |
| * @param relativeAccuracy Relative accuracy. |
| * @param absoluteAccuracy Absolute accuracy. |
| * @param functionValueAccuracy Function value accuracy. |
| */ |
| public BrentSolver(double relativeAccuracy, |
| double absoluteAccuracy, |
| double functionValueAccuracy) { |
| this.relativeAccuracy = relativeAccuracy; |
| this.absoluteAccuracy = absoluteAccuracy; |
| this.functionValueAccuracy = functionValueAccuracy; |
| } |
| |
| /** |
| * Search the function's zero within the given interval. |
| * |
| * @param func Function to solve. |
| * @param min Lower bound. |
| * @param max Upper bound. |
| * @return the root. |
| * @throws IllegalArgumentException if {@code min > max}. |
| * @throws IllegalArgumentException if the given interval does |
| * not bracket the root. |
| */ |
| public double findRoot(DoubleUnaryOperator func, |
| double min, |
| double max) { |
| return findRoot(func, min, 0.5 * (min + max), max); |
| } |
| |
| /** |
| * Search the function's zero within the given interval, |
| * starting from the given estimate. |
| * |
| * @param func Function to solve. |
| * @param min Lower bound. |
| * @param initial Initial guess. |
| * @param max Upper bound. |
| * @return the root. |
| * @throws IllegalArgumentException if {@code min > max} or |
| * {@code initial} is not in the {@code [min, max]} interval. |
| * @throws IllegalArgumentException if the given interval does |
| * not bracket the root. |
| */ |
| public double findRoot(DoubleUnaryOperator func, |
| double min, |
| double initial, |
| double max) { |
| if (min > max) { |
| throw new SolverException(SolverException.TOO_LARGE, min, max); |
| } |
| if (initial < min || |
| initial > max) { |
| throw new SolverException(SolverException.OUT_OF_RANGE, initial, min, max); |
| } |
| |
| // Return the initial guess if it is good enough. |
| final double yInitial = func.applyAsDouble(initial); |
| if (Math.abs(yInitial) <= functionValueAccuracy) { |
| return initial; |
| } |
| |
| // Return the first endpoint if it is good enough. |
| final double yMin = func.applyAsDouble(min); |
| if (Math.abs(yMin) <= functionValueAccuracy) { |
| return min; |
| } |
| |
| // Reduce interval if min and initial bracket the root. |
| if (yInitial * yMin < 0) { |
| return brent(func, min, initial, yMin, yInitial); |
| } |
| |
| // Return the second endpoint if it is good enough. |
| final double yMax = func.applyAsDouble(max); |
| if (Math.abs(yMax) <= functionValueAccuracy) { |
| return max; |
| } |
| |
| // Reduce interval if initial and max bracket the root. |
| if (yInitial * yMax < 0) { |
| return brent(func, initial, max, yInitial, yMax); |
| } |
| |
| throw new SolverException(SolverException.BRACKETING, min, yMin, max, yMax); |
| } |
| |
| /** |
| * Search for a zero inside the provided interval. |
| * This implementation is based on the algorithm described at page 58 of |
| * the book |
| * <blockquote> |
| * <b>Algorithms for Minimization Without Derivatives</b>, |
| * <i>Richard P. Brent</i>, |
| * Dover 0-486-41998-3 |
| * </blockquote> |
| * |
| * @param func Function to solve. |
| * @param lo Lower bound of the search interval. |
| * @param hi Higher bound of the search interval. |
| * @param fLo Function value at the lower bound of the search interval. |
| * @param fHi Function value at the higher bound of the search interval. |
| * @return the value where the function is zero. |
| */ |
| private double brent(DoubleUnaryOperator func, |
| double lo, double hi, |
| double fLo, double fHi) { |
| double a = lo; |
| double fa = fLo; |
| double b = hi; |
| double fb = fHi; |
| double c = a; |
| double fc = fa; |
| double d = b - a; |
| double e = d; |
| |
| final double t = absoluteAccuracy; |
| final double eps = relativeAccuracy; |
| |
| while (true) { |
| if (Math.abs(fc) < Math.abs(fb)) { |
| a = b; |
| b = c; |
| c = a; |
| fa = fb; |
| fb = fc; |
| fc = fa; |
| } |
| |
| final double tol = 2 * eps * Math.abs(b) + t; |
| final double m = 0.5 * (c - b); |
| |
| if (Math.abs(m) <= tol || |
| Precision.equals(fb, 0)) { |
| return b; |
| } |
| if (Math.abs(e) < tol || |
| Math.abs(fa) <= Math.abs(fb)) { |
| // Force bisection. |
| d = m; |
| e = d; |
| } else { |
| double s = fb / fa; |
| double p; |
| double q; |
| // The equality test (a == c) is intentional, |
| // it is part of the original Brent's method and |
| // it should NOT be replaced by proximity test. |
| if (a == c) { |
| // Linear interpolation. |
| p = 2 * m * s; |
| q = 1 - s; |
| } else { |
| // Inverse quadratic interpolation. |
| q = fa / fc; |
| final double r = fb / fc; |
| p = s * (2 * m * q * (q - r) - (b - a) * (r - 1)); |
| q = (q - 1) * (r - 1) * (s - 1); |
| } |
| if (p > 0) { |
| q = -q; |
| } else { |
| p = -p; |
| } |
| s = e; |
| e = d; |
| if (p >= 1.5 * m * q - Math.abs(tol * q) || |
| p >= Math.abs(0.5 * s * q)) { |
| // Inverse quadratic interpolation gives a value |
| // in the wrong direction, or progress is slow. |
| // Fall back to bisection. |
| d = m; |
| e = d; |
| } else { |
| d = p / q; |
| } |
| } |
| a = b; |
| fa = fb; |
| |
| if (Math.abs(d) > tol) { |
| b += d; |
| } else if (m > 0) { |
| b += tol; |
| } else { |
| b -= tol; |
| } |
| fb = func.applyAsDouble(b); |
| if ((fb > 0 && fc > 0) || |
| (fb <= 0 && fc <= 0)) { |
| c = a; |
| fc = fa; |
| d = b - a; |
| e = d; |
| } |
| } |
| } |
| } |