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Java example source code file (BrentSolver.java)

This example Java source code file (BrentSolver.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractunivariatesolver, brentsolver, default_absolute_accuracy, nobracketingexception, numberistoolargeexception, override, toomanyevaluationsexception

The BrentSolver.java Java example source code

/*
 * 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.math3.analysis.solvers;


import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.NumberIsTooLargeException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.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> * The reference implementation is given in chapter 4 of * <blockquote> * <b>Algorithms for Minimization Without Derivatives, * <em>Richard P. Brent, * Dover, 2002 * </blockquote> * * @see BaseAbstractUnivariateSolver */ public class BrentSolver extends AbstractUnivariateSolver { /** Default absolute accuracy. */ private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6; /** * Construct a solver with default absolute accuracy (1e-6). */ public BrentSolver() { this(DEFAULT_ABSOLUTE_ACCURACY); } /** * Construct a solver. * * @param absoluteAccuracy Absolute accuracy. */ public BrentSolver(double absoluteAccuracy) { super(absoluteAccuracy); } /** * Construct a solver. * * @param relativeAccuracy Relative accuracy. * @param absoluteAccuracy Absolute accuracy. */ public BrentSolver(double relativeAccuracy, double absoluteAccuracy) { super(relativeAccuracy, absoluteAccuracy); } /** * Construct a solver. * * @param relativeAccuracy Relative accuracy. * @param absoluteAccuracy Absolute accuracy. * @param functionValueAccuracy Function value accuracy. * * @see BaseAbstractUnivariateSolver#BaseAbstractUnivariateSolver(double,double,double) */ public BrentSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy) { super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy); } /** * {@inheritDoc} */ @Override protected double doSolve() throws NoBracketingException, TooManyEvaluationsException, NumberIsTooLargeException { double min = getMin(); double max = getMax(); final double initial = getStartValue(); final double functionValueAccuracy = getFunctionValueAccuracy(); verifySequence(min, initial, max); // Return the initial guess if it is good enough. double yInitial = computeObjectiveValue(initial); if (FastMath.abs(yInitial) <= functionValueAccuracy) { return initial; } // Return the first endpoint if it is good enough. double yMin = computeObjectiveValue(min); if (FastMath.abs(yMin) <= functionValueAccuracy) { return min; } // Reduce interval if min and initial bracket the root. if (yInitial * yMin < 0) { return brent(min, initial, yMin, yInitial); } // Return the second endpoint if it is good enough. double yMax = computeObjectiveValue(max); if (FastMath.abs(yMax) <= functionValueAccuracy) { return max; } // Reduce interval if initial and max bracket the root. if (yInitial * yMax < 0) { return brent(initial, max, yInitial, yMax); } throw new NoBracketingException(min, max, yMin, 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, * <it>Richard P. Brent, * Dover 0-486-41998-3 * </blockquote> * * @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(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 = getAbsoluteAccuracy(); final double eps = getRelativeAccuracy(); while (true) { if (FastMath.abs(fc) < FastMath.abs(fb)) { a = b; b = c; c = a; fa = fb; fb = fc; fc = fa; } final double tol = 2 * eps * FastMath.abs(b) + t; final double m = 0.5 * (c - b); if (FastMath.abs(m) <= tol || Precision.equals(fb, 0)) { return b; } if (FastMath.abs(e) < tol || FastMath.abs(fa) <= FastMath.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 - FastMath.abs(tol * q) || p >= FastMath.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 (FastMath.abs(d) > tol) { b += d; } else if (m > 0) { b += tol; } else { b -= tol; } fb = computeObjectiveValue(b); if ((fb > 0 && fc > 0) || (fb <= 0 && fc <= 0)) { c = a; fc = fa; d = b - a; e = d; } } } }

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