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Commons Math example source code file (BrentOptimizer.java)
The Commons Math BrentOptimizer.java 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.math.optimization.univariate; import org.apache.commons.math.FunctionEvaluationException; import org.apache.commons.math.MaxIterationsExceededException; import org.apache.commons.math.analysis.UnivariateRealFunction; import org.apache.commons.math.optimization.GoalType; /** * Implements Richard Brent's algorithm (from his book "Algorithms for * Minimization without Derivatives", p. 79) for finding minima of real * univariate functions. * * @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $ * @since 2.0 */ public class BrentOptimizer extends AbstractUnivariateRealOptimizer { /** * Golden section. */ private static final double GOLDEN_SECTION = 0.5 * (3 - Math.sqrt(5)); /** * Construct a solver. */ public BrentOptimizer() { super(100, 1E-10); } /** {@inheritDoc} */ public double optimize(final UnivariateRealFunction f, final GoalType goalType, final double min, final double max, final double startValue) throws MaxIterationsExceededException, FunctionEvaluationException { return optimize(f, goalType, min, max); } /** {@inheritDoc} */ public double optimize(final UnivariateRealFunction f, final GoalType goalType, final double min, final double max) throws MaxIterationsExceededException, FunctionEvaluationException { clearResult(); return localMin(f, goalType, min, max, relativeAccuracy, absoluteAccuracy); } /** * Find the minimum of the function {@code f} within the interval {@code (a, b)}. * * If the function {@code f} is defined on the interval {@code (a, b)}, then * this method finds an approximation {@code x} to the point at which {@code f} * attains its minimum.<br/> * {@code t} and {@code eps} define a tolerance {@code tol = eps |x| + t} and * {@code f} is never evaluated at two points closer together than {@code tol}. * {@code eps} should be no smaller than <em>2 macheps and preferable not * much less than <em>sqrt(macheps), where macheps is the relative * machine precision. {@code t} should be positive. * @param f the function to solve * @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE} * or {@link GoalType#MINIMIZE} * @param a Lower bound of the interval * @param b Higher bound of the interval * @param eps Relative accuracy * @param t Absolute accuracy * @return the point at which the function is minimal. * @throws MaxIterationsExceededException if the maximum iteration count * is exceeded. * @throws FunctionEvaluationException if an error occurs evaluating * the function. */ private double localMin(final UnivariateRealFunction f, final GoalType goalType, double a, double b, final double eps, final double t) throws MaxIterationsExceededException, FunctionEvaluationException { double x = a + GOLDEN_SECTION * (b - a); double v = x; double w = x; double e = 0; double fx = computeObjectiveValue(f, x); if (goalType == GoalType.MAXIMIZE) { fx = -fx; } double fv = fx; double fw = fx; int count = 0; while (count < maximalIterationCount) { double m = 0.5 * (a + b); double tol = eps * Math.abs(x) + t; double t2 = 2 * tol; // Check stopping criterion. if (Math.abs(x - m) > t2 - 0.5 * (b - a)) { double p = 0; double q = 0; double r = 0; double d = 0; double u = 0; if (Math.abs(e) > tol) { // Fit parabola. r = (x - w) * (fx - fv); q = (x - v) * (fx - fw); p = (x - v) * q - (x - w) * r; q = 2 * (q - r); if (q > 0) { p = -p; } else { q = -q; } r = e; e = d; } if (Math.abs(p) < Math.abs(0.5 * q * r) && (p < q * (a - x)) && (p < q * (b - x))) { // Parabolic interpolation step. d = p / q; u = x + d; // f must not be evaluated too close to a or b. if (((u - a) < t2) || ((b - u) < t2)) { d = (x < m) ? tol : -tol; } } else { // Golden section step. e = ((x < m) ? b : a) - x; d = GOLDEN_SECTION * e; } // f must not be evaluated too close to a or b. u = x + ((Math.abs(d) > tol) ? d : ((d > 0) ? tol : -tol)); double fu = computeObjectiveValue(f, u); if (goalType == GoalType.MAXIMIZE) { fu = -fu; } // Update a, b, v, w and x. if (fu <= fx) { if (u < x) { b = x; } else { a = x; } v = w; fv = fw; w = x; fw = fx; x = u; fx = fu; } else { if (u < x) { a = u; } else { b = u; } if ((fu <= fw) || (w == x)) { v = w; fv = fw; w = u; fw = fu; } else if ((fu <= fv) || (v == x) || (v == w)) { v = u; fv = fu; } } } else { // termination setResult(x, (goalType == GoalType.MAXIMIZE) ? -fx : fx, count); return x; } ++count; } throw new MaxIterationsExceededException(maximalIterationCount); } } Other Commons Math examples (source code examples)Here is a short list of links related to this Commons Math BrentOptimizer.java source code file: |
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