| /* |
| * 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.analysis.solvers; |
| |
| import org.apache.commons.math.ConvergenceException; |
| import org.apache.commons.math.FunctionEvaluationException; |
| import org.apache.commons.math.MathRuntimeException; |
| import org.apache.commons.math.analysis.UnivariateRealFunction; |
| import org.apache.commons.math.exception.util.LocalizedFormats; |
| import org.apache.commons.math.exception.NullArgumentException; |
| import org.apache.commons.math.util.FastMath; |
| |
| /** |
| * Utility routines for {@link UnivariateRealSolver} objects. |
| * |
| * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $ |
| */ |
| public class UnivariateRealSolverUtils { |
| |
| /** |
| * Default constructor. |
| */ |
| private UnivariateRealSolverUtils() { |
| super(); |
| } |
| |
| /** |
| * Convenience method to find a zero of a univariate real function. A default |
| * solver is used. |
| * |
| * @param f the function. |
| * @param x0 the lower bound for the interval. |
| * @param x1 the upper bound for the interval. |
| * @return a value where the function is zero. |
| * @throws ConvergenceException if the iteration count was exceeded |
| * @throws FunctionEvaluationException if an error occurs evaluating the function |
| * @throws IllegalArgumentException if f is null or the endpoints do not |
| * specify a valid interval |
| */ |
| public static double solve(UnivariateRealFunction f, double x0, double x1) |
| throws ConvergenceException, FunctionEvaluationException { |
| setup(f); |
| return LazyHolder.FACTORY.newDefaultSolver().solve(f, x0, x1); |
| } |
| |
| /** |
| * Convenience method to find a zero of a univariate real function. A default |
| * solver is used. |
| * |
| * @param f the function |
| * @param x0 the lower bound for the interval |
| * @param x1 the upper bound for the interval |
| * @param absoluteAccuracy the accuracy to be used by the solver |
| * @return a value where the function is zero |
| * @throws ConvergenceException if the iteration count is exceeded |
| * @throws FunctionEvaluationException if an error occurs evaluating the function |
| * @throws IllegalArgumentException if f is null, the endpoints do not |
| * specify a valid interval, or the absoluteAccuracy is not valid for the |
| * default solver |
| */ |
| public static double solve(UnivariateRealFunction f, double x0, double x1, |
| double absoluteAccuracy) throws ConvergenceException, |
| FunctionEvaluationException { |
| |
| setup(f); |
| UnivariateRealSolver solver = LazyHolder.FACTORY.newDefaultSolver(); |
| solver.setAbsoluteAccuracy(absoluteAccuracy); |
| return solver.solve(f, x0, x1); |
| } |
| |
| /** |
| * This method attempts to find two values a and b satisfying <ul> |
| * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li> |
| * <li> <code> f(a) * f(b) < 0 </code></li> |
| * </ul> |
| * If f is continuous on <code>[a,b],</code> this means that <code>a</code> |
| * and <code>b</code> bracket a root of f. |
| * <p> |
| * The algorithm starts by setting |
| * <code>a := initial -1; b := initial +1,</code> examines the value of the |
| * function at <code>a</code> and <code>b</code> and keeps moving |
| * the endpoints out by one unit each time through a loop that terminates |
| * when one of the following happens: <ul> |
| * <li> <code> f(a) * f(b) < 0 </code> -- success!</li> |
| * <li> <code> a = lower </code> and <code> b = upper</code> |
| * -- ConvergenceException </li> |
| * <li> <code> Integer.MAX_VALUE</code> iterations elapse |
| * -- ConvergenceException </li> |
| * </ul></p> |
| * <p> |
| * <strong>Note: </strong> this method can take |
| * <code>Integer.MAX_VALUE</code> iterations to throw a |
| * <code>ConvergenceException.</code> Unless you are confident that there |
| * is a root between <code>lowerBound</code> and <code>upperBound</code> |
| * near <code>initial,</code> it is better to use |
| * {@link #bracket(UnivariateRealFunction, double, double, double, int)}, |
| * explicitly specifying the maximum number of iterations.</p> |
| * |
| * @param function the function |
| * @param initial initial midpoint of interval being expanded to |
| * bracket a root |
| * @param lowerBound lower bound (a is never lower than this value) |
| * @param upperBound upper bound (b never is greater than this |
| * value) |
| * @return a two element array holding {a, b} |
| * @throws ConvergenceException if a root can not be bracketted |
| * @throws FunctionEvaluationException if an error occurs evaluating the function |
| * @throws IllegalArgumentException if function is null, maximumIterations |
| * is not positive, or initial is not between lowerBound and upperBound |
| */ |
| public static double[] bracket(UnivariateRealFunction function, |
| double initial, double lowerBound, double upperBound) |
| throws ConvergenceException, FunctionEvaluationException { |
| return bracket( function, initial, lowerBound, upperBound, |
| Integer.MAX_VALUE ) ; |
| } |
| |
| /** |
| * This method attempts to find two values a and b satisfying <ul> |
| * <li> <code> lowerBound <= a < initial < b <= upperBound</code> </li> |
| * <li> <code> f(a) * f(b) <= 0 </code> </li> |
| * </ul> |
| * If f is continuous on <code>[a,b],</code> this means that <code>a</code> |
| * and <code>b</code> bracket a root of f. |
| * <p> |
| * The algorithm starts by setting |
| * <code>a := initial -1; b := initial +1,</code> examines the value of the |
| * function at <code>a</code> and <code>b</code> and keeps moving |
| * the endpoints out by one unit each time through a loop that terminates |
| * when one of the following happens: <ul> |
| * <li> <code> f(a) * f(b) <= 0 </code> -- success!</li> |
| * <li> <code> a = lower </code> and <code> b = upper</code> |
| * -- ConvergenceException </li> |
| * <li> <code> maximumIterations</code> iterations elapse |
| * -- ConvergenceException </li></ul></p> |
| * |
| * @param function the function |
| * @param initial initial midpoint of interval being expanded to |
| * bracket a root |
| * @param lowerBound lower bound (a is never lower than this value) |
| * @param upperBound upper bound (b never is greater than this |
| * value) |
| * @param maximumIterations maximum number of iterations to perform |
| * @return a two element array holding {a, b}. |
| * @throws ConvergenceException if the algorithm fails to find a and b |
| * satisfying the desired conditions |
| * @throws FunctionEvaluationException if an error occurs evaluating the function |
| * @throws IllegalArgumentException if function is null, maximumIterations |
| * is not positive, or initial is not between lowerBound and upperBound |
| */ |
| public static double[] bracket(UnivariateRealFunction function, |
| double initial, double lowerBound, double upperBound, |
| int maximumIterations) throws ConvergenceException, |
| FunctionEvaluationException { |
| |
| if (function == null) { |
| throw new NullArgumentException(LocalizedFormats.FUNCTION); |
| } |
| if (maximumIterations <= 0) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.INVALID_MAX_ITERATIONS, maximumIterations); |
| } |
| if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) { |
| throw MathRuntimeException.createIllegalArgumentException( |
| LocalizedFormats.INVALID_BRACKETING_PARAMETERS, |
| lowerBound, initial, upperBound); |
| } |
| double a = initial; |
| double b = initial; |
| double fa; |
| double fb; |
| int numIterations = 0 ; |
| |
| do { |
| a = FastMath.max(a - 1.0, lowerBound); |
| b = FastMath.min(b + 1.0, upperBound); |
| fa = function.value(a); |
| |
| fb = function.value(b); |
| numIterations++ ; |
| } while ((fa * fb > 0.0) && (numIterations < maximumIterations) && |
| ((a > lowerBound) || (b < upperBound))); |
| |
| if (fa * fb > 0.0 ) { |
| throw new ConvergenceException( |
| LocalizedFormats.FAILED_BRACKETING, |
| numIterations, maximumIterations, initial, |
| lowerBound, upperBound, a, b, fa, fb); |
| } |
| |
| return new double[]{a, b}; |
| } |
| |
| /** |
| * Compute the midpoint of two values. |
| * |
| * @param a first value. |
| * @param b second value. |
| * @return the midpoint. |
| */ |
| public static double midpoint(double a, double b) { |
| return (a + b) * .5; |
| } |
| |
| /** |
| * Checks to see if f is null, throwing IllegalArgumentException if so. |
| * @param f input function |
| * @throws IllegalArgumentException if f is null |
| */ |
| private static void setup(UnivariateRealFunction f) { |
| if (f == null) { |
| throw new NullArgumentException(LocalizedFormats.FUNCTION); |
| } |
| } |
| |
| // CHECKSTYLE: stop HideUtilityClassConstructor |
| /** Holder for the factory. |
| * <p>We use here the Initialization On Demand Holder Idiom.</p> |
| */ |
| private static class LazyHolder { |
| /** Cached solver factory */ |
| private static final UnivariateRealSolverFactory FACTORY = UnivariateRealSolverFactory.newInstance(); |
| } |
| // CHECKSTYLE: resume HideUtilityClassConstructor |
| |
| } |
