src/java/org/apache/commons/math/analysis/UnivariateRealSolverUtils.java

/*
 * Copyright 2003-2004 The Apache Software Foundation.
 *
 * Licensed 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;

import org.apache.commons.math.FunctionEvaluationException;
import org.apache.commons.math.ConvergenceException;

/**
 * Utility routines for {@link UnivariateRealSolver} objects.
 * 
 * @version $Revision$ $Date$
 */
public class UnivariateRealSolverUtils {
    /**
     * Default constructor.
     */
    private UnivariateRealSolverUtils() {
        super();
    }
    
    /** Cached solver factory */
    private static UnivariateRealSolverFactory factory = null;

    /**
     * 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 factory.newDefaultSolver(f).solve(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 = factory.newDefaultSolver(f);
        solver.setAbsoluteAccuracy(absoluteAccuracy);
        return solver.solve(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>
     * <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.
     *
     * @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>
     * 
     * @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 IllegalArgumentException ("function is null.");
        }
        if (maximumIterations <= 0)  {
            throw new IllegalArgumentException
            ("bad value for maximumIterations: " + maximumIterations);
        }
        if (initial < lowerBound || initial > upperBound || lowerBound >= upperBound) {
            throw new IllegalArgumentException
            ("Invalid endpoint parameters:  lowerBound=" + lowerBound + 
              " initial=" + initial + " upperBound=" + upperBound);
        }
        double a = initial;
        double b = initial;
        double fa;
        double fb;
        int numIterations = 0 ;
    
        do {
            a = Math.max(a - 1.0, lowerBound);
            b = Math.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
            ("Number of iterations= " + numIterations +
              " maximum iterations= "  + maximumIterations +
              " initial= " + initial + " lowerBound=" + lowerBound +
              " upperBound=" + upperBound + " final a value=" + a +
              " final b value=" + b + " f(a)=" + fa + " f(b)=" + 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.
     * Also initializes factory if factory is null.
     * 
     * @param f  input function
     * @throws IllegalArgumentException if f is null
     */
    private static void setup(UnivariateRealFunction f) {
       
        if (f == null) {
            throw new IllegalArgumentException("function can not be null.");    
        }
        
        if (factory == null) {
            factory = UnivariateRealSolverFactory.newInstance();
        }       
    }
}