/*
* 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: 155427 $ $Date: 2005-02-26 06:11:52 -0700 (Sat, 26 Feb 2005) $
*/
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();
}
}
}