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The Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
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/*
* 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
* -
lowerBound <= a < initial < b <= upperBound
* -
f(a) * f(b) < 0
*
* If f is continuous on [a,b], this means that a
* and b bracket a root of f.
*
* The algorithm starts by setting
* a := initial -1; b := initial +1, examines the value of the
* function at a and b and keeps moving
* the endpoints out by one unit each time through a loop that terminates
* when one of the following happens:
* -
f(a) * f(b) < 0 -- success!
* -
a = lower and b = upper
* -- ConvergenceException
* -
Integer.MAX_VALUE iterations elapse
* -- ConvergenceException
*
*
* Note: this method can take
* Integer.MAX_VALUE iterations to throw a
* ConvergenceException. Unless you are confident that there
* is a root between lowerBound and upperBound
* near initial, 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
* -
lowerBound <= a < initial < b <= upperBound
* -
f(a) * f(b) <= 0
*
* If f is continuous on [a,b], this means that a
* and b bracket a root of f.
*
* The algorithm starts by setting
* a := initial -1; b := initial +1, examines the value of the
* function at a and b and keeps moving
* the endpoints out by one unit each time through a loop that terminates
* when one of the following happens:
* -
f(a) * f(b) <= 0 -- success!
* -
a = lower and b = upper
* -- ConvergenceException
* -
maximumIterations iterations elapse
* -- ConvergenceException
*
* @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.
* We use here the Initialization On Demand Holder Idiom.
*/
private static class LazyHolder {
/** Cached solver factory */
private static final UnivariateRealSolverFactory FACTORY = UnivariateRealSolverFactory.newInstance();
}
// CHECKSTYLE: resume HideUtilityClassConstructor
}