/*
* Copyright 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 java.io.IOException;
import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.FunctionEvaluationException;
/**
* Implements <a href="http://mathworld.wolfram.com/NewtonsMethod.html">
* Newton's Method</a> for finding zeros of real univariate functions.
* <p>
* The function should be continuous but not necessarily smooth.
*
* @version $Revision: 348791 $ $Date: 2005-11-24 12:50:36 -0700 (Thu, 24 Nov 2005) $
*/
public class NewtonSolver extends UnivariateRealSolverImpl {
/** Serializable version identifier */
private static final long serialVersionUID = 2606474895443431607L;
/** The first derivative of the target function. */
private transient UnivariateRealFunction derivative;
/**
* Construct a solver for the given function.
* @param f function to solve.
*/
public NewtonSolver(DifferentiableUnivariateRealFunction f) {
super(f, 100, 1E-6);
derivative = f.derivative();
}
/**
* Find a zero near the midpoint of <code>min</code> and <code>max</code>.
*
* @param min the lower bound for the interval
* @param max the upper bound for the interval
* @return the value where the function is zero
* @throws ConvergenceException if the maximum iteration count is exceeded
* @throws FunctionEvaluationException if an error occurs evaluating the
* function or derivative
* @throws IllegalArgumentException if min is not less than max
*/
public double solve(double min, double max) throws ConvergenceException,
FunctionEvaluationException {
return solve(min, max, UnivariateRealSolverUtils.midpoint(min, max));
}
/**
* Find a zero near the value <code>startValue</code>.
*
* @param min the lower bound for the interval (ignored).
* @param max the upper bound for the interval (ignored).
* @param startValue the start value to use.
* @return the value where the function is zero
* @throws ConvergenceException if the maximum iteration count is exceeded
* @throws FunctionEvaluationException if an error occurs evaluating the
* function or derivative
* @throws IllegalArgumentException if startValue is not between min and max
*/
public double solve(double min, double max, double startValue)
throws ConvergenceException, FunctionEvaluationException {
clearResult();
verifySequence(min, startValue, max);
double x0 = startValue;
double x1;
int i = 0;
while (i < maximalIterationCount) {
x1 = x0 - (f.value(x0) / derivative.value(x0));
if (Math.abs(x1 - x0) <= absoluteAccuracy) {
setResult(x1, i);
return x1;
}
x0 = x1;
++i;
}
throw new ConvergenceException
("Maximum number of iterations exceeded " + i);
}
/**
* Custom deserialization to initialize transient deriviate field.
*
* @param in serialized object input stream
* @throws IOException if IO error occurs
* @throws ClassNotFoundException if instantiation error occurs
*/
private void readObject(java.io.ObjectInputStream in)
throws IOException, ClassNotFoundException {
in.defaultReadObject();
derivative = ((DifferentiableUnivariateRealFunction) f).derivative();
}
}