/*
* 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.FunctionEvaluationException;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.MaxIterationsExceededException;
import org.apache.commons.math.analysis.DifferentiableUnivariateRealFunction;
import org.apache.commons.math.analysis.UnivariateRealFunction;
/**
* 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.</p>
*
* @version $Revision: 811685 $ $Date: 2009-09-05 13:36:48 -0400 (Sat, 05 Sep 2009) $
*/
public class NewtonSolver extends UnivariateRealSolverImpl {
/**
* Construct a solver for the given function.
*
* @param f function to solve.
* @deprecated as of 2.0 the function to solve is passed as an argument
* to the {@link #solve(UnivariateRealFunction, double, double)} or
* {@link UnivariateRealSolverImpl#solve(UnivariateRealFunction, double, double, double)}
* method.
*/
@Deprecated
public NewtonSolver(DifferentiableUnivariateRealFunction f) {
super(f, 100, 1E-6);
}
/**
* Construct a solver.
*/
public NewtonSolver() {
super(100, 1E-6);
}
/**
* {@inheritDoc}
*/
@Override
@Deprecated
public double solve(final double min, final double max)
throws MaxIterationsExceededException,
FunctionEvaluationException {
return solve(f, min, max);
}
/**
* {@inheritDoc}
*/
@Override
@Deprecated
public double solve(final double min, final double max, final double startValue)
throws MaxIterationsExceededException, FunctionEvaluationException {
return solve(f, min, max, startValue);
}
/**
* Find a zero near the midpoint of <code>min</code> and <code>max</code>.
*
* @param f the function to solve
* @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 MaxIterationsExceededException 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
*/
@Override
public double solve(final UnivariateRealFunction f,
final double min, final double max)
throws MaxIterationsExceededException, FunctionEvaluationException {
return solve(f, min, max, UnivariateRealSolverUtils.midpoint(min, max));
}
/**
* Find a zero near the value <code>startValue</code>.
*
* @param f the function to solve
* @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 MaxIterationsExceededException 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 or
* if function is not a {@link DifferentiableUnivariateRealFunction} instance
*/
@Override
public double solve(final UnivariateRealFunction f,
final double min, final double max, final double startValue)
throws MaxIterationsExceededException, FunctionEvaluationException {
try {
final UnivariateRealFunction derivative =
((DifferentiableUnivariateRealFunction) f).derivative();
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 MaxIterationsExceededException(maximalIterationCount);
} catch (ClassCastException cce) {
throw MathRuntimeException.createIllegalArgumentException("function is not differentiable");
}
}
}