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

/*
 * 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 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 $Revision$ $Date$
 */
public class NewtonSolver extends UnivariateRealSolverImpl {
    
    /** Serializable version identifier */
    static final long serialVersionUID = 2606474895443431607L;
    
    /** The first derivative of the target function. */
    private 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);
    }

}