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    1   /*
    2    * Copyright 2004 The Apache Software Foundation.
    3    *
    4    * Licensed under the Apache License, Version 2.0 (the "License");
    5    * you may not use this file except in compliance with the License.
    6    * You may obtain a copy of the License at
    7    *
    8    *      http://www.apache.org/licenses/LICENSE-2.0
    9    *
    10   * Unless required by applicable law or agreed to in writing, software
    11   * distributed under the License is distributed on an "AS IS" BASIS,
    12   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    13   * See the License for the specific language governing permissions and
    14   * limitations under the License.
    15   */
    16
    17  package org.apache.commons.math.analysis;
    18
    19  import org.apache.commons.math.ConvergenceException;
    20  import org.apache.commons.math.FunctionEvaluationException;
    21
    22  /***
    23   * Implements <a href="http://mathworld.wolfram.com/NewtonsMethod.html">
    24   * Newton's Method</a> for finding zeros of real univariate functions.
    25   * <p>
    26   * The function should be continuous but not necessarily smooth.
    27   *
    28   * @version $Revision: 1.6 $ $Date: 2004/07/17 21:19:39 $
    29   */
    30  public class NewtonSolver extends UnivariateRealSolverImpl {
    31
    32      /*** Serializable version identifier */
    33      static final long serialVersionUID = 2606474895443431607L;
    34
    35      /*** The first derivative of the target function. */
    36      private UnivariateRealFunction derivative;
    37
    38      /***
    39       * Construct a solver for the given function.
    40       * @param f function to solve.
    41       */
    42      public NewtonSolver(DifferentiableUnivariateRealFunction f) {
    43          super(f, 100, 1E-6);
    44          derivative = f.derivative();
    45      }
    46
    47      /***
    48       * Find a zero near the midpoint of <code>min</code> and <code>max</code>.
    49       *
    50       * @param min the lower bound for the interval
    51       * @param max the upper bound for the interval
    52       * @return the value where the function is zero
    53       * @throws ConvergenceException if the maximum iteration count is exceeded
    54       * @throws FunctionEvaluationException if an error occurs evaluating the
    55       * function or derivative
    56       * @throws IllegalArgumentException if min is not less than max
    57       */
    58      public double solve(double min, double max) throws ConvergenceException,
    59          FunctionEvaluationException  {
    60          return solve(min, max, UnivariateRealSolverUtils.midpoint(min, max));
    61      }
    62
    63      /***
    64       * Find a zero near the value <code>startValue</code>.
    65       *
    66       * @param min the lower bound for the interval (ignored).
    67       * @param max the upper bound for the interval (ignored).
    68       * @param startValue the start value to use.
    69       * @return the value where the function is zero
    70      * @throws ConvergenceException if the maximum iteration count is exceeded
    71       * @throws FunctionEvaluationException if an error occurs evaluating the
    72       * function or derivative
    73       * @throws IllegalArgumentException if startValue is not between min and max
    74       */
    75      public double solve(double min, double max, double startValue)
    76          throws ConvergenceException, FunctionEvaluationException {
    77
    78          clearResult();
    79          verifySequence(min, startValue, max);
    80
    81          double x0 = startValue;
    82          double x1;
    83
    84          int i = 0;
    85          while (i < maximalIterationCount) {
    86              x1 = x0 - (f.value(x0) / derivative.value(x0));
    87              if (Math.abs(x1 - x0) <= absoluteAccuracy) {
    88
    89                  setResult(x1, i);
    90                  return x1;
    91              }
    92
    93              x0 = x1;
    94              ++i;
    95          }
    96
    97          throw new ConvergenceException
    98              ("Maximum number of iterations exceeded " + i);
    99      }
    100
    101 }