View Javadoc

    1   /*
    2    * Copyright 2003-2004 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  package org.apache.commons.math.analysis;
    17
    18  import java.io.Serializable;
    19
    20  import org.apache.commons.math.ConvergenceException;
    21  import org.apache.commons.math.FunctionEvaluationException;
    22
    23
    24  /***
    25   * Implements a modified version of the
    26   * <a href="http://mathworld.wolfram.com/SecantMethod.html">secant method</a>
    27   * for approximating a zero of a real univariate function.
    28   * <p>
    29   * The algorithm is modified to maintain bracketing of a root by successive
    30   * approximations. Because of forced bracketing, convergence may be slower than
    31   * the unrestricted secant algorithm. However, this implementation should in
    32   * general outperform the
    33   * <a href="http://mathworld.wolfram.com/MethodofFalsePosition.html">
    34   * regula falsi method.</a>
    35   * <p>
    36   * The function is assumed to be continuous but not necessarily smooth.
    37   *
    38   * @version $Revision: 348519 $ $Date: 2005-11-23 12:12:18 -0700 (Wed, 23 Nov 2005) $
    39   */
    40  public class SecantSolver extends UnivariateRealSolverImpl implements Serializable {
    41
    42      /*** Serializable version identifier */
    43      private static final long serialVersionUID = 1984971194738974867L;
    44
    45      /***
    46       * Construct a solver for the given function.
    47       * @param f function to solve.
    48       */
    49      public SecantSolver(UnivariateRealFunction f) {
    50          super(f, 100, 1E-6);
    51      }
    52
    53      /***
    54       * Find a zero in the given interval.
    55       *
    56       * @param min the lower bound for the interval
    57       * @param max the upper bound for the interval
    58       * @param initial the start value to use (ignored)
    59       * @return the value where the function is zero
    60       * @throws ConvergenceException if the maximum iteration count is exceeded
    61       * @throws FunctionEvaluationException if an error occurs evaluating the
    62       * function
    63       * @throws IllegalArgumentException if min is not less than max or the
    64       * signs of the values of the function at the endpoints are not opposites
    65       */
    66      public double solve(double min, double max, double initial)
    67          throws ConvergenceException, FunctionEvaluationException {
    68
    69          return solve(min, max);
    70      }
    71
    72      /***
    73       * Find a zero in the given interval.
    74       * @param min the lower bound for the interval.
    75       * @param max the upper bound for the interval.
    76       * @return the value where the function is zero
    77       * @throws ConvergenceException  if the maximum iteration count is exceeded
    78       * @throws FunctionEvaluationException if an error occurs evaluating the
    79       * function
    80       * @throws IllegalArgumentException if min is not less than max or the
    81       * signs of the values of the function at the endpoints are not opposites
    82       */
    83      public double solve(double min, double max) throws ConvergenceException,
    84          FunctionEvaluationException {
    85
    86          clearResult();
    87          verifyInterval(min, max);
    88
    89          // Index 0 is the old approximation for the root.
    90          // Index 1 is the last calculated approximation  for the root.
    91          // Index 2 is a bracket for the root with respect to x0.
    92          // OldDelta is the length of the bracketing interval of the last
    93          // iteration.
    94          double x0 = min;
    95          double x1 = max;
    96          double y0 = f.value(x0);
    97          double y1 = f.value(x1);
    98
    99          // Verify bracketing
    100         if (y0 * y1 >= 0) {
    101             throw new IllegalArgumentException
    102             ("Function values at endpoints do not have different signs." +
    103                     "  Endpoints: [" + min + "," + max + "]" +
    104                     "  Values: [" + y0 + "," + y1 + "]");
    105         }
    106
    107         double x2 = x0;
    108         double y2 = y0;
    109         double oldDelta = x2 - x1;
    110         int i = 0;
    111         while (i < maximalIterationCount) {
    112             if (Math.abs(y2) < Math.abs(y1)) {
    113                 x0 = x1;
    114                 x1 = x2;
    115                 x2 = x0;
    116                 y0 = y1;
    117                 y1 = y2;
    118                 y2 = y0;
    119             }
    120             if (Math.abs(y1) <= functionValueAccuracy) {
    121                 setResult(x1, i);
    122                 return result;
    123             }
    124             if (Math.abs(oldDelta) <
    125                 Math.max(relativeAccuracy * Math.abs(x1), absoluteAccuracy)) {
    126                 setResult(x1, i);
    127                 return result;
    128             }
    129             double delta;
    130             if (Math.abs(y1) > Math.abs(y0)) {
    131                 // Function value increased in last iteration. Force bisection.
    132                 delta = 0.5 * oldDelta;
    133             } else {
    134                 delta = (x0 - x1) / (1 - y0 / y1);
    135                 if (delta / oldDelta > 1) {
    136                     // New approximation falls outside bracket.
    137                     // Fall back to bisection.
    138                     delta = 0.5 * oldDelta;
    139                 }
    140             }
    141             x0 = x1;
    142             y0 = y1;
    143             x1 = x1 + delta;
    144             y1 = f.value(x1);
    145             if ((y1 > 0) == (y2 > 0)) {
    146                 // New bracket is (x0,x1).
    147                 x2 = x0;
    148                 y2 = y0;
    149             }
    150             oldDelta = x2 - x1;
    151             i++;
    152         }
    153         throw new ConvergenceException("Maximal iteration number exceeded" + i);
    154     }
    155
    156 }