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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      https://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  /*
19   * This is not the original file distributed by the Apache Software Foundation
20   * It has been modified by the Hipparchus project
21   */
22  
23  package org.hipparchus.analysis.solvers;
24  
25  /**
26   * Implements the <em>Regula Falsi</em> or <em>False position</em> method for
27   * root-finding (approximating a zero of a univariate real function). It is a
28   * modified {@link SecantSolver <em>Secant</em>} method.
29   *
30   * <p>The <em>Regula Falsi</em> method is included for completeness, for
31   * testing purposes, for educational purposes, for comparison to other
32   * algorithms, etc. It is however <strong>not</strong> intended to be used
33   * for actual problems, as one of the bounds often remains fixed, resulting
34   * in very slow convergence. Instead, one of the well-known modified
35   * <em>Regula Falsi</em> algorithms can be used ({@link IllinoisSolver
36   * <em>Illinois</em>} or {@link PegasusSolver <em>Pegasus</em>}). These two
37   * algorithms solve the fundamental issues of the original <em>Regula
38   * Falsi</em> algorithm, and greatly out-performs it for most, if not all,
39   * (practical) functions.
40   *
41   * <p>Unlike the <em>Secant</em> method, the <em>Regula Falsi</em> guarantees
42   * convergence, by maintaining a bracketed solution. Note however, that due to
43   * the finite/limited precision of Java's {@link Double double} type, which is
44   * used in this implementation, the algorithm may get stuck in a situation
45   * where it no longer makes any progress. Such cases are detected and result
46   * in a {@code MathIllegalStateException} exception being thrown. In other words,
47   * the algorithm theoretically guarantees convergence, but the implementation
48   * does not.</p>
49   *
50   * <p>The <em>Regula Falsi</em> method assumes that the function is continuous,
51   * but not necessarily smooth.</p>
52   *
53   * <p>Implementation based on the following article: M. Dowell and P. Jarratt,
54   * <em>A modified regula falsi method for computing the root of an
55   * equation</em>, BIT Numerical Mathematics, volume 11, number 2,
56   * pages 168-174, Springer, 1971.</p>
57   *
58   */
59  public class RegulaFalsiSolver extends BaseSecantSolver {
60  
61      /** Construct a solver with default accuracy (1e-6). */
62      public RegulaFalsiSolver() {
63          super(DEFAULT_ABSOLUTE_ACCURACY, Method.REGULA_FALSI);
64      }
65  
66      /**
67       * Construct a solver.
68       *
69       * @param absoluteAccuracy Absolute accuracy.
70       */
71      public RegulaFalsiSolver(final double absoluteAccuracy) {
72          super(absoluteAccuracy, Method.REGULA_FALSI);
73      }
74  
75      /**
76       * Construct a solver.
77       *
78       * @param relativeAccuracy Relative accuracy.
79       * @param absoluteAccuracy Absolute accuracy.
80       */
81      public RegulaFalsiSolver(final double relativeAccuracy,
82                               final double absoluteAccuracy) {
83          super(relativeAccuracy, absoluteAccuracy, Method.REGULA_FALSI);
84      }
85  
86      /**
87       * Construct a solver.
88       *
89       * @param relativeAccuracy Relative accuracy.
90       * @param absoluteAccuracy Absolute accuracy.
91       * @param functionValueAccuracy Maximum function value error.
92       */
93      public RegulaFalsiSolver(final double relativeAccuracy,
94                               final double absoluteAccuracy,
95                               final double functionValueAccuracy) {
96          super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy, Method.REGULA_FALSI);
97      }
98  }