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 }