| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You 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.math4.legacy.analysis.solvers; |
| |
| /** |
| * Implements the <em>Regula Falsi</em> or <em>False position</em> method for |
| * root-finding (approximating a zero of a univariate real function). It is a |
| * modified {@link SecantSolver <em>Secant</em>} method. |
| * |
| * <p>The <em>Regula Falsi</em> method is included for completeness, for |
| * testing purposes, for educational purposes, for comparison to other |
| * algorithms, etc. It is however <strong>not</strong> intended to be used |
| * for actual problems, as one of the bounds often remains fixed, resulting |
| * in very slow convergence. Instead, one of the well-known modified |
| * <em>Regula Falsi</em> algorithms can be used ({@link IllinoisSolver |
| * <em>Illinois</em>} or {@link PegasusSolver <em>Pegasus</em>}). These two |
| * algorithms solve the fundamental issues of the original <em>Regula |
| * Falsi</em> algorithm, and greatly out-performs it for most, if not all, |
| * (practical) functions. |
| * |
| * <p>Unlike the <em>Secant</em> method, the <em>Regula Falsi</em> guarantees |
| * convergence, by maintaining a bracketed solution. Note however, that due to |
| * the finite/limited precision of Java's {@link Double double} type, which is |
| * used in this implementation, the algorithm may get stuck in a situation |
| * where it no longer makes any progress. Such cases are detected and result |
| * in a {@code ConvergenceException} exception being thrown. In other words, |
| * the algorithm theoretically guarantees convergence, but the implementation |
| * does not.</p> |
| * |
| * <p>The <em>Regula Falsi</em> method assumes that the function is continuous, |
| * but not necessarily smooth.</p> |
| * |
| * <p>Implementation based on the following article: M. Dowell and P. Jarratt, |
| * <em>A modified regula falsi method for computing the root of an |
| * equation</em>, BIT Numerical Mathematics, volume 11, number 2, |
| * pages 168-174, Springer, 1971.</p> |
| * |
| * @since 3.0 |
| */ |
| public class RegulaFalsiSolver extends BaseSecantSolver { |
| |
| /** Construct a solver with default accuracy (1e-6). */ |
| public RegulaFalsiSolver() { |
| super(DEFAULT_ABSOLUTE_ACCURACY, Method.REGULA_FALSI); |
| } |
| |
| /** |
| * Construct a solver. |
| * |
| * @param absoluteAccuracy Absolute accuracy. |
| */ |
| public RegulaFalsiSolver(final double absoluteAccuracy) { |
| super(absoluteAccuracy, Method.REGULA_FALSI); |
| } |
| |
| /** |
| * Construct a solver. |
| * |
| * @param relativeAccuracy Relative accuracy. |
| * @param absoluteAccuracy Absolute accuracy. |
| */ |
| public RegulaFalsiSolver(final double relativeAccuracy, |
| final double absoluteAccuracy) { |
| super(relativeAccuracy, absoluteAccuracy, Method.REGULA_FALSI); |
| } |
| |
| /** |
| * Construct a solver. |
| * |
| * @param relativeAccuracy Relative accuracy. |
| * @param absoluteAccuracy Absolute accuracy. |
| * @param functionValueAccuracy Maximum function value error. |
| */ |
| public RegulaFalsiSolver(final double relativeAccuracy, |
| final double absoluteAccuracy, |
| final double functionValueAccuracy) { |
| super(relativeAccuracy, absoluteAccuracy, functionValueAccuracy, Method.REGULA_FALSI); |
| } |
| } |