001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018package org.apache.commons.math3.analysis.solvers;
019
020import org.apache.commons.math3.RealFieldElement;
021import org.apache.commons.math3.analysis.RealFieldUnivariateFunction;
022
023/** Interface for {@link UnivariateSolver (univariate real) root-finding
024 * algorithms} that maintain a bracketed solution. There are several advantages
025 * to having such root-finding algorithms:
026 * <ul>
027 *  <li>The bracketed solution guarantees that the root is kept within the
028 *      interval. As such, these algorithms generally also guarantee
029 *      convergence.</li>
030 *  <li>The bracketed solution means that we have the opportunity to only
031 *      return roots that are greater than or equal to the actual root, or
032 *      are less than or equal to the actual root. That is, we can control
033 *      whether under-approximations and over-approximations are
034 *      {@link AllowedSolution allowed solutions}. Other root-finding
035 *      algorithms can usually only guarantee that the solution (the root that
036 *      was found) is around the actual root.</li>
037 * </ul>
038 *
039 * <p>For backwards compatibility, all root-finding algorithms must have
040 * {@link AllowedSolution#ANY_SIDE ANY_SIDE} as default for the allowed
041 * solutions.</p>
042 *
043 * @see AllowedSolution
044 * @param <T> the type of the field elements
045 * @since 3.6
046 */
047public interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>> {
048
049    /**
050     * Get the maximum number of function evaluations.
051     *
052     * @return the maximum number of function evaluations.
053     */
054    int getMaxEvaluations();
055
056    /**
057     * Get the number of evaluations of the objective function.
058     * The number of evaluations corresponds to the last call to the
059     * {@code optimize} method. It is 0 if the method has not been
060     * called yet.
061     *
062     * @return the number of evaluations of the objective function.
063     */
064    int getEvaluations();
065
066    /**
067     * Get the absolute accuracy of the solver.  Solutions returned by the
068     * solver should be accurate to this tolerance, i.e., if &epsilon; is the
069     * absolute accuracy of the solver and {@code v} is a value returned by
070     * one of the {@code solve} methods, then a root of the function should
071     * exist somewhere in the interval ({@code v} - &epsilon;, {@code v} + &epsilon;).
072     *
073     * @return the absolute accuracy.
074     */
075    T getAbsoluteAccuracy();
076
077    /**
078     * Get the relative accuracy of the solver.  The contract for relative
079     * accuracy is the same as {@link #getAbsoluteAccuracy()}, but using
080     * relative, rather than absolute error.  If &rho; is the relative accuracy
081     * configured for a solver and {@code v} is a value returned, then a root
082     * of the function should exist somewhere in the interval
083     * ({@code v} - &rho; {@code v}, {@code v} + &rho; {@code v}).
084     *
085     * @return the relative accuracy.
086     */
087    T getRelativeAccuracy();
088
089    /**
090     * Get the function value accuracy of the solver.  If {@code v} is
091     * a value returned by the solver for a function {@code f},
092     * then by contract, {@code |f(v)|} should be less than or equal to
093     * the function value accuracy configured for the solver.
094     *
095     * @return the function value accuracy.
096     */
097    T getFunctionValueAccuracy();
098
099    /**
100     * Solve for a zero in the given interval.
101     * A solver may require that the interval brackets a single zero root.
102     * Solvers that do require bracketing should be able to handle the case
103     * where one of the endpoints is itself a root.
104     *
105     * @param maxEval Maximum number of evaluations.
106     * @param f Function to solve.
107     * @param min Lower bound for the interval.
108     * @param max Upper bound for the interval.
109     * @param allowedSolution The kind of solutions that the root-finding algorithm may
110     * accept as solutions.
111     * @return A value where the function is zero.
112     * @throws org.apache.commons.math3.exception.MathIllegalArgumentException
113     * if the arguments do not satisfy the requirements specified by the solver.
114     * @throws org.apache.commons.math3.exception.TooManyEvaluationsException if
115     * the allowed number of evaluations is exceeded.
116     */
117    T solve(int maxEval, RealFieldUnivariateFunction<T> f, T min, T max,
118            AllowedSolution allowedSolution);
119
120    /**
121     * Solve for a zero in the given interval, start at {@code startValue}.
122     * A solver may require that the interval brackets a single zero root.
123     * Solvers that do require bracketing should be able to handle the case
124     * where one of the endpoints is itself a root.
125     *
126     * @param maxEval Maximum number of evaluations.
127     * @param f Function to solve.
128     * @param min Lower bound for the interval.
129     * @param max Upper bound for the interval.
130     * @param startValue Start value to use.
131     * @param allowedSolution The kind of solutions that the root-finding algorithm may
132     * accept as solutions.
133     * @return A value where the function is zero.
134     * @throws org.apache.commons.math3.exception.MathIllegalArgumentException
135     * if the arguments do not satisfy the requirements specified by the solver.
136     * @throws org.apache.commons.math3.exception.TooManyEvaluationsException if
137     * the allowed number of evaluations is exceeded.
138     */
139    T solve(int maxEval, RealFieldUnivariateFunction<T> f, T min, T max, T startValue,
140            AllowedSolution allowedSolution);
141
142}