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.math4.analysis.solvers;
019
020import org.apache.commons.math4.analysis.UnivariateFunction;
021
022/** Interface for {@link UnivariateSolver (univariate real) root-finding
023 * algorithms} that maintain a bracketed solution. There are several advantages
024 * to having such root-finding algorithms:
025 * <ul>
026 *  <li>The bracketed solution guarantees that the root is kept within the
027 *      interval. As such, these algorithms generally also guarantee
028 *      convergence.</li>
029 *  <li>The bracketed solution means that we have the opportunity to only
030 *      return roots that are greater than or equal to the actual root, or
031 *      are less than or equal to the actual root. That is, we can control
032 *      whether under-approximations and over-approximations are
033 *      {@link AllowedSolution allowed solutions}. Other root-finding
034 *      algorithms can usually only guarantee that the solution (the root that
035 *      was found) is around the actual root.</li>
036 * </ul>
037 *
038 * <p>For backwards compatibility, all root-finding algorithms must have
039 * {@link AllowedSolution#ANY_SIDE ANY_SIDE} as default for the allowed
040 * solutions.</p>
041 * @param <FUNC> Type of function to solve.
042 *
043 * @see AllowedSolution
044 * @since 3.0
045 */
046public interface BracketedUnivariateSolver<FUNC extends UnivariateFunction>
047    extends BaseUnivariateSolver<FUNC> {
048
049    /**
050     * Solve for a zero in the given interval.
051     * A solver may require that the interval brackets a single zero root.
052     * Solvers that do require bracketing should be able to handle the case
053     * where one of the endpoints is itself a root.
054     *
055     * @param maxEval Maximum number of evaluations.
056     * @param f Function to solve.
057     * @param min Lower bound for the interval.
058     * @param max Upper bound for the interval.
059     * @param allowedSolution The kind of solutions that the root-finding algorithm may
060     * accept as solutions.
061     * @return A value where the function is zero.
062     * @throws org.apache.commons.math4.exception.MathIllegalArgumentException
063     * if the arguments do not satisfy the requirements specified by the solver.
064     * @throws org.apache.commons.math4.exception.TooManyEvaluationsException if
065     * the allowed number of evaluations is exceeded.
066     */
067    double solve(int maxEval, FUNC f, double min, double max,
068                 AllowedSolution allowedSolution);
069
070    /**
071     * Solve for a zero in the given interval, start at {@code startValue}.
072     * A solver may require that the interval brackets a single zero root.
073     * Solvers that do require bracketing should be able to handle the case
074     * where one of the endpoints is itself a root.
075     *
076     * @param maxEval Maximum number of evaluations.
077     * @param f Function to solve.
078     * @param min Lower bound for the interval.
079     * @param max Upper bound for the interval.
080     * @param startValue Start value to use.
081     * @param allowedSolution The kind of solutions that the root-finding algorithm may
082     * accept as solutions.
083     * @return A value where the function is zero.
084     * @throws org.apache.commons.math4.exception.MathIllegalArgumentException
085     * if the arguments do not satisfy the requirements specified by the solver.
086     * @throws org.apache.commons.math4.exception.TooManyEvaluationsException if
087     * the allowed number of evaluations is exceeded.
088     */
089    double solve(int maxEval, FUNC f, double min, double max, double startValue,
090                 AllowedSolution allowedSolution);
091
092}