/*
* 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.math3.analysis.solvers;
import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.analysis.RealFieldUnivariateFunction;
/** Interface for {@link UnivariateSolver (univariate real) root-finding
* algorithms} that maintain a bracketed solution. There are several advantages
* to having such root-finding algorithms:
* <ul>
* <li>The bracketed solution guarantees that the root is kept within the
* interval. As such, these algorithms generally also guarantee
* convergence.</li>
* <li>The bracketed solution means that we have the opportunity to only
* return roots that are greater than or equal to the actual root, or
* are less than or equal to the actual root. That is, we can control
* whether under-approximations and over-approximations are
* {@link AllowedSolution allowed solutions}. Other root-finding
* algorithms can usually only guarantee that the solution (the root that
* was found) is around the actual root.</li>
* </ul>
*
* <p>For backwards compatibility, all root-finding algorithms must have
* {@link AllowedSolution#ANY_SIDE ANY_SIDE} as default for the allowed
* solutions.</p>
*
* @see AllowedSolution
* @param <T> the type of the field elements
* @since 3.6
*/
public interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>> {
/**
* Get the maximum number of function evaluations.
*
* @return the maximum number of function evaluations.
*/
int getMaxEvaluations();
/**
* Get the number of evaluations of the objective function.
* The number of evaluations corresponds to the last call to the
* {@code optimize} method. It is 0 if the method has not been
* called yet.
*
* @return the number of evaluations of the objective function.
*/
int getEvaluations();
/**
* Get the absolute accuracy of the solver. Solutions returned by the
* solver should be accurate to this tolerance, i.e., if ε is the
* absolute accuracy of the solver and {@code v} is a value returned by
* one of the {@code solve} methods, then a root of the function should
* exist somewhere in the interval ({@code v} - ε, {@code v} + ε).
*
* @return the absolute accuracy.
*/
T getAbsoluteAccuracy();
/**
* Get the relative accuracy of the solver. The contract for relative
* accuracy is the same as {@link #getAbsoluteAccuracy()}, but using
* relative, rather than absolute error. If ρ is the relative accuracy
* configured for a solver and {@code v} is a value returned, then a root
* of the function should exist somewhere in the interval
* ({@code v} - ρ {@code v}, {@code v} + ρ {@code v}).
*
* @return the relative accuracy.
*/
T getRelativeAccuracy();
/**
* Get the function value accuracy of the solver. If {@code v} is
* a value returned by the solver for a function {@code f},
* then by contract, {@code |f(v)|} should be less than or equal to
* the function value accuracy configured for the solver.
*
* @return the function value accuracy.
*/
T getFunctionValueAccuracy();
/**
* Solve for a zero in the given interval.
* A solver may require that the interval brackets a single zero root.
* Solvers that do require bracketing should be able to handle the case
* where one of the endpoints is itself a root.
*
* @param maxEval Maximum number of evaluations.
* @param f Function to solve.
* @param min Lower bound for the interval.
* @param max Upper bound for the interval.
* @param allowedSolution The kind of solutions that the root-finding algorithm may
* accept as solutions.
* @return A value where the function is zero.
* @throws org.apache.commons.math3.exception.MathIllegalArgumentException
* if the arguments do not satisfy the requirements specified by the solver.
* @throws org.apache.commons.math3.exception.TooManyEvaluationsException if
* the allowed number of evaluations is exceeded.
*/
T solve(int maxEval, RealFieldUnivariateFunction<T> f, T min, T max,
AllowedSolution allowedSolution);
/**
* Solve for a zero in the given interval, start at {@code startValue}.
* A solver may require that the interval brackets a single zero root.
* Solvers that do require bracketing should be able to handle the case
* where one of the endpoints is itself a root.
*
* @param maxEval Maximum number of evaluations.
* @param f Function to solve.
* @param min Lower bound for the interval.
* @param max Upper bound for the interval.
* @param startValue Start value to use.
* @param allowedSolution The kind of solutions that the root-finding algorithm may
* accept as solutions.
* @return A value where the function is zero.
* @throws org.apache.commons.math3.exception.MathIllegalArgumentException
* if the arguments do not satisfy the requirements specified by the solver.
* @throws org.apache.commons.math3.exception.TooManyEvaluationsException if
* the allowed number of evaluations is exceeded.
*/
T solve(int maxEval, RealFieldUnivariateFunction<T> f, T min, T max, T startValue,
AllowedSolution allowedSolution);
}