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/*
* 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;
/** The kinds of solutions that a {@link BracketedUnivariateSolver
* (bracketed univariate real) root-finding algorithm} may accept as solutions.
* This basically controls whether or not under-approximations and
* over-approximations are allowed.
*
* <p>If all solutions are accepted ({@link #ANY_SIDE}), then the solution
* that the root-finding algorithm returns for a given root may be equal to the
* actual root, but it may also be an approximation that is slightly smaller
* or slightly larger than the actual root. Root-finding algorithms generally
* only guarantee that the returned solution is within the requested
* tolerances. In certain cases however, in particular for
* {@link org.apache.commons.math3.ode.events.EventHandler state events} of
* {@link org.apache.commons.math3.ode.ODEIntegrator ODE solvers}, it
* may be necessary to guarantee that a solution is returned that lies on a
* specific side the solution.</p>
*
* @see BracketedUnivariateSolver
* @since 3.0
*/
public enum AllowedSolution {
/** There are no additional side restriction on the solutions for
* root-finding. That is, both under-approximations and over-approximations
* are allowed. So, if a function f(x) has a root at x = x0, then the
* root-finding result s may be smaller than x0, equal to x0, or greater
* than x0.
*/
ANY_SIDE,
/** Only solutions that are less than or equal to the actual root are
* acceptable as solutions for root-finding. In other words,
* over-approximations are not allowed. So, if a function f(x) has a root
* at x = x0, then the root-finding result s must satisfy s <= x0.
*/
LEFT_SIDE,
/** Only solutions that are greater than or equal to the actual root are
* acceptable as solutions for root-finding. In other words,
* under-approximations are not allowed. So, if a function f(x) has a root
* at x = x0, then the root-finding result s must satisfy s >= x0.
*/
RIGHT_SIDE,
/** Only solutions for which values are less than or equal to zero are
* acceptable as solutions for root-finding. So, if a function f(x) has
* a root at x = x0, then the root-finding result s must satisfy f(s) <= 0.
*/
BELOW_SIDE,
/** Only solutions for which values are greater than or equal to zero are
* acceptable as solutions for root-finding. So, if a function f(x) has
* a root at x = x0, then the root-finding result s must satisfy f(s) >= 0.
*/
ABOVE_SIDE;
}
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