/*
 * 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 
(bracketed univariate real) root-finding algorithm may accept as solutions. This basically controls whether or not under-approximations and over-approximations are allowed. 
If all solutions are accepted (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 state events of ODE solvers, it may be necessary to guarantee that a solution is returned that lies on a specific side the solution.
See Also:
BracketedUnivariateSolver
Since:
3.0/** 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.
/** 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.
/** 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 &lt;= 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.
/** 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 &gt;= 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.
/** 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) &lt;= 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.
/** 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) &gt;= 0.
     */
    ABOVE_SIDE;

}