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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math3.analysis.solvers;
19  
20  
21  /** The kinds of solutions that a {@link BracketedUnivariateSolver
22   * (bracketed univariate real) root-finding algorithm} may accept as solutions.
23   * This basically controls whether or not under-approximations and
24   * over-approximations are allowed.
25   *
26   * <p>If all solutions are accepted ({@link #ANY_SIDE}), then the solution
27   * that the root-finding algorithm returns for a given root may be equal to the
28   * actual root, but it may also be an approximation that is slightly smaller
29   * or slightly larger than the actual root. Root-finding algorithms generally
30   * only guarantee that the returned solution is within the requested
31   * tolerances. In certain cases however, in particular for
32   * {@link org.apache.commons.math3.ode.events.EventHandler state events} of
33   * {@link org.apache.commons.math3.ode.ODEIntegrator ODE solvers}, it
34   * may be necessary to guarantee that a solution is returned that lies on a
35   * specific side the solution.</p>
36   *
37   * @see BracketedUnivariateSolver
38   * @since 3.0
39   * @version $Id: AllowedSolution.java 1364387 2012-07-22 18:14:11Z tn $
40   */
41  public enum AllowedSolution {
42      /** There are no additional side restriction on the solutions for
43       * root-finding. That is, both under-approximations and over-approximations
44       * are allowed. So, if a function f(x) has a root at x = x0, then the
45       * root-finding result s may be smaller than x0, equal to x0, or greater
46       * than x0.
47       */
48      ANY_SIDE,
49  
50      /** Only solutions that are less than or equal to the actual root are
51       * acceptable as solutions for root-finding. In other words,
52       * over-approximations are not allowed. So, if a function f(x) has a root
53       * at x = x0, then the root-finding result s must satisfy s &lt;= x0.
54       */
55      LEFT_SIDE,
56  
57      /** Only solutions that are greater than or equal to the actual root are
58       * acceptable as solutions for root-finding. In other words,
59       * under-approximations are not allowed. So, if a function f(x) has a root
60       * at x = x0, then the root-finding result s must satisfy s &gt;= x0.
61       */
62      RIGHT_SIDE,
63  
64      /** Only solutions for which values are less than or equal to zero are
65       * acceptable as solutions for root-finding. So, if a function f(x) has
66       * a root at x = x0, then the root-finding result s must satisfy f(s) &lt;= 0.
67       */
68      BELOW_SIDE,
69  
70      /** Only solutions for which values are greater than or equal to zero are
71       * acceptable as solutions for root-finding. So, if a function f(x) has
72       * a root at x = x0, then the root-finding result s must satisfy f(s) &gt;= 0.
73       */
74      ABOVE_SIDE;
75  
76  }