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    
018    package org.apache.commons.math3.analysis.solvers;
019    
020    
021    /** The kinds of solutions that a {@link BracketedUnivariateSolver
022     * (bracketed univariate real) root-finding algorithm} may accept as solutions.
023     * This basically controls whether or not under-approximations and
024     * over-approximations are allowed.
025     *
026     * <p>If all solutions are accepted ({@link #ANY_SIDE}), then the solution
027     * that the root-finding algorithm returns for a given root may be equal to the
028     * actual root, but it may also be an approximation that is slightly smaller
029     * or slightly larger than the actual root. Root-finding algorithms generally
030     * only guarantee that the returned solution is within the requested
031     * tolerances. In certain cases however, in particular for
032     * {@link org.apache.commons.math3.ode.events.EventHandler state events} of
033     * {@link org.apache.commons.math3.ode.ODEIntegrator ODE solvers}, it
034     * may be necessary to guarantee that a solution is returned that lies on a
035     * specific side the solution.</p>
036     *
037     * @see BracketedUnivariateSolver
038     * @since 3.0
039     * @version $Id: AllowedSolution.java 1364387 2012-07-22 18:14:11Z tn $
040     */
041    public enum AllowedSolution {
042        /** There are no additional side restriction on the solutions for
043         * root-finding. That is, both under-approximations and over-approximations
044         * are allowed. So, if a function f(x) has a root at x = x0, then the
045         * root-finding result s may be smaller than x0, equal to x0, or greater
046         * than x0.
047         */
048        ANY_SIDE,
049    
050        /** Only solutions that are less than or equal to the actual root are
051         * acceptable as solutions for root-finding. In other words,
052         * over-approximations are not allowed. So, if a function f(x) has a root
053         * at x = x0, then the root-finding result s must satisfy s &lt;= x0.
054         */
055        LEFT_SIDE,
056    
057        /** Only solutions that are greater than or equal to the actual root are
058         * acceptable as solutions for root-finding. In other words,
059         * under-approximations are not allowed. So, if a function f(x) has a root
060         * at x = x0, then the root-finding result s must satisfy s &gt;= x0.
061         */
062        RIGHT_SIDE,
063    
064        /** Only solutions for which values are less than or equal to zero are
065         * acceptable as solutions for root-finding. So, if a function f(x) has
066         * a root at x = x0, then the root-finding result s must satisfy f(s) &lt;= 0.
067         */
068        BELOW_SIDE,
069    
070        /** Only solutions for which values are greater than or equal to zero are
071         * acceptable as solutions for root-finding. So, if a function f(x) has
072         * a root at x = x0, then the root-finding result s must satisfy f(s) &gt;= 0.
073         */
074        ABOVE_SIDE;
075    
076    }