    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    }