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 <= 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 >= 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) <= 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) >= 0. 073 */ 074 ABOVE_SIDE; 075 076 }