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    package org.apache.commons.math3.analysis.solvers;
018    
019    import org.apache.commons.math3.util.FastMath;
020    import org.apache.commons.math3.exception.NoBracketingException;
021    import org.apache.commons.math3.exception.TooManyEvaluationsException;
022    
023    /**
024     * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
025     * Ridders' Method</a> for root finding of real univariate functions. For
026     * reference, see C. Ridders, <i>A new algorithm for computing a single root
027     * of a real continuous function </i>, IEEE Transactions on Circuits and
028     * Systems, 26 (1979), 979 - 980.
029     * <p>
030     * The function should be continuous but not necessarily smooth.</p>
031     *
032     * @version $Id: RiddersSolver.java 1379560 2012-08-31 19:40:30Z erans $
033     * @since 1.2
034     */
035    public class RiddersSolver extends AbstractUnivariateSolver {
036        /** Default absolute accuracy. */
037        private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;
038    
039        /**
040         * Construct a solver with default accuracy (1e-6).
041         */
042        public RiddersSolver() {
043            this(DEFAULT_ABSOLUTE_ACCURACY);
044        }
045        /**
046         * Construct a solver.
047         *
048         * @param absoluteAccuracy Absolute accuracy.
049         */
050        public RiddersSolver(double absoluteAccuracy) {
051            super(absoluteAccuracy);
052        }
053        /**
054         * Construct a solver.
055         *
056         * @param relativeAccuracy Relative accuracy.
057         * @param absoluteAccuracy Absolute accuracy.
058         */
059        public RiddersSolver(double relativeAccuracy,
060                             double absoluteAccuracy) {
061            super(relativeAccuracy, absoluteAccuracy);
062        }
063    
064        /**
065         * {@inheritDoc}
066         */
067        @Override
068        protected double doSolve()
069            throws TooManyEvaluationsException,
070                   NoBracketingException {
071            double min = getMin();
072            double max = getMax();
073            // [x1, x2] is the bracketing interval in each iteration
074            // x3 is the midpoint of [x1, x2]
075            // x is the new root approximation and an endpoint of the new interval
076            double x1 = min;
077            double y1 = computeObjectiveValue(x1);
078            double x2 = max;
079            double y2 = computeObjectiveValue(x2);
080    
081            // check for zeros before verifying bracketing
082            if (y1 == 0) {
083                return min;
084            }
085            if (y2 == 0) {
086                return max;
087            }
088            verifyBracketing(min, max);
089    
090            final double absoluteAccuracy = getAbsoluteAccuracy();
091            final double functionValueAccuracy = getFunctionValueAccuracy();
092            final double relativeAccuracy = getRelativeAccuracy();
093    
094            double oldx = Double.POSITIVE_INFINITY;
095            while (true) {
096                // calculate the new root approximation
097                final double x3 = 0.5 * (x1 + x2);
098                final double y3 = computeObjectiveValue(x3);
099                if (FastMath.abs(y3) <= functionValueAccuracy) {
100                    return x3;
101                }
102                final double delta = 1 - (y1 * y2) / (y3 * y3);  // delta > 1 due to bracketing
103                final double correction = (FastMath.signum(y2) * FastMath.signum(y3)) *
104                                          (x3 - x1) / FastMath.sqrt(delta);
105                final double x = x3 - correction;                // correction != 0
106                final double y = computeObjectiveValue(x);
107    
108                // check for convergence
109                final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy);
110                if (FastMath.abs(x - oldx) <= tolerance) {
111                    return x;
112                }
113                if (FastMath.abs(y) <= functionValueAccuracy) {
114                    return x;
115                }
116    
117                // prepare the new interval for next iteration
118                // Ridders' method guarantees x1 < x < x2
119                if (correction > 0.0) {             // x1 < x < x3
120                    if (FastMath.signum(y1) + FastMath.signum(y) == 0.0) {
121                        x2 = x;
122                        y2 = y;
123                    } else {
124                        x1 = x;
125                        x2 = x3;
126                        y1 = y;
127                        y2 = y3;
128                    }
129                } else {                            // x3 < x < x2
130                    if (FastMath.signum(y2) + FastMath.signum(y) == 0.0) {
131                        x1 = x;
132                        y1 = y;
133                    } else {
134                        x1 = x3;
135                        x2 = x;
136                        y1 = y3;
137                        y2 = y;
138                    }
139                }
140                oldx = x;
141            }
142        }
143    }