    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    }