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Java example source code file (RiddersSolver.java)

This example Java source code file (RiddersSolver.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

abstractunivariatesolver, default_absolute_accuracy, nobracketingexception, override, ridderssolver, toomanyevaluationsexception

The RiddersSolver.java Java example source code

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.analysis.solvers;

import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.exception.TooManyEvaluationsException;

/**
 * Implements the <a href="http://mathworld.wolfram.com/RiddersMethod.html">
 * Ridders' Method</a> for root finding of real univariate functions. For
 * reference, see C. Ridders, <i>A new algorithm for computing a single root
 * of a real continuous function </i>, IEEE Transactions on Circuits and
 * Systems, 26 (1979), 979 - 980.
 * <p>
 * The function should be continuous but not necessarily smooth.</p>
 *
 * @since 1.2
 */
public class RiddersSolver extends AbstractUnivariateSolver {
    /** Default absolute accuracy. */
    private static final double DEFAULT_ABSOLUTE_ACCURACY = 1e-6;

    /**
     * Construct a solver with default accuracy (1e-6).
     */
    public RiddersSolver() {
        this(DEFAULT_ABSOLUTE_ACCURACY);
    }
    /**
     * Construct a solver.
     *
     * @param absoluteAccuracy Absolute accuracy.
     */
    public RiddersSolver(double absoluteAccuracy) {
        super(absoluteAccuracy);
    }
    /**
     * Construct a solver.
     *
     * @param relativeAccuracy Relative accuracy.
     * @param absoluteAccuracy Absolute accuracy.
     */
    public RiddersSolver(double relativeAccuracy,
                         double absoluteAccuracy) {
        super(relativeAccuracy, absoluteAccuracy);
    }

    /**
     * {@inheritDoc}
     */
    @Override
    protected double doSolve()
        throws TooManyEvaluationsException,
               NoBracketingException {
        double min = getMin();
        double max = getMax();
        // [x1, x2] is the bracketing interval in each iteration
        // x3 is the midpoint of [x1, x2]
        // x is the new root approximation and an endpoint of the new interval
        double x1 = min;
        double y1 = computeObjectiveValue(x1);
        double x2 = max;
        double y2 = computeObjectiveValue(x2);

        // check for zeros before verifying bracketing
        if (y1 == 0) {
            return min;
        }
        if (y2 == 0) {
            return max;
        }
        verifyBracketing(min, max);

        final double absoluteAccuracy = getAbsoluteAccuracy();
        final double functionValueAccuracy = getFunctionValueAccuracy();
        final double relativeAccuracy = getRelativeAccuracy();

        double oldx = Double.POSITIVE_INFINITY;
        while (true) {
            // calculate the new root approximation
            final double x3 = 0.5 * (x1 + x2);
            final double y3 = computeObjectiveValue(x3);
            if (FastMath.abs(y3) <= functionValueAccuracy) {
                return x3;
            }
            final double delta = 1 - (y1 * y2) / (y3 * y3);  // delta > 1 due to bracketing
            final double correction = (FastMath.signum(y2) * FastMath.signum(y3)) *
                                      (x3 - x1) / FastMath.sqrt(delta);
            final double x = x3 - correction;                // correction != 0
            final double y = computeObjectiveValue(x);

            // check for convergence
            final double tolerance = FastMath.max(relativeAccuracy * FastMath.abs(x), absoluteAccuracy);
            if (FastMath.abs(x - oldx) <= tolerance) {
                return x;
            }
            if (FastMath.abs(y) <= functionValueAccuracy) {
                return x;
            }

            // prepare the new interval for next iteration
            // Ridders' method guarantees x1 < x < x2
            if (correction > 0.0) {             // x1 < x < x3
                if (FastMath.signum(y1) + FastMath.signum(y) == 0.0) {
                    x2 = x;
                    y2 = y;
                } else {
                    x1 = x;
                    x2 = x3;
                    y1 = y;
                    y2 = y3;
                }
            } else {                            // x3 < x < x2
                if (FastMath.signum(y2) + FastMath.signum(y) == 0.0) {
                    x1 = x;
                    y1 = y;
                } else {
                    x1 = x3;
                    x2 = x;
                    y1 = y3;
                    y2 = y;
                }
            }
            oldx = x;
        }
    }
}

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