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Java example source code file (ContinuedFraction.java)

This example Java source code file (ContinuedFraction.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

continuedfraction, convergenceexception, default_epsilon, maxcountexceededexception

The ContinuedFraction.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.util;

import org.apache.commons.math3.exception.ConvergenceException;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.util.LocalizedFormats;

/**
 * Provides a generic means to evaluate continued fractions.  Subclasses simply
 * provided the a and b coefficients to evaluate the continued fraction.
 *
 * <p>
 * References:
 * <ul>
 * <li>
 * Continued Fraction</a>
 * </ul>
 * </p>
 *
 */
public abstract class ContinuedFraction {
    /** Maximum allowed numerical error. */
    private static final double DEFAULT_EPSILON = 10e-9;

    /**
     * Default constructor.
     */
    protected ContinuedFraction() {
        super();
    }

    /**
     * Access the n-th a coefficient of the continued fraction.  Since a can be
     * a function of the evaluation point, x, that is passed in as well.
     * @param n the coefficient index to retrieve.
     * @param x the evaluation point.
     * @return the n-th a coefficient.
     */
    protected abstract double getA(int n, double x);

    /**
     * Access the n-th b coefficient of the continued fraction.  Since b can be
     * a function of the evaluation point, x, that is passed in as well.
     * @param n the coefficient index to retrieve.
     * @param x the evaluation point.
     * @return the n-th b coefficient.
     */
    protected abstract double getB(int n, double x);

    /**
     * Evaluates the continued fraction at the value x.
     * @param x the evaluation point.
     * @return the value of the continued fraction evaluated at x.
     * @throws ConvergenceException if the algorithm fails to converge.
     */
    public double evaluate(double x) throws ConvergenceException {
        return evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE);
    }

    /**
     * Evaluates the continued fraction at the value x.
     * @param x the evaluation point.
     * @param epsilon maximum error allowed.
     * @return the value of the continued fraction evaluated at x.
     * @throws ConvergenceException if the algorithm fails to converge.
     */
    public double evaluate(double x, double epsilon) throws ConvergenceException {
        return evaluate(x, epsilon, Integer.MAX_VALUE);
    }

    /**
     * Evaluates the continued fraction at the value x.
     * @param x the evaluation point.
     * @param maxIterations maximum number of convergents
     * @return the value of the continued fraction evaluated at x.
     * @throws ConvergenceException if the algorithm fails to converge.
     * @throws MaxCountExceededException if maximal number of iterations is reached
     */
    public double evaluate(double x, int maxIterations)
        throws ConvergenceException, MaxCountExceededException {
        return evaluate(x, DEFAULT_EPSILON, maxIterations);
    }

    /**
     * Evaluates the continued fraction at the value x.
     * <p>
     * The implementation of this method is based on the modified Lentz algorithm as described
     * on page 18 ff. in:
     * <ul>
     *   <li>
     *   I. J. Thompson,  A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
     *   <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
     *   http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
     *   </li>
     * </ul>
     * <b>Note: the implementation uses the terms ai and bi as defined in
     * <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld.
     * </p>
     *
     * @param x the evaluation point.
     * @param epsilon maximum error allowed.
     * @param maxIterations maximum number of convergents
     * @return the value of the continued fraction evaluated at x.
     * @throws ConvergenceException if the algorithm fails to converge.
     * @throws MaxCountExceededException if maximal number of iterations is reached
     */
    public double evaluate(double x, double epsilon, int maxIterations)
        throws ConvergenceException, MaxCountExceededException {
        final double small = 1e-50;
        double hPrev = getA(0, x);

        // use the value of small as epsilon criteria for zero checks
        if (Precision.equals(hPrev, 0.0, small)) {
            hPrev = small;
        }

        int n = 1;
        double dPrev = 0.0;
        double cPrev = hPrev;
        double hN = hPrev;

        while (n < maxIterations) {
            final double a = getA(n, x);
            final double b = getB(n, x);

            double dN = a + b * dPrev;
            if (Precision.equals(dN, 0.0, small)) {
                dN = small;
            }
            double cN = a + b / cPrev;
            if (Precision.equals(cN, 0.0, small)) {
                cN = small;
            }

            dN = 1 / dN;
            final double deltaN = cN * dN;
            hN = hPrev * deltaN;

            if (Double.isInfinite(hN)) {
                throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_INFINITY_DIVERGENCE,
                                               x);
            }
            if (Double.isNaN(hN)) {
                throw new ConvergenceException(LocalizedFormats.CONTINUED_FRACTION_NAN_DIVERGENCE,
                                               x);
            }

            if (FastMath.abs(deltaN - 1.0) < epsilon) {
                break;
            }

            dPrev = dN;
            cPrev = cN;
            hPrev = hN;
            n++;
        }

        if (n >= maxIterations) {
            throw new MaxCountExceededException(LocalizedFormats.NON_CONVERGENT_CONTINUED_FRACTION,
                                                maxIterations, x);
        }

        return hN;
    }

}

Other Java examples (source code examples)

Here is a short list of links related to this Java ContinuedFraction.java source code file:



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