

Java example source code file (ContinuedFraction.java)
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/LICENSE2.0 * * 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 = 10e9; /** * Default constructor. */ protected ContinuedFraction() { super(); } /** * Access the nth 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 nth a coefficient. */ protected abstract double getA(int n, double x); /** * Access the nth 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 nth 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/ThompsonJCP64p490.pdf"> * http://www.fresco.org.uk/papers/ThompsonJCP64p490.pdf</a> * </li> * </ul> * <b>Note: the implementation uses the terms a_{i} and b_{i} 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 = 1e50; 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: 
Copyright 19982021 Alvin Alexander, alvinalexander.com
All Rights Reserved.
A percentage of advertising revenue from
pages under the /java/jwarehouse
URI on this website is
paid back to open source projects.