| /* |
| * 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.numbers.fraction; |
| |
| import org.apache.commons.numbers.core.Precision; |
| |
| /** |
| * Provides a generic means to evaluate |
| * <a href="https://mathworld.wolfram.com/ContinuedFraction.html">continued fractions</a>. |
| * |
| * <p>The continued fraction uses the following form for the numerator ({@code a}) and |
| * denominator ({@code b}) coefficients: |
| * <pre> |
| * a1 |
| * b0 + ------------------ |
| * b1 + a2 |
| * ------------- |
| * b2 + a3 |
| * -------- |
| * b3 + ... |
| * </pre> |
| * |
| * <p>Subclasses must provide the {@link #getA(int,double) a} and {@link #getB(int,double) b} |
| * coefficients to evaluate the continued fraction. |
| */ |
| public abstract class ContinuedFraction { |
| /** |
| * The value for any number close to zero. |
| * |
| * <p>"The parameter small should be some non-zero number less than typical values of |
| * eps * |b_n|, e.g., 1e-50". |
| */ |
| private static final double SMALL = 1e-50; |
| |
| /** |
| * Defines the <a href="https://mathworld.wolfram.com/ContinuedFraction.html"> |
| * {@code n}-th "a" coefficient</a> of the continued fraction. |
| * |
| * @param n Index of the coefficient to retrieve. |
| * @param x Evaluation point. |
| * @return the coefficient <code>a<sub>n</sub></code>. |
| */ |
| protected abstract double getA(int n, double x); |
| |
| /** |
| * Defines the <a href="https://mathworld.wolfram.com/ContinuedFraction.html"> |
| * {@code n}-th "b" coefficient</a> of the continued fraction. |
| * |
| * @param n Index of the coefficient to retrieve. |
| * @param x Evaluation point. |
| * @return the coefficient <code>b<sub>n</sub></code>. |
| */ |
| protected abstract double getB(int n, double x); |
| |
| /** |
| * Evaluates the continued fraction. |
| * |
| * @param x the evaluation point. |
| * @param epsilon Maximum error allowed. |
| * @return the value of the continued fraction evaluated at {@code x}. |
| * @throws ArithmeticException if the algorithm fails to converge. |
| * @throws ArithmeticException if the maximal number of iterations is reached |
| * before the expected convergence is achieved. |
| * |
| * @see #evaluate(double,double,int) |
| */ |
| public double evaluate(double x, double epsilon) { |
| return evaluate(x, epsilon, Integer.MAX_VALUE); |
| } |
| |
| /** |
| * Evaluates the continued fraction. |
| * <p> |
| * The implementation of this method is based on the modified Lentz algorithm as described |
| * on page 508 in: |
| * </p> |
| * |
| * <ul> |
| * <li> |
| * I. J. Thompson, A. R. Barnett (1986). |
| * "Coulomb and Bessel Functions of Complex Arguments and Order." |
| * Journal of Computational Physics 64, 490-509. |
| * <a target="_blank" href="https://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf"> |
| * https://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a> |
| * </li> |
| * </ul> |
| * |
| * @param x Point at which to evaluate the continued fraction. |
| * @param epsilon Maximum error allowed. |
| * @param maxIterations Maximum number of iterations. |
| * @return the value of the continued fraction evaluated at {@code x}. |
| * @throws ArithmeticException if the algorithm fails to converge. |
| * @throws ArithmeticException if the maximal number of iterations is reached |
| * before the expected convergence is achieved. |
| */ |
| public double evaluate(double x, double epsilon, int maxIterations) { |
| double hPrev = updateIfCloseToZero(getB(0, x)); |
| |
| int n = 1; |
| double dPrev = 0.0; |
| double cPrev = hPrev; |
| double hN; |
| |
| while (n <= maxIterations) { |
| final double a = getA(n, x); |
| final double b = getB(n, x); |
| |
| double dN = updateIfCloseToZero(b + a * dPrev); |
| final double cN = updateIfCloseToZero(b + a / cPrev); |
| |
| dN = 1 / dN; |
| final double deltaN = cN * dN; |
| hN = hPrev * deltaN; |
| |
| if (Double.isInfinite(hN)) { |
| throw new FractionException( |
| "Continued fraction convergents diverged to +/- infinity for value {0}", x); |
| } |
| if (Double.isNaN(hN)) { |
| throw new FractionException( |
| "Continued fraction diverged to NaN for value {0}", x); |
| } |
| |
| if (Math.abs(deltaN - 1) < epsilon) { |
| return hN; |
| } |
| |
| dPrev = dN; |
| cPrev = cN; |
| hPrev = hN; |
| ++n; |
| } |
| |
| throw new FractionException("maximal count ({0}) exceeded", maxIterations); |
| } |
| |
| /** |
| * Returns the value, or if close to zero returns a small epsilon. |
| * |
| * <p>This method is used in Thompson & Barnett to monitor both the numerator and denominator |
| * ratios for approaches to zero. |
| * |
| * @param value the value |
| * @return the value (or small epsilon) |
| */ |
| private static double updateIfCloseToZero(double value) { |
| return Precision.equals(value, 0.0, SMALL) ? SMALL : value; |
| } |
| } |