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https://issues.apache.org/jira/browse/NUMBERS-175?focusedWorklogId=685815&page=com.atlassian.jira.plugin.system.issuetabpanels:worklog-tabpanel#worklog-685815
]
ASF GitHub Bot logged work on NUMBERS-175:
------------------------------------------
Author: ASF GitHub Bot
Created on: 24/Nov/21 13:06
Start Date: 24/Nov/21 13:06
Worklog Time Spent: 10m
Work Description: asfgit merged pull request #109:
URL: https://github.com/apache/commons-numbers/pull/109
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Issue Time Tracking
-------------------
Worklog Id: (was: 685815)
Time Spent: 20m (was: 10m)
> Add continued fraction implementations using a generator of terms
> -----------------------------------------------------------------
>
> Key: NUMBERS-175
> URL: https://issues.apache.org/jira/browse/NUMBERS-175
> Project: Commons Numbers
> Issue Type: Improvement
> Components: fraction
> Affects Versions: 1.0
> Reporter: Alex Herbert
> Priority: Minor
> Time Spent: 20m
> Remaining Estimate: 0h
>
> The ContinuedFraction class allows computation of:
> {noformat}
> b0 + a1
> ------------------
> b1 + a2
> -------------
> b2 + a3
> --------
> b3 + ...{noformat}
> This is done using an abstract class that is extended to implement the
> methods to get the terms:
> {code:java}
> double getA(int n, double x);
> double getB(int n, double x);{code}
> This allows the fraction to be reused to generate results for different
> points to evaluate. However:
> * It does not lend itself to fractions where the terms can be computed using
> recursion:
> {noformat}
> b(n+1) = f( b(n) ) {noformat}
> * It requires two method calls to generate terms a_n and b_n for each
> iteration thus preventing optimisation of the computation using the input n
> for values shared between computation of a and b.
> An alternative method is to support a generator of the paired terms a_n and
> b_n:
> {code:java}
> static double continuedFraction(Supplier<double[]> gen);{code}
> To be used in a single evaluation as:
> {code:java}
> Supplier<double[]> goldenRatio = () -> return new double[] {1, 1};
> double gr = continuedFraction(goldenRatio);
> // gr = 1.61803398874...{code}
> An additional feature is to support a simple continued fraction where all
> partial numerators are 1:
> {noformat}
> b0 + 1
> ------------------
> b1 + 1
> -------------
> b2 + 1
> --------
> b3 + ...
> {noformat}
> E.g. using:
> {code:java}
> static double simpleContinuedFraction(DoubleSupplier gen); {code}
> h3. Addition
> In some situations it is an advantage to not evaluate the leading term b0.
> The term may not be part of a regular series, or may be zero:
> {noformat}
> a1
> ------------------
> b1 + a2
> -------------
> b2 + a3
> --------
> b3 + ...
> {noformat}
> h3. API
> Using the nomeclature from Wikipedia and Wolfram suggests the following:
> {code:java}
> public static final class GeneralizedContinuedFraction {
> /**
> * Evaluate the continued fraction from the generator for partial
> numerator
> * a and partial denominator b.
> * <pre>
> * b0 + a1
> * ------------------
> * b1 + a2
> * -------------
> * b2 + a3
> * --------
> * b3 + ...
> * </pre>
> *
> * <p>Note: The first generated partial numerator a0 is discarded.
> *
> * @param gen Generator
> * @return the continued fraction value
> */
> public static double value(Supplier<double[]> gen);
> /**
> * Evaluate the continued fraction from the generator for partial
> numerator
> * a and partial denominator b.
> * <pre>
> * a1
> * ------------------
> * b1 + a2
> * -------------
> * b2 + a3
> * --------
> * b3 + ...
> * </pre>
> *
> * <p>Note: Both of the first terms a and b are used.
> *
> * @param gen Generator
> * @return the continued fraction value
> */
> public static double valueA(Supplier<double[]> gen);
> }
> public static final class SimpleContinuedFraction {
> public static double value(DoubleSupplier gen);
> public static double valueA(DoubleSupplier gen);
> }
> {code}
> The API should support the optional parameters to control the convergence
> tolerance and the maximum number of iterations.
> The variant to evaluate without the leading b0 term is not essential. It can
> be evaluated by starting the generator at the next iteration using:
> {code:java}
> Supplier<double[]> gen = ...; // Start at terms (a1,b1)
> // Evaluation will discard a1;
> // this value (separately computed) is then used to compute the result
> double value = a1 / GeneralizedContinuedFraction.value(gen);{code}
> This variant is present in the Boost c++ library and used to evaluate terms
> for the gamma function.
> See:
> [https://en.wikipedia.org/wiki/Continued_fraction]
> [https://mathworld.wolfram.com/SimpleContinuedFraction.html]
> [https://mathworld.wolfram.com/GeneralizedContinuedFraction.html]
> [Boost Continued Fraction (v
> 1_77_0)|https://www.boost.org/doc/libs/1_77_0/libs/math/doc/html/math_toolkit/internals/cf.html]
>
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