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RobinHankin / contfrac

Utilities for creating and evaluating continued fractions in R
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Continued fractions in R

Build Status CRAN\_Status\_Badge Rdoc

Continued fractions

A continued fraction is an expression of the form

a\_0 +\\frac{1}{a\_1+\\frac{1}{a\_2+\\frac{1}{\\ddots}}}= a\_0+\\frac{1}{a\_1+}\\, \\frac{1}{a\_2+}\\ldots

Such expressions are interesting and useful in a number of mathematical applications. A generalized continued fraction is an expression of the form

b\_0 +\\frac{a\_1}{b\_1+\\frac{a\_2}{b\_2+\\frac{a\_3}{b\_3+\\ddots}}} = b\_0+\\frac{a\_1}{b\_1+}\\, \\frac{a\_2}{b\_2+} \\frac{a\_3}{b\_3+}\\ldots

The contfrac package provides functionality to deal with both these.

Installation

To install the most recent stable version on CRAN, use install.packages() at the R prompt:

R> install.packages("contfrac")

And then to load the package use library():

library("contfrac")

Package features

The package provides functionality for dealing with continued fractions.

as_cf(pi,n=7)   # convert pi to continued fraction form
#> [1]   3   7  15   1 292   1   1

We can evaluate convergents of any sequence using convergents() or nconv():

convergents(1:8)
#> $A
#> [1]     1     3    10    43   225  1393  9976 81201
#> 
#> $B
#> [1]     1     2     7    30   157   972  6961 56660
nconv(1:8)
#> [1] 1.433127

The package uses standard IEEE arithmetic so is not reliable past a certain point, shown here by expanding the golden ratio:

as_cf((1+sqrt(5))/2,n=50)
#>  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [39] 2 2 1 8 2 2 2 3 2 1 2 3

Further information

For more details, and some discussion of the mathematics of continued fractions, see the package vignette.