CF {contfrac}R Documentation

Continued fraction convergent

Description

Returns continued fraction convergent using the modified Lenz's algorithm; function CF() deals with continued fractions and GCF() deals with generalized continued fractions.

Usage

CF(a, finite = FALSE, tol=0)
GCF(a,b, b0=0, finite = FALSE, tol=0)

Arguments

a,b In function CF(), the elements of a are the partial denomintors; in GCF() the elements of a are the partial numerators and the elements of b the partial denominators
finite Boolean, with default FALSE meaning to iterate Lenz's algorithm until convergence (a warning is given if the sequence has not converged); and TRUE meaning to evaluate the finite continued fraction
b0 In function GCF(), floor of the continued fraction
tol tolerance, with default 0 silently replaced with .Machine$double.eps

Details

Function CF() treats the first element of its argument as the integer part of the convergent.

Function CF() is a wrapper for GCF(); it includes special dispensation for infinite values (in which case the value of the appropriate finite CF is returned).

The implementation is in C; the real and complex cases are treated separately in the interests of efficiency.

The algorithm terminates when the convergence criterion is achieved irrespective of the value of finite.

Author(s)

Robin K. S. Hankin

References

See Also

convergents

Examples


phi <- (sqrt(5)+1)/2
phi_cf <- CF(rep(1,100))
phi - phi_cf     # should be small

# The tan function:

"tan_cf" <-
function(z,n=20){GCF(c(z, rep(-z^2,n-1)), seq(from=1,by=2, len=n)) }

z <- 1+1i
tan(z) - tan_cf(z)   # should be small


[Package contfrac version 1.1-7 Index]