CF {contfrac} | R Documentation |
Returns continued fraction convergent using the modified Lenz's
algorithm; function CF()
deals with continued fractions and
GCF()
deals with generalized continued fractions.
CF(a, finite = FALSE, tol=0) GCF(a,b, b0=0, finite = FALSE, tol=0)
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 |
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
.
Robin K. S. Hankin
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