| 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