[R] Fibonacci

[David Winsemius]

On Apr 21, 2011, at 9:04 AM, Michael Dewey wrote:

> At 10:42 20/04/2011, Georgina Imberger wrote:
>> Hi!
>>
>> I am trying to work out the code to get a Fibonacci sequence, using  
>> the
>> while() loop and only one variable. And I can't figure it out.
>
>
> > phi <- 0.5 * (1 + sqrt(5))
> > phi
> [1] 1.618034
> > fib <- function(n) {(phi ^ n - (1 - phi) ^ n) / sqrt(5)}
> > fib(1:10)
> [1]  1  1  2  3  5  8 13 21 34 55
> >
>
> Admittedly this does not use a while loop as you requested

I like it!

 > test <-c(  1,  1,  2,  3,  5,  8, 13, 21, 34, 55)
 > test == fib(1:10)
  [1]  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE

To avoid such FAQ-tual puzzlement, it might be better to round to zero  
digits:

fib2 <- function(n) {round( (phi ^ n - (1 - phi) ^ n) / sqrt(5) ) }

 > test == fib2(1:10)
  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE


There are several packages that offer fib() functions of one name or  
another, including the gmp package which always seems to "think  
bigger" than I do. I cannot (trivially) see how that author does it  
with fibnum(), because it is in a .Call()

-- 
David
>
> Courtesy of Wikipedia
>
>
>> Fibonacci<-c(1,1)
>> while (max(Fibonacci)<500){
>> Fibonacci<-c(Fibonacci, (max(Fibonacci) + ?(Fibanacci)))
>> }
>>
>>
>> How can I tell R to take the value one before the max value? (Without
>> defining another variable)
>>
>> (Probably super easy... I am a beginner...)
>>
>> Thanks,
>> Georgie
>>
>>        [[alternative HTML version deleted]]
>
> Michael Dewey
> info at aghmed.fsnet.co.uk
> http://www.aghmed.fsnet.co.uk/home.html
>
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David Winsemius, MD
West Hartford, CT