Fibonacci series matrix version

fibonacci.R

#with expm

require(expm)
matrix(   c(0,1,1,1),   2,2 )    -> fibonacci
c(1L,1L)    -> start

start %*% (fibonacci %*% 1337)         #1337'th term-pair in Fibonacci series

#              [,1]          [,2]
#[1,] 1.887894e+279 3.054677e+279



eigen(fibonacci)  #think about THAT one!

#$values
#[1]  1.618034 -0.618034
#
#$vectors
#          [,1]       [,2]
#[1,] 0.5257311 -0.8506508
#[2,] 0.8506508  0.5257311





#without expm -- using metaprogramming instead

pm <- function(x) paste(x,collapse=" %*% ")


#build a string
pm( 'start', pm(rep( 'fibonacci', 12)), sep=' %*% ' )   -> i.wish.you.were.a.call   #why is the second sep necessary?

# [1] "start %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci %*% fibonacci"

eval(i.wish.you.were.a.call)    #i wish you worked