Talk:Arithmetic-geometric mean
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What is the arithmetic-geometric mean of 1 and 2? AxelBoldt
- To answer this, I added a Scheme implementation of the algorithm. (agmean 1 2 .000000001) => 1.4567910310469068 -- Damian Yerrick
Here is an alternative implementation in Scheme that is conceptually similar but is simpler (I checked this in Guile and it works):
(define (agm a b epsilon)
;; Determine if two numbers are already very close together
(define (ratio-diff a b) (abs (/ (- a b) b)))
;; Actually do the computation
(define (loop a b)
;; If they're already really close together, just return the arithmetic mean
(if (< (ratio-diff a b) epsilon)
(/ (+ a b) 2)
(loop (sqrt (* a b)) (/ (+ a b) 2)))) ; otherwise, do another step
;; Error checking
(if (or (not (real? a))
(not (real? b))
(<= a 0)
(<= b 0))
(error 'agm "~s and ~s must both be positive real numbers" a b)
(loop a b)))
