square root by newton raphson method

gistfile1.clj

(ns newton-raphson
  (:use
    [clojure.contrib.math :only (abs)]
    [clojure.contrib.seq  :only (find-first)]))


(defn newton-raphson [improve, init]
  (iterate improve init))

(defn within [eps xs]
  (second
    (find-first
      (fn [[a b]] (<= (abs (/ (- a b) b)) eps))
      (partition 2 1 xs))))


(defn improve-sqrt [n x]
  (/ (+ x (/ n x)) 2))

(defn sqrt-seq-nr [n]
  (newton-raphson (partial improve-sqrt n) 1))

(defn sqrt-nr [n eps]
  (within eps (sqrt-seq-nr n)))


;; newton-raphson> (take 10 (map double (sqrt-seq-nr 36)))
;; (1.0 18.5 10.22297297297297 6.872226737643129 6.055351744849479 6.000252984119419 6.000000005333189 6.0 6.0 6.0)
;; newton-raphson> (double (sqrt-nr 2 (/ 1 100000)))
;; 1.41421356237469