From: Ramakrishnan Muthukrishnan Date: Mon, 17 May 2010 08:01:45 +0000 (+0530) Subject: Solution to 1.36. X-Git-Url: https://git.rkrishnan.org/pf/content/en/seg/bcase/%22news.html/index.php?a=commitdiff_plain;h=b1d84232d29f1b6fc3ac980188d55bc4e66ee1b9;p=sicp.git Solution to 1.36. --- diff --git a/src/sicp/ex1_36.clj b/src/sicp/ex1_36.clj new file mode 100644 index 0000000..5de257a --- /dev/null +++ b/src/sicp/ex1_36.clj @@ -0,0 +1,89 @@ +;; Exercise 1.36. Modify fixed-point so that it prints the sequence +;; of approximations it generates, using the newline and display +;; primitives shown in exercise 1.22. Then find a solution to +;; x^x = 1000 +;; by finding a fixed point of x |-> log(1000)/log(x). +;; +;; Compare the number of steps this takes with and without average damping. +(ns sicp.ex1_36 + (:use [sicp utils] + [clojure.contrib test-is])) + +(defn close-enough? [x y tolerance] + (< (abs (- x y)) tolerance)) + +(defn fixed-point [f guess] + (let [next (f guess) + nsteps 0] + (do + (println "new guess is " next) + (if (close-enough? next guess 0.00001) + next + (fixed-point f next))))) + +;; fixed point +(comment +(fixed-point #(/ (Math/log 1000) (Math/log %)) 1.1) +new guess is 72.47657378429035 +new guess is 1.6127318474109593 +new guess is 14.45350138636525 +new guess is 2.5862669415385087 +new guess is 7.269672273367045 +new guess is 3.4822383620848467 +new guess is 5.536500810236703 +new guess is 4.036406406288111 +new guess is 4.95053682041456 +new guess is 4.318707390180805 +new guess is 4.721778787145103 +new guess is 4.450341068884912 +new guess is 4.626821434106115 +new guess is 4.509360945293209 +new guess is 4.586349500915509 +new guess is 4.535372639594589 +new guess is 4.568901484845316 +new guess is 4.546751100777536 +new guess is 4.561341971741742 +new guess is 4.551712230641226 +new guess is 4.558059671677587 +new guess is 4.55387226495538 +new guess is 4.556633177654167 +new guess is 4.554812144696459 +new guess is 4.556012967736543 +new guess is 4.555220997683307 +new guess is 4.555743265552239 +new guess is 4.555398830243649 +new guess is 4.555625974816275 +new guess is 4.555476175432173 +new guess is 4.555574964557791 +new guess is 4.555509814636753 +new guess is 4.555552779647764 +new guess is 4.555524444961165 +new guess is 4.555543131130589 +new guess is 4.555530807938518 +new guess is 4.555538934848503 +;; => 4.555538934848503 +) + +;; with average damping +(comment +(defn average [x y] (/ (+ x y) 2.0)) +(fixed-point #(average % (/ (Math/log 1000) (Math/log %))) 1.1) +new guess is 36.78828689214517 +new guess is 19.352175531882512 +new guess is 10.84183367957568 +new guess is 6.870048352141772 +new guess is 5.227224961967156 +new guess is 4.701960195159289 +new guess is 4.582196773201124 +new guess is 4.560134229703681 +new guess is 4.5563204194309606 +new guess is 4.555669361784037 +new guess is 4.555558462975639 +new guess is 4.55553957996306 +new guess is 4.555536364911781 +;; => 4.555536364911781 +) + +(comment +"As we can see, average damping significantly reduces the number of steps." +) \ No newline at end of file