Clean up Monte Carlo integration in Racket (#781)

* Clean up Monte Carlo integration in Racket

* Add blank lines in Monte Carlo integration in Clojure

* Change Racket lang include from lisp to racket

Author: berquist

contents/monte_carlo_integration/code/clojure/monte_carlo.clj

@@ -8,9 +8,11 @@
       (map #(* % %))
       (reduce +))
      (* r r)))
+
 (defn rand-point [r]
   "return a random point from (0,0) inclusive to (r,r) exclusive"
   (repeatedly 2 #(rand r)))
+
 (defn monte-carlo [n r]
   "take the number of random points and radius return an estimate to
 pi"
@@ -22,11 +24,12 @@ pi"
                  (if (in-circle? (rand-point r) r)
                    (inc count)
                    count))))))
+
 (defn -main []
   (let [constant-pi Math/PI
         computed-pi (monte-carlo 10000000 2) ;; this may take some time on lower end machines
         difference (Math/abs (- constant-pi computed-pi))
         error (* 100 (/ difference constant-pi))]
     (println "world's PI: " constant-pi
-             ",our PI: "    (double computed-pi)
+             ",our PI: " (double computed-pi)
              ",error: " error)))

contents/monte_carlo_integration/code/racket/monte_carlo.rkt

@@ -1,22 +1,25 @@
-#lang racket
-(define (in_circle x y)
-  (< (+ (sqr x) (sqr y)) 1)
- )
+#lang racket/base
 
-(define (monte_carlo_pi n)
-  (* (/ (local ((define (monte_carlo* n count)
+(require racket/local)
+(require racket/math)
+
+(define (in-circle x y)
+  "Checks if a point is in a unit circle"
+  (< (+ (sqr x) (sqr y)) 1))
+
+(define (monte-carlo-pi n)
+  "Returns an approximation of pi"
+  (* (/ (local ((define (monte-carlo-pi* n count)
                   (if (= n 0)
                       count
-                      (monte_carlo_pi* (sub1 n) 
-                                    (if (in_circle (random) (random)) 
-                                        (add1 count)
-                                        count
-                                    )
-                      )
-                  )
-               )) (monte_carlo_pi* n 0)
-        ) n) 4)
-  )
-
+                      (monte-carlo-pi* (sub1 n) 
+                                       (if (in-circle (random) (random)) 
+                                           (add1 count)
+                                           count)))))
+          (monte-carlo-pi* n 0)) n) 4))
 
-(display  (monte_carlo_pi 1000))
+(define nsamples 5000000)
+(define pi-estimate (monte-carlo-pi nsamples))
+(displayln (string-append "Estimate (rational): " (number->string pi-estimate)))
+(displayln (string-append "Estimate (float): " (number->string (real->single-flonum pi-estimate))))
+(displayln (string-append "Error:" (number->string (* (/ (abs (- pi-estimate pi)) pi) 100))))

contents/monte_carlo_integration/monte_carlo_integration.md

@@ -80,7 +80,7 @@ each point is tested to see whether it's in the circle or not:
 {% sample lang="lua" %}
 [import:2-4, lang="lua"](code/lua/monte_carlo.lua)
 {% sample lang="racket" %}
-[import:2-4, lang:"lisp"](code/racket/monte_carlo.rkt)
+[import:6-8, lang:"racket"](code/racket/monte_carlo.rkt)
 {% sample lang="scala" %}
 [import:3-3, lang:"scala"](code/scala/monte_carlo.scala)
 {% sample lang="lisp" %}
@@ -188,7 +188,7 @@ Feel free to submit your version via pull request, and thanks for reading!
 {% sample lang="lua" %}
 [import, lang="lua"](code/lua/monte_carlo.lua)
 {% sample lang="racket" %}
-[import, lang:"lisp"](code/racket/monte_carlo.rkt)
+[import, lang:"racket"](code/racket/monte_carlo.rkt)
 {% sample lang="scala" %}
 [import, lang:"scala"](code/scala/monte_carlo.scala)
 {% sample lang="lisp" %}