solution to 1.44. Extremely interesting problem

diff --git a/src/sicp/ex1_44.clj b/src/sicp/ex1_44.clj
new file mode 100644 (file)
index 0000000..e6cf38b
--- /dev/null
+++ b/src/sicp/ex1_44.clj
@@ -0,0 +1,50 @@
+(ns sicp.ex1_44
+  (:use [clojure.contrib test-is]
+       [sicp utils]
+       [sicp ch1_3]
+       [sicp ex1_43]))
+
+(def dx1 0.00001)
+
+(defn smooth [f]
+  (fn [x]
+    (average (f (- x dx1))
+            (f x)
+            (f (+ x dx1)))))
+
+;; smooth takes a function as argument. repeated takes a function
+;; which needs to be repeated. Here it is the smooth function and
+;; the number of times it needs to be repeated. We call the function
+;; returned by repeated with f.
+(defn smooth-repeatedly [f n]
+  ((repeated smooth n) f))
+
+;; borrowing an idea from Drew Hess' solutions, we generate a test impulse
+;; function
+(defn impulse-maker [x a]
+  (fn [y] (if (= y x)
+           a
+           0)))
+
+;; we define a function which has an impulse at x=2 with a value 10.
+(defn my-impulse-func [x]
+  ((impulse-maker 2 10) x))
+
+(comment
+((smooth my-impulse-func) 2)
+;;=> 3.3333333
+user> ((smooth my-impulse-func) 1)
+;;=> 0.0
+user> ((smooth (smooth my-impulse-func)) 2)
+;;=> 3.3333333
+user> ((smooth (smooth (smooth my-impulse-func))) 2)
+;;=> 2.5925925
+
+;; now using our new function
+((smooth-repeatedly my-impulse-func 1) 2)
+;;=> 3.3333333
+user> ((smooth-repeatedly my-impulse-func 2) 2)
+;;=> 3.3333333
+user> ((smooth-repeatedly my-impulse-func 3) 2)
+;;=> 2.5925925
+)
\ No newline at end of file