From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Thu, 27 May 2010 06:52:47 +0000 (+0530)
Subject: worked thru parts of 1.3.4
X-Git-Url: https://git.rkrishnan.org/vdrive/%22news.html/simplejson//%22%3C?a=commitdiff_plain;h=4deef005777d579d07885ecb96752a2a859f80a2;p=sicp.git

worked thru parts of 1.3.4
---

diff --git a/src/sicp/ch1_3.clj b/src/sicp/ch1_3.clj
index ebf7a20..5aaf159 100644
--- a/src/sicp/ch1_3.clj
+++ b/src/sicp/ch1_3.clj
@@ -92,4 +92,41 @@
 ;;;=> 3.162277660168379
 (mysqrt 4)
 ;;;=> 2.000000000000002
-)
\ No newline at end of file
+)
+
+;; section 1.3.4
+(defn average-damp [f]
+  (fn [x] (average x (f x))))
+
+(defn new-sqrt [x]
+  (fixed-point (average-damp (fn [y] (/ x y)))
+	       1.0))
+
+(defn new-cuberoot [x]
+  (fixed-point (average-damp (fn [y] (/ x (square y))))
+	       1.0))
+
+;; newton's method of root finding
+;; values of x for which g(x) = 0 is the same as
+;; fixed point of f(x) where f(x) = x - g(x)/Dg(x)
+;; where Dg(x) is the derivative of g(x)
+
+(def dx 0.00001)
+
+(defn deriv [g]
+  (fn [x] (/ (- (g (+ x dx))
+		(g x))
+	     dx)))
+
+(defn newton-transform [g]
+  (fn [x] (- x
+	     (/ (g x)
+		((deriv g) x)))))
+
+(defn newton-method [g guess]
+  (fixed-point (newton-transform g)
+	       1.0))
+
+(defn newton-sqrt [x]
+  (newton-method (fn [y] (- (square y) x))
+		 1.0))
\ No newline at end of file
diff --git a/src/sicp/utils.clj b/src/sicp/utils.clj
index 3ab538c..f5c3e9c 100644
--- a/src/sicp/utils.clj
+++ b/src/sicp/utils.clj
@@ -35,8 +35,9 @@
     a
     (gcd b (rem a b))))
 
-(defn average [a b]
-  (/ (+ a b) 2.0))
+(defn average [ & coll]
+  (/ (reduce + coll)
+     (float (count coll))))
 
 (defmacro microbench
   " Evaluates the expression n number of times, returning the average