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Implementation of Newton Raphson algorithm in clojure
(ns newton-raphson.core)
;;utility function for list manipulation
(defn keep-list [expr]
(if (and (coll? expr) (not (= 1 (count expr)))) (list expr) expr))
(defn to-list [expr]
(cond (list? expr) expr
(coll? expr) (seq expr)
:default (list expr)))
(defn replace-in-list [coll old-val new-val]
(map #(cond
(coll? %) (replace-in-list % old-val new-val)
(= % old-val) new-val
:default %)
coll))
(defn derivative-prod [expr variable]
(conj
(let [elts (rest expr)]
(loop [members elts
res ()
tmp (first elts)
previous ()
next (rest elts)]
(cond (= () members) res
:default
(recur
(rest members)
(conj res (concat '(*) previous (keep-list (to-list (derivative tmp variable))) next)) ;;inelegant
(second members)
(conj previous tmp)
(rest next)))))
'+))
;;messy implementation of mathematical derivative
(defn derivative [expr variable]
;;not simplified derivative calculations
(cond (number? expr) 0;;(list 0)
(symbol? expr) (if (= variable expr) 1 0);;(list 1) (list 0))
:default
(let [op (first expr)
args (rest expr)
der #(derivative % variable)]
(cond (= '+ op) (conj (map #(derivative % variable) (rest expr)) '+)
(= '* op) (derivative-prod expr variable)
(= '- op) (conj (map #(derivative % variable) (rest expr)) '-)
;;(= '- op) (list '- (derivative (second expr) variable) (map #(derivative % variable) (rest (rest expr))))
(= '/ op) (if (= 2 (count args)) (let [u (first args)
v (second args)]
(list '/ (list '- (list '* (der u) v) (list '* u (der v))) (list '* v v)))
(der (list '/ (first args) (concat '(*) (rest args)))))
(= 'sin (first expr)) (list '* (derivative (second expr) variable) (list 'cos (second expr)))
(= 'cos op) (list '* -1 (der (second expr)) (list 'sin (second expr)))
(= 'exp op) (list '* (der (first args)) (list 'exp (first args)))
:default (do (println (first expr) "not handled yet...") nil)))))
(defn my-eval [expr variable value]
(let [new-expr (replace-in-list expr variable value)]
(eval new-expr)))
(defn abs [x]
(if (< x 0) (- x) x))
(defn to-bigdec [x]
(if (ratio? x) (/ (bigdec (numerator x)) (bigdec (denominator x))) (bigdec x)))
;;implementation of newton-raphson algorithm
(defn nr-solve [expr variable start tol]
"solve (expr = 0) as an equation in *variable*"
(let [der (derivative expr variable)
run-algo
(fn [s]
(let [slope (my-eval der variable s)
k (my-eval expr variable s)
candidate (- s (/ k slope))]
(if (< (abs (my-eval expr variable candidate)) tol)
candidate
(recur candidate ))))
sol (run-algo start)]
sol))
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