Created
December 16, 2011 23:20
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Calculate polynomials and their derivatives
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; Credit: http://java.ociweb.com/mark/clojure/article.html | |
(defn- polynomial | |
"computes the value of a polynomial | |
with the given coefficients for a given value x" | |
[coefs x] | |
; For example, if coefs contains 3 values then exponents is (2 1 0). | |
(let [exponents (reverse (range (count coefs)))] | |
; Multiply each coefficient by x raised to the corresponding exponent | |
; and sum those results. | |
; coefs go into %1 and exponents go into %2. | |
(apply + (map #(* %1 (Math/pow x %2)) coefs exponents)))) | |
(defn- derivative | |
"computes the value of the derivative of a polynomial | |
with the given coefficients for a given value x" | |
[coefs x] | |
; The coefficients of the derivative function are obtained by | |
; multiplying all but the last coefficient by its corresponding exponent. | |
; The extra exponent will be ignored. | |
(let [exponents (reverse (range (count coefs))) | |
derivative-coefs (map #(* %1 %2) (butlast coefs) exponents)] | |
(polynomial derivative-coefs x))) | |
(def f (partial polynomial [2 1 3])) ; 2x^2 + x + 3 | |
(def f-prime (partial derivative [2 1 3])) ; 4x + 1 | |
(println "f(2) =" (f 2)) ; -> 13.0 | |
(println "f'(2) =" (f-prime 2)) ; -> 9.0 |
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