clj-auto-diff

This is a library for automatic differentiation in Clojure. It's based and initiall ported from R6RS-AD.

Usage

Include it in your project using clojars,

[clj-auto-diff "0.1.3"]

An example where being able to compute a derivative lets us solve easily using Newton's method. Here we're solving for x, where e^x - 1.5 = tan^{-1}(x). We do this by finding the root of e^x - 1.5 - tan^{-1}(x) = 0.

(let [f (fn [x] (- (- (exp x) 1.5)
                   (atan x)))
      f' (diff f)
      convergent? (fn [{:keys [steps error] :or {steps 0
                                                error 1}}]
                    (or (< error 0.00001)
                        (> steps 20)))
      next-guess (fn [{:keys [x last steps] :or {last 0
                                                steps 0}}]
                   (let [guess (- x (/ (f x)
                                       (f' x)))]
                     {:steps (inc steps)
                      :error (- last guess)
                      :last x
                      :x guess}))]
  (first (drop-while #(not (convergent? %))
                     (iterate #(next-guess %)
                              {:x -7})))
  => {:error 1.8005508195528819E-9
      :last -14.101269772739967
      :steps 7
      :x -14.101269772739967})

License

This library is a port of R6RS-AD which was originally licensed GPL, but permission has been given by the original author to publish this under the MIT license.