analysis.egi

(assert-equal "d/d - case 1"
  (d/d (** x 2) x)
  (* 2 x))

(assert-equal "d/d - case 2"
  (d/d (** a (** x 2)) x)
  (* 2 (** a x^2) (log a) x))

(assert-equal "d/d - case 3"
  (d/d (* (cos x) (sin x)) x)
  (+ (* -1 (sin x)^2) (cos x)^2))

(assert-equal "d/d - case 4"
  (d/d (sigmoid z) z)
  (/ (exp (* -1 z)) (+ 1 (* 2 (exp (* -1 z))) (exp (* -1 z))^2)))

(assert-equal "d/d - case 5"
  (d/d (d/d (log x) x) x)
  (/ -1 x^2))

(assert-equal "tailor-expansion - case 1"
  (take 4 (taylor-expansion (** e (* i x)) x 0))
  {1 (* i x) (/ (* -1 x^2) 2) (/ (* -1 i x^3) 6)})

(assert-equal "tailor-expansion - case 2"
  (take 4 (taylor-expansion (* i (sin x)) x 0))
  {0 (* i x) 0 (/ (* -1 i x^3) 6)})

;(assert-equal "multivariate-tailor-expansion - case 1"
;  (take 3 (multivariate-taylor-expansion (f x y) [| x y |] [| 0 0 |]))
;  {(f 0 0) (+ (* x (f|1 0 0)) (* y (f|2 0 0))) (/ (+ (* x^2 (f|1|1 0 0)) (* 2 x y (f|1|2 0 0)) (* y^2 (f|2|2 0 0))) 2)})

(assert-equal "multivariate-tailor-expansion - case 2"
  (take 3 (multivariate-taylor-expansion (** e (+ x y)) [| x y |] [| 0 0 |]))
  {1 (+ x y) (/ (+ x^2 (* 2 x y) y^2) 2)})

(assert-equal "function expr"
  (let {[$f (function [x y])]}
    (d/d f y))
  (let {[$f (function [x y])]}
    (user-refs f {y})))