Gradient descent: Difference between revisions
→{{header|Racket}}
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The minimum is at x[1] = 0.1073980565405569, x[1] = -1.2233251778997771 -- (32 bit)
</pre>
=={{header|Racket}}==
{{trans|Go}}
Note the different implementation of <code>grad</code>. I believe that the vector should be reset and only the partial derivative in a particular dimension is to be used. For this reason, I've _yet another_ result!
I could have used ∇ and Δ in the variable names, but it looked too confusing, so I've gone with _grad-_ and _del-_
<lang racket>#lang racket
(define (apply-vector f v)
(apply f (vector->list v)))
;; Provides a rough calculation of gradient g(v).
(define ((grad/del f) v δ #:fv (fv (apply-vector f v)))
(define dim (vector-length v))
(define tmp (vector-copy v))
(define grad (for/vector #:length dim ((i dim)
(v_i v))
(vector-set! tmp i (+ v_i δ))
(define ∂f/∂v_i (/ (- (apply-vector f tmp) fv) δ))
(vector-set! tmp i v_i)
∂f/∂v_i))
(values grad (sqrt (for/sum ((∂_i grad)) (sqr ∂_i)))))
(define (steepest-descent g x α tolerance)
(define grad/del-g (grad/del g))
(define (loop x δ α gx grad-gx del-gx b)
(cond
[(<= del-gx tolerance) x]
[else
(define δ´ (/ δ 2))
(define x´ (vector-map + (vector-map (curry * (- b)) grad-gx) x))
(define gx´ (apply-vector g x´))
(define-values (grad-gx´ del-gx´) (grad/del-g x´ δ´ #:fv gx´))
(define b´ (/ α del-gx´))
(if (> gx´ gx)
(loop x´ δ´ (/ α 2) gx grad-gx´ del-gx´ b´)
(loop x´ δ´ α gx´ grad-gx´ del-gx´ b´))]))
(define gx (apply-vector g x))
(define δ tolerance)
(define-values (grad-gx del-gx) (grad/del-g x δ #:fv gx))
(loop x δ α gx grad-gx del-gx (/ α del-gx)))
(define (Gradient-descent)
(steepest-descent
(λ (x y)
(+ (* (- x 1) (- x 1) (exp (- (sqr y))))
(* y (+ y 2) (exp (- (* 2 (sqr x)))))))
#(0.1 -1.) 0.1 0.0000006))
(module+ main
(Gradient-descent))
</lang>
{{out}}
<pre>'#(0.10760797905122492 -1.2232993981966753)</pre>
=={{header|TypeScript}}==
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