Data commit

Task/Demings-funnel/Racket/demings-funnel.rkt

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+#lang racket
+(require math/distributions math/statistics plot)
+
+(define dxs '(-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275 1.251 -0.231
+              -0.401 0.269 0.491 0.951 1.150 0.001 -0.382 0.161 0.915 2.080 -2.337
+              0.034 -0.126 0.014 0.709 0.129 -1.093 -0.483 -1.193 0.020 -0.051
+              0.047 -0.095 0.695 0.340 -0.182 0.287 0.213 -0.423 -0.021 -0.134 1.798
+              0.021 -1.099 -0.361 1.636 -1.134 1.315 0.201 0.034 0.097 -0.170 0.054
+              -0.553 -0.024 -0.181 -0.700 -0.361 -0.789 0.279 -0.174 -0.009 -0.323
+              -0.658 0.348 -0.528 0.881 0.021 -0.853 0.157 0.648 1.774 -1.043 0.051
+              0.021 0.247 -0.310 0.171 0.000 0.106 0.024 -0.386 0.962 0.765 -0.125
+              -0.289 0.521 0.017 0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598
+              0.443 -0.521 -0.799 0.087))
+
+(define dys '(0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395 0.490 -0.682 -0.065
+              0.242 -0.288 0.658 0.459 0.000 0.426 0.205 -0.765 -2.188 -0.742 -0.010
+              0.089 0.208 0.585 0.633 -0.444 -0.351 -1.087 0.199 0.701 0.096 -0.025
+              -0.868 1.051 0.157 0.216 0.162 0.249 -0.007 0.009 0.508 -0.790 0.723
+              0.881 -0.508 0.393 -0.226 0.710 0.038 -0.217 0.831 0.480 0.407 0.447
+              -0.295 1.126 0.380 0.549 -0.445 -0.046 0.428 -0.074 0.217 -0.822 0.491
+              1.347 -0.141 1.230 -0.044 0.079 0.219 0.698 0.275 0.056 0.031 0.421 0.064
+              0.721 0.104 -0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477 1.537
+              -0.901 0.939 -0.411 0.341 -0.411 0.106 0.224 -0.947 -1.424 -0.542 -1.032))
+
+;(define radii (map abs (sample (normal-dist 0 1) 100)))
+;(define angles (sample (uniform-dist (- pi) pi) 100))
+;(define dxs (map (λ (r theta) (* r (cos theta))) radii angles))
+;(define dys (map (λ (r theta) (* r (sin theta))) radii angles))
+
+(define (funnel dxs rule)
+  (let ([x 0])
+    (for/fold ([rxs null])
+      ([dx dxs])
+      (let ([rx (+ x dx)])
+        (set! x (rule x dx))
+        (cons rx rxs)))))
+
+(define (experiment label rule)
+  (define (p s) (real->decimal-string s 4))
+  (let ([rxs (funnel dxs rule)]
+        [rys (funnel dys rule)])
+    (displayln label)
+    (printf "Mean x, y   : ~a, ~a\n" (p (mean rxs)) (p (mean rys)))
+    (printf "Std dev x, y: ~a, ~a\n\n" (p (stddev rxs)) (p (stddev rys)))
+    #;(plot (points (map vector rxs rys)
+          #:x-min -15 #:x-max 15 #:y-min -15 #:y-max 15))))
+
+(experiment "Rule 1:" (λ (z dz) 0))
+(experiment "Rule 2:" (λ (z dz) (- dz)))
+(experiment "Rule 3:" (λ (z dz) (- (+ z dz))))
+(experiment "Rule 4:" (λ (z dz) (+ z dz)))