attempt at quadratic regression search

quadraticregression.clj

@@ -0,0 +1,66 @@
+;; What is the best fit for a+bx+cxx here?
+(defn fit [[ a b c]]
+  (let [predictions (map #(+ a (* b %) (* c % %)) (range 1 8))]
+    [(reduce + (map #(* % %)
+                    (map - predictions                    
+                         [2 6 14 26 40 60 96]))) 
+     [a b c]
+     predictions]))
+
+
+(defn improve-guess [a b c delta]
+  (let [candidates (list [a b c]
+                         [(+ a delta) b c] 
+                         [(- a delta) b c]
+                         [a (+ b delta) c] 
+                         [a (- b delta) c]
+                         [a b (+ c delta)] 
+                         [a b (- c delta)])
+        scores (sort (map fit candidates))
+        ]
+    (first scores)))
+
+
+
+
+(improve-guess 1 1 1 4) ;-> [639 [1 5 1] (7 15 25 37 51 67 85)]
+(improve-guess 1 5 1 4) ;-> [407 [-3 5 1] (3 11 21 33 47 63 81)]
+(improve-guess -3 5 1 4) ;-> [399 [-7 5 1] (-1 7 17 29 43 59 77)]
+(improve-guess -7 5 1 4) ;-> [399 [-7 5 1] (-1 7 17 29 43 59 77)]
+(improve-guess -7 5 1 2) ;-> [375 [-5 5 1] (1 9 19 31 45 61 79)]
+(improve-guess -5 5 1 2) ;-> [375 [-5 5 1] (1 9 19 31 45 61 79)]
+(improve-guess -5 5 1 1) ;-> [375 [-5 5 1] (1 9 19 31 45 61 79)]
+(improve-guess -5 5 1 0.5) ;-> [362.0 [-5 5.5 1] (1.5 10.0 20.5 33.0 47.5 64.0 82.5)]
+
+
+(defn refine [a b c delta]
+  (let [[score [na nb nc ] predictions ] (improve-guess a b c delta)]
+    (if (= [na nb nc] [a b c])
+      [[score [na nb nc ] predictions ]]
+      (refine na nb nc delta))))
+
+;; [2 6 14 26 40 60 96]
+
+(refine -5 5 1 0.1) ;-> [[203.7099999999998 [-7.89999999999999 4.200000000000003 1.3000000000000003] (-2.3999999999999866 5.700000000000017 16.40000000000002 29.700000000000024 45.60000000000003 64.10000000000004 85.20000000000005)]]
+(refine 1 1 1 0.1) ;-> [[125.31000000000004 [-3.1000000000000014 1.0 1.7000000000000006] (-0.4000000000000008 5.700000000000001 15.200000000000003 28.10000000000001 44.40000000000001 64.10000000000002 87.20000000000002)]]
+(refine 4.41 -4.48 2.41 0.01) ;-> [[50.068 [4.42 -4.49 2.42] (2.3499999999999996 5.119999999999999 12.73 25.18 42.47 64.6 91.57)]]
+(refine 4.42 -4.49 2.42 0.005)
+
+
+
+
+
+(refine 1 1 1 4) ;-> [[399 [-7 5 1] (-1 7 17 29 43 59 77)] [399 [-7 5 1] (-1 7 17 29 43 59 77)]]
+(refine -7 5 1 2) ;-> [[375 [-5 5 1] (1 9 19 31 45 61 79)] [375 [-5 5 1] (1 9 19 31 45 61 79)]]
+(refine -5 5 1 1) ;-> [[375 [-5 5 1] (1 9 19 31 45 61 79)] [375 [-5 5 1] (1 9 19 31 45 61 79)]]
+(refine -5 5 1 0.5) ;-> [[330.0 [-7.0 5.5 1] (-0.5 8.0 18.5 31.0 45.5 62.0 80.5)] [330.0 [-7.0 5.5 1] (-0.5 8.0 18.5 31.0 45.5 62.0 80.5)]]
+(refine -7 5.5 1 0.1) ;-> [[227.50999999999982 [-9.099999999999993 5.000000000000002 1.2000000000000002] (-2.8999999999999906 5.700000000000012 16.700000000000014 30.100000000000016 45.90000000000002 64.10000000000002 84.70000000000003)] [227.50999999999982 [-9.099999999999993 5.000000000000002 1.2000000000000002] (-2.8999999999999906 5.700000000000012 16.700000000000014 30.100000000000016 45.90000000000002 64.10000000000002 84.70000000000003)]]
+
+(refine 1 1 1 4)
+
+
+
+
+
+
+