Clay

(ns demo
  (:require [fastmath.interpolation :as interpolation]
            [scicloj.tableplot.v1.plotly :as plotly]
            [tablecloth.api :as tc]))

(def px [0 1 3 4 5 8 9])

(def py [0 0 1 7 3 4 6])

(def in    (tc/dataset {:x (range 0 8.0 0.01)}))

subset of available interpolations.

(def kinds [:linear
            :cubic
            :monotone
            :akima
            :neville
            :divided-difference
            :polynomial
            :sprague
            :step-before
            :step-after])

kinds

[:linear
 :cubic
 :monotone
 :akima
 :neville
 :divided-difference
 :polynomial
 :sprague
 :step-before
 :step-after]

(def results
  (->> (for [k kinds]
         (let [f (interpolation/interpolation k px py)]
           [k (mapv f x)]))
       (reduce (fn [acc [k v]]
                 (tc/add-column acc k v)) in)))

results

_unnamed [801 11]:

:x	:linear	:cubic	:monotone	:akima	:neville	:divided-difference	:polynomial	:sprague	:step-before	:step-after
0.00	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	0.00000000	0.0	0.0
0.01	0.00000000	0.00446629	0.00000000	-0.00165000	0.22014219	0.22014219	0.22014219	0.00277052	0.0	0.0
0.02	0.00000000	0.00892990	0.00000000	-0.00326667	0.43246557	0.43246557	0.43246557	0.00499778	0.0	0.0
0.03	0.00000000	0.01338816	0.00000000	-0.00485000	0.63710020	0.63710020	0.63710020	0.00673977	0.0	0.0
0.04	0.00000000	0.01783837	0.00000000	-0.00640000	0.83417486	0.83417486	0.83417486	0.00805164	0.0	0.0
0.05	0.00000000	0.02227786	0.00000000	-0.00791667	1.02381716	1.02381716	1.02381716	0.00898572	0.0	0.0
0.06	0.00000000	0.02670395	0.00000000	-0.00940000	1.20615347	1.20615347	1.20615347	0.00959164	0.0	0.0
0.07	0.00000000	0.03111396	0.00000000	-0.01085000	1.38130896	1.38130896	1.38130896	0.00991630	0.0	0.0
0.08	0.00000000	0.03550521	0.00000000	-0.01226667	1.54940760	1.54940760	1.54940760	0.01000402	0.0	0.0
0.09	0.00000000	0.03987503	0.00000000	-0.01365000	1.71057218	1.71057218	1.71057218	0.00989652	0.0	0.0
...	...	...	...	...	...	...	...	...	...	...
7.90	3.96666667	3.76230369	3.94385424	3.84786640	2.16554602	2.16554602	2.16554602	3.91362364	4.0	3.0
7.91	3.97000000	3.78645412	3.94968130	3.86252746	2.34982188	2.34982188	2.34982188	3.92220521	4.0	3.0
7.92	3.97333333	3.81052613	3.95546286	3.87731014	2.53405268	2.53405268	2.53405268	3.93079788	4.0	3.0
7.93	3.97666667	3.83451739	3.96119829	3.89221484	2.71818748	2.71818748	2.71818748	3.93940212	4.0	3.0
7.94	3.98000000	3.85842558	3.96688694	3.90724200	2.90217458	2.90217458	2.90217458	3.94801845	4.0	3.0
7.95	3.98333333	3.88224837	3.97252815	3.92239203	3.08596148	3.08596148	3.08596148	3.95664736	4.0	3.0
7.96	3.98666667	3.90598344	3.97812128	3.93766535	3.26949488	3.26949488	3.26949488	3.96528938	4.0	3.0
7.97	3.99000000	3.92962847	3.98366568	3.95306239	3.45272072	3.45272072	3.45272072	3.97394508	4.0	3.0
7.98	3.99333333	3.95318112	3.98916070	3.96858357	3.63558411	3.63558411	3.63558411	3.98261502	4.0	3.0
7.99	3.99666667	3.97663907	3.99460569	3.98422929	3.81802937	3.81802937	3.81802937	3.99129979	4.0	3.0
8.00	4.00000000	4.00000000	4.00000000	4.00000000	4.00000000	4.00000000	4.00000000	4.00000000	4.0	3.0

(defn plot-it [data kind]
  (-> data
      (plotly/layer-line
       {:=x :x
        :=y kind})))

(for [k kinds]
  `(~'plot-it ~'results ~k))

((plot-it results :linear)
 (plot-it results :cubic)
 (plot-it results :monotone)
 (plot-it results :akima)
 (plot-it results :neville)
 (plot-it results :divided-difference)
 (plot-it results :polynomial)
 (plot-it results :sprague)
 (plot-it results :step-before)
 (plot-it results :step-after))

(plot-it results :linear)

(plot-it results :cubic)

(plot-it results :monotone)

(plot-it results :akima)

(plot-it results :neville)

(plot-it results :divided-difference)

(plot-it results :polynomial)

(plot-it results :sprague)

(plot-it results :step-before)

(plot-it results :step-after)

(def indices
  (->> kinds (map-indexed (fn [idx x] [x idx])) (into {})))

(def wide-results
  (-> (tc/pivot->longer results
                        (complement #{:x})
                        {:target-columns    :interpolation
                         :value-column-name :y})
      (tc/map-rows (fn [{:keys [interpolation] :as r}]
                     {:z (indices interpolation)}))))

wide-results

_unnamed [8010 4]:

:x	:interpolation	:y	:z
0.00	:monotone	0.00000000	2
0.01	:monotone	0.00000000	2
0.02	:monotone	0.00000000	2
0.03	:monotone	0.00000000	2
0.04	:monotone	0.00000000	2
0.05	:monotone	0.00000000	2
0.06	:monotone	0.00000000	2
0.07	:monotone	0.00000000	2
0.08	:monotone	0.00000000	2
0.09	:monotone	0.00000000	2
...	...	...	...
7.90	:akima	3.84786640	3
7.91	:akima	3.86252746	3
7.92	:akima	3.87731014	3
7.93	:akima	3.89221484	3
7.94	:akima	3.90724200	3
7.95	:akima	3.92239203	3
7.96	:akima	3.93766535	3
7.97	:akima	3.95306239	3
7.98	:akima	3.96858357	3
7.99	:akima	3.98422929	3
8.00	:akima	4.00000000	3

(-> wide-results
    (plotly/layer-line
     {:=x :x
      :=y :y
      :=color :interpolation }))

(-> wide-results
    (plotly/layer-line
     {:=x :x
      :=y :y
      :=z :z
      :=color :interpolation
      :=coordinates :3d}))

source: demo.clj