Linear Interpolation and sorted-map
Sorted collections (with subseq and rsubseq) can help when working with a partition of disjoint intervals, eg when you need to interpolate.
(defn interpolator "Takes a coll of 2D points (vectors) and returns their linear interpolation function." [points] (let [m (into (sorted-map) points)] (fn [x] (let [[[x1 y1]] (rsubseq m <= x) [[x2 y2]] (subseq m > x)] (if x2 (+ y1 (* (- x x1) (/ (- y2 y1) (- x2 x1)))) y1))))) ;; => (map (interpolator [[0 0] [1 1] [3 2] [4 3]]) (range 0 9/2 1/2)) ;; (0 1/2 1 5/4 3/2 7/4 2 5/2 3)
Nice.
The function does something sensible for inputs that outside the range of points.
(map (interpolator points) (range 0 19/2 1/2))
; (0 1/2 1 5/4 3/2 7/4 2 5/2 3 3 3 3 3 3 3 3 3 3 3)
But only on one side
(map (interpolator points) (range -1 19/2 1/2)) ; java.lang.NullPointerException
@john, true, here is an amended version:
(defn interpolator
"Takes a coll of 2D points (vectors) and returns
their linear interpolation function."
[points]
(let [m (into (sorted-map) points)]
(fn [x]
(let [[[x1 y1]] (rsubseq m <= x)
[[x2 y2]] (subseq m > x)]
(cond
(not x2) y1
(not x1) y2
:else (+ y1 (* (- x x1) (/ (- y2 y1) (- x2 x1)))))))))
;; => (map (interpolator [[0 0] [1 1] [3 2] [4 3]]) (range -1 11/2 1/2))
;; (0 0 0 1/2 1 5/4 3/2 7/4 2 5/2 3 3 3)