infix_examples.clj

(use 'incanter.core)

;; basic arithmetic
($= 7 + 8 - 2 * 6 / 2) ; => 9


;; add 5 to each element of the vector [1 2 3]
($= [1 2 3] + 5) ; => (6 7 8)

;; element-by-element arithmetic on vectors
($= [1 2 3] + [4 5 6])
($= [1 2 3] * [1 2 3])
($= [1 2 3] * [1 2 3])
($= [1 2 3] / (sq [1 2 3]) + [5 6 7])

($= [1 2 3] + (sin [4 5 6]))

;; element-by-element operations on matrices
($= (matrix [[1 2] [4 5]]) + 6)
($= (trans [[1 2] [4 5]]) + 6)


;; exponents
($= 8 ** 3)
($= 8 ** 1/2)
($= 2 ** -2)
($= [1 2 3] ** 2)

;; grouping with parens
($= 10 + 20 * (4 - 5) / 6)
($= (10 + 20) * 4 - 5 / 6)
($= 10 + 20 * (4 - 5 / 6))

($= 20 * (4 - 5) / 6)
($= ((5 + 4 * (3 - 4)) / (5 + 8) * 6))
;; arbitrarily nested groupings
($= ((((5 + 4) * 5))))

;; with variables
(let [x 10
      y -5]
  ($= x + y / -10))

;; mathematical functions
($= sqrt 5 * 5 + 3 * 3)
($= sq [1 2 3] + [1 2 3])

($= sin 2 * Math/PI * 2)
($= (cos 0) * 10)
($= (tan 2) * Math/PI * 10) 
($= (asin 1/2) * 10)
($= (acos 1/2) * 10)
($= (atan 1/2) * 10)


;; boolean tests
($= 3 > (5 * 2/7))
($= 3 <= (5 * 2/7))
($= 3 != (5 * 2/7))
($= 3 == (5 * 2/7))
($= 3 != 8 && 6 < 12)
($= 3 != 8 || 6 > 12)


;; matrix operations
;; matrix multiplication
($= [1 2 3] <*> (trans [1 2 3]))
($= (trans [[1 2] [4 5]]) <*> (matrix [[1 2] [4 5]]))
($= (trans [1 2 3 4]) <*> [1 2 3 4])
($= [1 2 3 4] <*> (trans [1 2 3 4]))




;; kronecker product
($= [1 2 3] <x> [1 2 3])
($= (matrix [[1 2] [3 4] [5 6]]) <x> 4)
($= (matrix [[1 2] [3 4] [5 6]]) <x> (matrix [[1 2] [3 4]]))
($= [1 2 3 4] <x> 4)
($= [1 2 3 4] <x> (trans [1 2 3 4]))




;; plot cubic function and add LaTeX annotation
(use '(incanter core charts latex))
(doto (function-plot (fn [x] ($= x ** 3 - 5 * x ** 2 + 3 * x + 5)) -10 10)
  (add-latex 0 250 "x^3 - 5x^2 + 3x +5")
  view)


;; plot car speed to breaking distance sample data, partitioning data where the ratio of dist/speed is less than 2 and 
;; adding a line showing the threshold.

;; use with-data macro, passing it the 'cars' sample data. Use the $where function to filter the data, using a $fn,
;; which is a bit of syntax sugar for defining functions that operate on data sets. 
;; ($fn [x y] (...)) => (fn [{:keys x y}] (...))
;; The parameter names correspond to the column names of the dataset.


(use '(incanter core datasets charts))
(with-data (get-dataset :cars)
  (doto (scatter-plot :speed :dist 
          :data ($where ($fn [speed dist] 
                          ($= dist / speed < 2))))
    (add-points :speed :dist 
      :data ($where ($fn [speed dist] 
                      ($= dist / speed >= 2))))
    (add-lines ($ :speed) ($= 2 * ($ :speed)))
    view))