NumHask.Array.Example

Experimental api following https://pechersky.github.io/haskell-numpy-docs/quickstart.basics.html

The Basics

>>> :set -XDataKinds
>>> :set -XOverloadedLists
>>> :set -XNoImplicitPrelude
>>> :set -XFlexibleContexts
>>> import NumHask.Array as A
>>> import GHC.Exts (fromList)
>>> -- import NumHask.Space hiding (singleton)
>>> -- import NumHask.Range
>>> import qualified Data.Vector as V

An Example

construction can be lazy; and zero pads

>>> let z = [] :: Array '[2] Int
>>> z
[0, 0]
>>> let a = [0..] :: Array '[3,5] Int
>>> a
[[0, 1, 2, 3, 4],
 [5, 6, 7, 8, 9],
 [10, 11, 12, 13, 14]]
>>> shape a
[3,5]
>>> length (shape a) -- dimension
2
>>> :t a
a :: Array '[3, 5] Int
>>> import qualified Data.Vector as V
>>> let v = V.fromList [6,7,8]
>>> :t v
v :: Num a => V.Vector a
>>> let b = Array v
>>> :t b
b :: Num a => Array r a
>>> b :: Array '[3] Int
[6, 7, 8]

Array Creation

>>> -- fixed size arrays are fully shape specified at the type level
>>> let a = [2, 3, 4] :: Array '[3] Int
>>> a
[2, 3, 4]
>>> [1.2, 3.5, 5.1] :: Array '[3] Double
[1.2, 3.5, 5.1]

>>> -- lists of lists is not a thing, and need to be flattened
>>> let ls = [[1.0,2.0,3.0],[4.0,5.0,6.0]] :: [[Double]]
>>> fromList (concat ls) :: Array '[2,3] Double
[[1.0, 2.0, 3.0],
 [4.0, 5.0, 6.0]]

>>> fromList ((\x -> (fromIntegral x) :+ zero) <$> [1,2,3,4]) :: Array '[2,2] (Complex Double)
[[1.0 :+ 0.0, 2.0 :+ 0.0],
 [3.0 :+ 0.0, 4.0 :+ 0.0]]
>>> let z = [] :: Array '[3,4] Int
>>> z
[[0, 0, 0, 0],
 [0, 0, 0, 0],
 [0, 0, 0, 0]]
>>> let o = singleton one :: Array '[2,3,4] Int
>>> o
[[[1, 1, 1, 1],
  [1, 1, 1, 1],
  [1, 1, 1, 1]],
 [[1, 1, 1, 1],
  [1, 1, 1, 1],
  [1, 1, 1, 1]]]
>>> let empt = singleton nan :: Array '[2,3] Double
>>> empt
[[NaN, NaN, NaN],
 [NaN, NaN, NaN]]

>>> [10,15 .. 30] :: Array '[4] Int
[10, 15, 20, 25]
>>> [0, 0.3.. 2] :: Array '[7] Double
[0.0, 0.3, 0.6, 0.8999999999999999, 1.1999999999999997, 1.4999999999999996, 1.7999999999999994]

todo: fix NumHask.Range grid
fromList (grid OuterPos (Range 0 2) 8) :: Array '[9] Double
[0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0]
let x = fromList (grid OuterPos (Range 0 (2*pi)) 100) :: Array '[101] Double
let f = fmap sin x

Printing Arrays

>>> show ([0..] :: Array '[6] Int) :: Text
"[0, 1, 2, 3, 4, 5]"
>>> [0..] :: Array '[2,3] Int
[[0, 1, 2],
 [3, 4, 5]]
>>> [0..] :: Array '[1,2,3,1] Int
[[[[0],
   [1],
   [2]],
  [[3],
   [4],
   [5]]]]

todo: implement display
import Formatting
display (left 7 . fixed 2) ", " (fromList $ fromIntegral <$> [0..] :: Array '[100,100] Double)
[[   0.00,    1.00,    2.00 ..   98.00   99.00],
 [ 100.00,  101.00,  102.00 ..  198.00  199.00],
 [ 200.00,  201.00,  202.00 ..  298.00  299.00],
 ..
 [9800.00, 9801.00, 9802.00 .. 9898.00 9899.00],
 [9900.00, 9901.00, 9902.00 .. 9998.00 9999.00]]

Universal Functions

>>> let a = [0..] :: Array '[3] Double
>>> exp <$> a
[1.0, 2.718281828459045, 7.38905609893065]
>>> sqrt <$> a
[0.0, 1.0, 1.4142135623730951]

Indexing, Slicing and Iterating

>>> let a = (\x -> x*x*x) <$> [0..] :: Array '[10] Int
>>> index a [2]
8
>>> let s = (\i -> index a [i]) <$> [2..5] :: Array '[4] Int
>>> s
[8, 27, 64, 125]
>>> :t s
s :: Array '[4] Int
>>> -- replace every second number with -1000
>>> let a' = (tabulate (\[i] -> if i `mod` 2 == 0 then -1000 else (index a [i]))) :: Array '[10] Int
>>> a'
[-1000, 1, -1000, 27, -1000, 125, -1000, 343, -1000, 729]

-- todo: reverse fix
let a'' = (let (n:_) = shape a in tabulate (\[i] -> index a [n-i])) :: Array '[4] Int
a''
[729, -1000, 343, -1000, 125, -1000, 27, -1000, 1, -1000]

-- todo: slicing api

Shape Manipulation

-- todo:

Fancy indexing and index tricks

-- todo:

Linear Algebra

-- todo:

Tricks and Tips

-- todo: