NumHask.Examples

NumHask usage examples

Imports and Pragmas

NumHask.Prelude is a replacement for the standard prelude with the NoImplicitPrelude extension explicitly required.

>>> :set -XNoImplicitPrelude
>>> import NumHask.Prelude

Int, Integer, Double and Float are from base. NumHask takes these classes and redefines the basic arithmetic operators.

>>> 1 + 1
2
>>> 1 - 1
0
>>> 1 * 1
1
>>> 1 / 1
1.0

Note that the literal numbers in the divide above defaulted to Float rather than Int.

>>> 1 / (1::Int)
...
... No instance for (MultiplicativeGroup Int)
...

>>> 1 / fromIntegral (1::Int)
1.0

Float and Double are Field instances.

>>> zero == 0.0
True
>>> one == 1.0
True
>>> 1.0 + 1.0
2.0
>>> 1.0 - 1.0
0.0
>>> 1.0 * 1.0
1.0
>>> 1.0 / 1.0
1.0

QuotientField

>>> 1 `div` 2
0
>>> 3 `mod` 2
1

BoundedField

>>> one/zero
Infinity
>>> -one/zero
-Infinity
>>> zero/zero+one
NaN

ExpField

>>> logBase 2 4
2.0
>>> 2 ** 2
4.0
>>> sqrt 4
2.0
>>> exp 2
7.38905609893065
>>> log 2
0.6931471805599453

Complex numbers

>>> let a = 1 :+ 2
>>> a
1 :+ 2
>>> zero - a
(-1) :+ (-2)
>>> (1 :+ (-2)) * ((-2) :+ 4)
6 :+ 8
>>> (1 :+ (-1)) / (2 :+ 2)
0.0 :+ (-0.5)

Vectors

A Vector is a Representable Functor where the representation is an Int.

>>> import NumHask.Vector
>>> :set -XDataKinds
>>> :set -XOverloadedLists
>>> [] :: Vector 3 Int
[0,0,0]
>>> let a = [1..] :: Vector 3 Int
>>> a
[1,2,3]
>>> let b = [3,2] :: Vector 3 Int
>>> b
[3,2,0]
>>> a+zero==a
True
>>> zero+a==a
True
>>> a+b
[4,4,3]
>>> a-a == zero
True
>>> a * b
[3,4,0]
>>> let a' = unsafeToVector . someVector $ a :: Vector 2 Int
>>> let b' = unsafeToVector . someVector $ b :: Vector 2 Int
>>> a' `divMod` b'
([0,1],[1,0])
>>> let c = [1.0,2.0] :: Vector 3 Float
>>> let d = [3.0,2.0] :: Vector 3 Float
>>> c / d
[0.33333334,1.0,NaN]
>>> size c :: Float
2.236068
>>> distance c d :: Float
2.0
>>> c <.> d :: Float
7.0

The type of an outer product of two vectors is a Vector m (Vector n), and is a perfectly formed Matrix representation.

>>> a >< b
[[3,2,0],[6,4,0],[9,6,0]]

>>> (a >< b) >< (b >< a)
[[[9,12,0],[6,8,0],[0,0,0]],[[18,24,0],[12,16,0],[0,0,0]],[[27,36,0],[18,24,0],[0,0,0]]]

Matrices

A Matrix is a Representable Functor where the representation is an (Int,Int).

>>> import NumHask.Matrix
>>> :set -XDataKinds
>>> :set -XOverloadedLists
>>> [] :: Matrix 2 1 Int
[[0]
 [0]]
>>> let a = [1..] :: Matrix 2 3 Int
>>> let b = trans a
>>> a
[[1,2,3]
 [4,5,6]]
>>> b
[[1,4]
 [2,5]
 [3,6]]
>>> mmult a b
[[14,32]
 [32,77]]
>>> getDiag one == (one :: Vector 6 Int)
True
>>> diagonal one == (one :: Matrix 4 4 Int)
True
>>> let a = [1..] :: Matrix 3 3 Int
>>> a <.> a
285
>>> toVV a <.> toVV a
[66,93,126]