Quaternion type: Difference between revisions

=={{header|Haskell}}==

<lang haskell>import Control.Monad

import Control.Arrow

import Data.List

data Quaternion = Q Double Double Double Double

deriving (Show, Ord, Eq)

realQ :: Quaternion -> Double

realQ (Q r _ _ _) = r

imagQ :: Quaternion -> [Double]

imagQ (Q _ i j k) = [i, j, k]

quaternionFromScalar s = Q s 0 0 0

listFromQ (Q a b c d) = [a,b,c,d]

quaternionFromList [a, b, c, d] = Q a b c d

addQ, subQ, mulQ :: Quaternion -> Quaternion -> Quaternion

addQ (Q a b c d) (Q p q r s) = Q (a+p) (b+q) (c+r) (d+s)

subQ (Q a b c d) (Q p q r s) = Q (a-p) (b-q) (c-r) (d-s)

mulQ (Q a b c d) (Q p q r s) =

Q (a*p - b*q - c*r - d*s)

(a*q + b*p + c*s - d*r)

(a*r - b*s + c*p + d*q)

(a*s + b*r - c*q + d*p)

normQ = sqrt. sum. join (zipWith (*)). listFromQ

conjQ, negQ :: Quaternion -> Quaternion

conjQ (Q a b c d) = Q a (-b) (-c) (-d)

negQ (Q a b c d) = Q (-a) (-b) (-c) (-d)</lang>

To use with the Examples:

<lang haskell>[q,q1,q2] = map quaternionFromList [[1..4],[2..5],[3..6]]

-- a*b == b*a

test :: Quaternion -> Quaternion -> Bool

test a b = a `mulQ` b == b `mulQ` a</lang>

Examples:

<pre>*Main> mulQ (Q 0 1 0 0) $ mulQ (Q 0 0 1 0) (Q 0 0 0 1) -- i*j*k

Q (-1.0) 0.0 0.0 0.0

*Main> test q1 q2

False

*Main> mulQ q1 q2

Q (-56.0) 16.0 24.0 26.0

*Main> flip mulQ q1 q2

Q (-56.0) 18.0 20.0 28.0

*Main> imagQ q

[2.0,3.0,4.0]</pre>