Vector products: Difference between revisions

Or using '''Either''' and '''(>>=)''', rather than '''error''', to pass on intelligible messages:

<lang haskell>dotProduct

:: Num a

=> [a] -> [a] -> Either String a

dotProduct xs ys

| length xs /= length ys =

Left "Dot product not defined - vectors differ in dimension."

| otherwise = Right (sum $ zipWith (*) xs ys)

crossProduct

:: Num a

=> [a] -> [a] -> Either String [a]

crossProduct xs ys

| 3 /= length xs || 3 /= length ys =

Left "crossProduct is defined only for 3d vectors."

| otherwise = Right [x2 * y3 - x3 * y2, x3 * y1 - x1 * y3, x1 * y2 - x2 * y1]

where

[x1, x2, x3] = xs

[y1, y2, y3] = ys

scalarTriple

:: Num a

=> [a] -> [a] -> [a] -> Either String a

scalarTriple q r s = crossProduct r s >>= dotProduct q

vectorTriple

:: Num a

=> [a] -> [a] -> [a] -> Either String [a]

vectorTriple q r s = crossProduct r s >>= crossProduct q

-- TEST ---------------------------------------------------

a = [3, 4, 5]

b = [4, 3, 5]

c = [-5, -12, -13]

d = [3, 4, 5, 6]

main :: IO ()

main =

mapM_ putStrLn $

zipWith

(++)

["a . b", "a x b", "a . b x c", "a x b x c", "a . d", "a . (b x d)"]

[ sh $ dotProduct a b

, sh $ crossProduct a b

, sh $ scalarTriple a b c

, sh $ vectorTriple a b c

, sh $ dotProduct a d

, sh $ scalarTriple a b d

]

sh

:: Show a

=> Either String a -> String

sh = either (" => " ++) ((" = " ++) . show)</lang>

{{Out}}

<pre>a . b = 49

a x b = [5,5,-7]

a . b x c = 6

a x b x c = [-267,204,-3]

a . d => Dot product not defined - vectors differ in dimension.

a . (b x d) => crossProduct is defined only for 3d vectors.</pre>