haskell matrix power without using if-else statement

Question

I have the following function to obtain power of a matrix

X^0 = identity matrix, X^1 =X;
X^2 = X'X;
X^3 = X X' X;
X^4 = X' X X' X ......

I tried with following function:

import Numeric.Container
import Numeric.LinearAlgebra 

mpow :: Field t => (Matrix t) -> Integer -> (Matrix t) 
mpow x 0 = ident $ cols x 
mpow x 1 = x
mpow x n =
    if (mod n 2) == 0 then 
        multiply (trans x) (mpow x $ n - 1)
    else 
        multiply x (mpow x $ n - 1)

Is it possible to rewrite this function without using the if-else statement ?

Answer 1

Yes, you could use guards. But quite often it will compile into the same internal representation in Haskell.

import Numeric.Container
import Numeric.LinearAlgebra

mpow :: Field t => (Matrix t) -> Integer -> (Matrix t)
mpow x 0 = ident $ cols x
mpow x 1 = x
mpow x n | (mod n 2) == 0 = multiply (trans x) (mpow x $ n - 1)
         | otherwise      = multiply x (mpow x $ n - 1)

Answer 2

As freyrs mentioned, guards and if statements are exactly equivalent as they are both converted to case of when you compile your code. But, you can still get rid of them:

mpow' :: Field t => (Matrix t) -> Integer -> (Matrix t) 
mpow' x 0 = ident $ cols x 
mpow' x 1 = x
mpow' x n = multiply (head (drop n' fs) $ x) (mpow' x $ n - 1)
    where fs = [trans, id]
          n' = fromInteger (mod n 2)

However, this isn't more concise, nor does it better communicate what your function is doing to the reader. So don't do this, unless you really hate conditionals.