# [Haskell-cafe] Automated Differentiation of Matrices (hmatrix)

Dominic Steinitz dominic at steinitz.org
Tue Apr 9 16:46:17 CEST 2013

```Hi Cafe,

Suppose I want to find the grad of a function then it's easy I just

import Data.Foldable (Foldable)
import Data.Traversable (Traversable)

data MyMatrix a = MyMatrix (a, a)
deriving (Show, Functor, Foldable, Traversable)

f :: Floating a => MyMatrix a -> a
f (MyMatrix (x, y)) = exp \$ negate \$ (x^2 + y^2) / 2.0

main :: IO ()
main = do
putStrLn \$ show \$ f \$ MyMatrix (0.0, 0.0)
putStrLn \$ show \$ grad f \$ MyMatrix (0.0, 0.0)

But now suppose I am doing some matrix calculations
http://hackage.haskell.org/package/hmatrix-0.14.1.0 and I want to find
the grad of a function of a matrix:

import Numeric.LinearAlgebra
import Data.Foldable (Foldable)
import Data.Traversable (Traversable)

g :: (Element a, Floating a) => Matrix a -> a
g m = exp \$ negate \$ (x^2 + y^2) / 2.0
where r = (toLists m)!!0
x = r!!0
y = r!!1

main :: IO ()
main = do
putStrLn \$ show \$ g \$ (1 >< 2) ([0.0, 0.0] :: [Double])
putStrLn \$ show \$ grad g \$ (1 >< 2) ([0.0, 0.0] :: [Double])

Then I am in trouble:

No instance for (Traversable Matrix) arising from a use of `grad'
Possible fix: add an instance declaration for (Traversable Matrix)
In the second argument of `(\$)', namely
`grad g \$ (1 >< 2) ([0.0, 0.0] :: [Double])'
In the second argument of `(\$)', namely
`show \$ grad g \$ (1 >< 2) ([0.0, 0.0] :: [Double])'

Could not deduce (Element
arising from a use of `g'
bound by a type expected by the context:
Possible fix:
In the first argument of `grad', namely `g'
In the second argument of `(\$)', namely
`grad g \$ (1 >< 2) ([0.0, 0.0] :: [Double])'

What are my options here? Clearly I can convert my matrix into a list
(which is traversable), find the grad and convert it back into a
matrix but given I am doing numerical calculations and speed is an
important factor, this seems undesirable.

I think I would have the same problem with: