Sooooo ... as it turns out going from fake matrices to hmatrix
datatypes turns out to be nontrivial :)
Preamble for reference:
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ParallelListComp #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}
import Numeric.LinearAlgebra.HMatrix
import Numeric.AD
reconstruct :: (Container Vector a, Num (Vector a))
=> [a] -> [Matrix a] -> Matrix a
reconstruct as φs = sum [ a `scale` φ | a <- as | φ <- φs ]
preserveInfo :: (Container Vector a, Num (Vector a))
=> Matrix a -> [a] -> [Matrix a] -> a
preserveInfo img as φs = sumElements (errImg * errImg)
where errImg = img - (reconstruct as φs)
And the call to the gradientDescent
function:
gradientDescentOverAs :: forall m a. (Floating a, Ord a, Num (Vector a))
=> Matrix a -> [Matrix a] -> [a] -> [[a]]
gradientDescentOverAs img φs as0 = gradientDescent go as0
where go as = preserveInfo img as φs
edit: this is not the code in the original question but boiled down as much as possible. GHC requires some constraints on the go
sub-function, but the answer proposed in the linked question doesn't apply here.
edit2, quoting myself from below:
I come to believe it can't be done.
Matrix
requires it's elements to be in theElement
class. The only elements there areDouble
,Float
and theirComplex
forms. All of these are not accepted bygradientDescent
.
So basically this is the same question as the one linked above, but for the hmatrix
datatypes instead of my handrolled ones.
edit3
Relevant, email conversation between Edward Kmett and Dominic Steinitz on the topic: https://mail.haskell.org/pipermail/haskell-cafe/2013-April/107561.html
I found this series of blog posts to be very helpful:
https://idontgetoutmuch.wordpress.com/2014/09/09/fun-with-extended-kalman-filters-4/
(both HMatrix with static size guarantees and the jacobian
function from AD are demonstrated).
HTH
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