hmatrix and ad don't (currently) mix.

The problem is that hmatrix uses a packed structure that can't hold any of the AD mode variants we have as an Element. =(

I've been working with Alex Lang to explore in ad 4.0 ways that we can support monomorphic AD modes and still present largely the same API. We've seen a number of performance gains off of this refactoring already, but it doesn't go far enough to address what you need.

A goal a bit farther out is to support AD on vector/matrix operations, but it is a much bigger refactoring than the one currently in the pipeline. =/

To support automatic differentiation on vector-based operations in a form that works with standard BLAS-like storage like the packed matrix rep used in hmatrix we need to convert from a 'matrix of AD variables' to an 'AD mode over of matrices'. This is similar to the difference between a matrix of complex numbers and a real matrix plus an imaginary matrix.

This is a long term goal, but not one you're likely to see support for out of 'ad' in the short term.

I can't build AD on hmatrix itself due in part to licensing restrictions and differing underlying storage requirements, so there are a lot of little issues in making that latter vision a reality.

-Edward

On Tue, Apr 9, 2013 at 10:46 AM, Dominic Steinitz <dominic@steinitz.org> wrote:

Hi Cafe,

Suppose I want to find the grad of a function then it's easy I just
use http://hackage.haskell.org/package/ad-3.4:

import Numeric.AD
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.AD
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:

/Users/dom/Dropbox/Private/Whales/MyAD.hs:24:21:
    No instance for (Traversable Matrix) arising from a use of `grad'
    Possible fix: add an instance declaration for (Traversable Matrix)
    In the expression: grad g
    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])'

/Users/dom/Dropbox/Private/Whales/MyAD.hs:24:26:
    Could not deduce (Element
                        (ad-3.4:Numeric.AD.Internal.Types.AD s Double))
      arising from a use of `g'
    from the context (Numeric.AD.Internal.Classes.Mode s)
      bound by a type expected by the context:
                 Numeric.AD.Internal.Classes.Mode s =>
                 Matrix (ad-3.4:Numeric.AD.Internal.Types.AD s Double)
                 -> ad-3.4:Numeric.AD.Internal.Types.AD s Double
      at /Users/dom/Dropbox/Private/Whales/MyAD.hs:24:21-26
    Possible fix:
      add an instance declaration for
      (Element (ad-3.4:Numeric.AD.Internal.Types.AD s Double))
    In the first argument of `grad', namely `g'
    In the expression: grad 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:

http://hackage.haskell.org/package/repa
http://hackage.haskell.org/package/yarr-1.3.1

although I haven'¯t checked.

Thanks, Dominic.


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