automatic-differentiation

The closest-related implementation in Haskell I have seen is the forward mode at http://hackage.haskell.org/packages/archive/fad/1.0/doc/html/Numeric-FAD.html . The closest related related research appears to be reverse mode for another functional language related to Scheme at http://www.bcl.hamilton.ie/~qobi/stalingrad/ . I see reverse mode in Haskell as kind of a holy grail for a lot of tasks, with the hopes that it could use Haskell's nested data parallelism to gain a nice speedup in heavy numerical optimization. In response to this question, I've uploaded a package named ad to Hackage for

I'm trying to work with Numeric.AD and a custom Expr type. I wish to calculate the symbolic gradient of user inputted expression. The first trial with a constant expression works nicely: calcGrad0 :: [Expr Double] calcGrad0 = grad df vars where df [x,y] = eval (env [x,y]) (EVar "x"*EVar "y") env vs = zip varNames vs varNames = ["x","y"] vars = map EVar varNames This works: >calcGrad0 [Const 0.0 :+ (Const 0.0 :+ (EVar "y" :* Const 1.0)),Const 0.0 :+ (Const 0.0 :+ (EVar "x" :* Const 1.0))] However, if I pull the expression out as a parameter: calcGrad1 :: [Expr Double] calcGrad1 = calcGrad1'

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

I have a problem in using the apache commons math library. I just want to create functions like f(x) = 4x^2 + 2x and I want to compute the derivative of this function --> f'(x) = 8x + 2 I read the article about Differentiation ( http://commons.apache.org/proper/commons-math/userguide/analysis.html , section 4.7). There is an example which I don't understand: int params = 1; int order = 3; double xRealValue = 2.5; DerivativeStructure x = new DerivativeStructure(params, order, 0, xRealValue); DerivativeStructure y = f(x); //COMPILE ERROR System.out.println("y = " + y.getValue(); System.out

We need two matrices of differential operators [B] and [C] such as: B = sympy.Matrix([[ D(x), D(y) ], [ D(y), D(x) ]]) C = sympy.Matrix([[ D(x), D(y) ]]) ans = B * sympy.Matrix([[x*y**2], [x**2*y]]) print ans [x**2 + y**2] [ 4*x*y] ans2 = ans * C print ans2 [2*x, 2*y] [4*y, 4*x] This could also be applied to calculate the curl of a vector field like: culr = sympy.Matrix([[ D(x), D(y), D(z) ]]) field = sympy.Matrix([[ x**2*y, x*y*z, -x**2*y**2 ]]) To solve this using Sympy the following Python class had to be created: import sympy class D( sympy.Derivative ): def __init__( self, var ): super( D

Given a very simple Matrix definition based on Vector: import Numeric.AD import qualified Data.Vector as V newtype Mat a = Mat { unMat :: V.Vector a } scale' f = Mat . V.map (*f) . unMat add' a b = Mat $ V.zipWith (+) (unMat a) (unMat b) sub' a b = Mat $ V.zipWith (-) (unMat a) (unMat b) mul' a b = Mat $ V.zipWith (*) (unMat a) (unMat b) pow' a e = Mat $ V.map (^e) (unMat a) sumElems' :: Num a => Mat a -> a sumElems' = V.sum . unMat (for demonstration purposes ... I am using hmatrix but thought the problem was there somehow) And an error function ( eq3 ): eq1' :: Num a => [a] -> [Mat a] -> Mat