I’ve been puttering around with some ideas about how linear algebra could work in Haskell.

So I decided to check out what has been done. hmatrix binds to the gnu scientific libraries and lapack.

There is also htensor and repa which I need to check out.

This is the hello word of scientific programs. I could write this is numpy, scipy, matplotlib FAST. But I’m super used to those. Maybe not a fair comparison.

I build a circulant function for the 1d periodic Laplace equation matrix. I did not find good constructors that would elegantly construct the thing so I make a circulant routine using the fft. That’s ok I guess.

I got the eigenvalues and eigenvectors with eigSH.

Then I plot it out to an external svg file using Cairo. I do not like the mental overhead of a monad.But I guess you can just copy and paste and ignore all that.

The Plt.line function takes a label and a list of (x,y) tuples

runghc hello_laplace.hs

-- runghc Laplace.hs import Numeric.GSL.Fourier import Numeric.LinearAlgebra import Data.Complex -- Some of the namespace crashes with the algebra stuff. import qualified Graphics.Rendering.Chart.Easy as Plt import Graphics.Rendering.Chart.Backend.Diagrams(toFile) fftRow m = fromRows $ (map fft) $ toRows m fftCol m = fromColumns $ (map fft) $ toColumns m ifftRow :: Matrix (Complex Double) -> Matrix (Complex Double) ifftRow m = fromRows $ (map ifft) $ toRows m ifftCol m = fromColumns $ (map ifft) $ toColumns m circulant :: Vector (Complex Double) -> Matrix (Complex Double) circulant v = ifftCol $ fftRow $ diag $ fft v {- -- nevermind rotate :: Int -> [a] -> [a] rotate _ [] = [] rotate n xs = zipWith const (drop n (cycle xs)) xs -} num = 20 c = assoc num 0 [(0,-2),(1,1),(num-1,1)] :: Vector C kmat = circulant c sol = eigSH (trustSym kmat) -- doesn't check hermiticty --sol = eigSH' kmat eigvals = fst sol -- a plotting function signal :: [Int] -> [(Double,Double)] signal xs = [ (fromIntegral x, realPart $ (c ! x) )| x <- xs ] pltVec label v = (Plt.line label [zip [0..] (toList v)]) main = toFile Plt.def "example1_big.svg" $ do Plt.plot (Plt.line "Matrix Row" [signal [0..(num-1)]]) Plt.plot (pltVec "eigenvalues" eigvals)

Ok. Actually on reflection it’s not bad. Scratching my head around the circulant matrix constructor took some time. And so did installing stuff. I did also keep slamming into type mismatches. and it didn’t like eigSH’ which I don’t get.

Maybe Haskell for Mac would work well here? I did buy a copy.

Maybe Julia would be better? I think Julia has lots of functional and pythony things.

I should refactor the fftRow stuff into a higher order combinator that maps into rows and columns

mapRow f m = fromRows $ (map f) $ toRows m