negLogDet.hs

import Numeric.LinearAlgebra
import Control.Monad (replicateM)
import System.Random (randomIO)
import Graphics.Gnuplot.Simple (plotFunc)

-- Test 100 random lines for convexity.
main = replicateM 100 $ do
    -- Two 5x5 symmetric positive definite matrices that determine the line.
    a <- randomSnPD 5
    v <- randomSnPD 5
    disp a
    disp v
    let nld t = (negate . log . det) (a + scale t v)
        domain = [0, 0.05 ..1]
        opts = []
     in plotFunc opts domain nld

randomSnPD n = fmap toSPD (randomSquare n)
    -- Add transpose to make it symmetric, then add nI to ensure PD.
    where toSPD m = m + trans m + scale (fromIntegral n) (ident n)

randomSquare n = fmap matFromSeed randomIO
    where matFromSeed s = reshape n $ randomVector s Uniform (n * n)

disp = putStr . dispf 2