1 files changed, 58 insertions, 32 deletions

diff --git a/01.06.hs b/01.06.hs
index 7a92197..1ab017a 100644
--- a/01.06.hs
+++ b/01.06.hs
@@ -1,70 +1,96 @@
-
 {-# LANGUAGE FlexibleInstances #-}
 
-import System.Random
-import Data.Random.Normal
 import Control.Monad.State
+import Data.Random.Normal
 import Numeric.LinearAlgebra as Lin
+import System.Random
 
-import Control.Monad(void)
+import Control.Monad (void)
 import Graphics.Rendering.Chart
+import Graphics.Rendering.Chart.Backend.Cairo
 import Graphics.Rendering.Chart.Easy
 import Graphics.Rendering.Chart.Grid
-import Graphics.Rendering.Chart.Backend.Cairo
-import Graphics.Rendering.Chart.Plot.Histogram(defaultNormedPlotHist)
+import Graphics.Rendering.Chart.Plot.Histogram (defaultNormedPlotHist)
+
 instance Default (PlotHist x Double) where
-    def = defaultNormedPlotHist
+  def = defaultNormedPlotHist
 
 -- | Evaluates the Winger surmise.
 ρWinger :: Floating t => t -> t
-ρWinger s = pi * s / 2 * exp(- pi * s^2 / 4)
+ρWinger s = pi * s / 2 * exp (-pi * s ^ 2 / 4)
 
 -- | Computes the splitting of the center eigenvalues of a symmetric matrix.
 eigenSplitting :: Herm Double -> Double
 eigenSplitting m = e2 - e1
-                   where
-                     e = sortVector $ eigenvaluesSH m
-                     i = (Lin.size e) `quot` 2
-                     e1 = e Lin.! (i - 1)
-                     e2 = e Lin.! i
+  where
+    e = sortVector $ eigenvaluesSH m
+    i = (Lin.size e) `quot` 2
+    e1 = e Lin.! (i - 1)
+    e2 = e Lin.! i
 
 -- | Produces random GOE matrices.
 goeGen :: RandomGen g => Int -> State g (Herm Double)
-goeGen n = get >>= (\g -> let (g1, g2) = split g in 
-  (put g1) >> (return $ sym $ matrix n $ take (n^2) $ normals' (0.0, 2.0) g2))
+goeGen n =
+  get >>=
+  (\g ->
+     let (g1, g2) = split g
+      in (put g1) >> (return $ sym $ matrix n $ take (n ^ 2) $ normals' (0.0, 2.0) g2))
 
 -- | Produces random ∓1 matrices.
 pm1Gen :: RandomGen g => Int -> State g (Herm Double)
-pm1Gen n = state (\g -> let (m, g2) = runState (goeGen n) g in (trustSym $ cmap signum (unSym m), g2))
+pm1Gen n =
+  state
+    (\g ->
+       let (m, g2) = runState (goeGen n) g
+        in (trustSym $ cmap signum (unSym m), g2))
 
 -- | Produces n eigenvalue splittings from the matrix ensemble m.
 eigenSplittings :: RandomGen g => Int -> State g (Herm Double) -> State g [Double]
-eigenSplittings n m = state (\g -> let (mats, g2) = runState (sequence $ replicate n m) g in (eigenSplitting <$> mats, g2))
+eigenSplittings n m =
+  state
+    (\g ->
+       let (mats, g2) = runState (sequence $ replicate n m) g
+        in (eigenSplitting <$> mats, g2))
 
 hsChart :: RandomGen g => g -> State g (Herm Double) -> Int -> Int -> String -> Layout Double Double
-hsChart g gen num bins tit = execEC $ do
-  plot $ fmap histToPlot $ liftEC $ do
-    plot_hist_title .= tit
-    plot_hist_bins .= bins
-    plot_hist_values .= scaledData
-    plot_hist_range .= Just (0.0, 5.0)
-    plot_hist_norm_func .= const (\x -> fromIntegral bins * fromIntegral x / fromIntegral num / 5.0)
-  plot (line "ρ_Winger" [ [(s,ρWinger s) | s <- [0,0.005..5]] ])
+hsChart g gen num bins tit =
+  execEC $ do
+    plot $
+      fmap histToPlot $
+      liftEC $ do
+        plot_hist_title .= tit
+        plot_hist_bins .= bins
+        plot_hist_values .= scaledData
+        plot_hist_range .= Just (0.0, 5.0)
+        plot_hist_norm_func .=
+          const (\x -> fromIntegral bins * fromIntegral x / fromIntegral num / 5.0)
+    plot (line "ρ_Winger" [[(s, ρWinger s) | s <- [0,0.005 .. 5]]])
   where
     rawData = evalState (eigenSplittings num gen) g
     mean = sum rawData / fromIntegral (length rawData)
     scaledData = (\x -> x / mean) <$> rawData
 
-mkgrid g num bins = title `wideAbove` aboveN [ besideN [ layoutToGrid (hsChart g ((fst gen) n) num bins (snd gen Prelude.<> show n)) | gen <- gens] | n <- ns]
+mkgrid g num bins =
+  title `wideAbove`
+  aboveN
+    [ besideN
+      [layoutToGrid (hsChart g ((fst gen) n) num bins (snd gen Prelude.<> show n)) | gen <- gens]
+    | n <- ns
+    ]
   where
     gens = [(goeGen, "GOE, N = "), (pm1Gen, "±1, N = ")]
     ns = [2, 4, 10]
-    title = setPickFn nullPickFn $ label ls HTA_Centre VTA_Centre "Winger surmise compared with eigenvalue splitting of random matrices"
-    ls = def { _font_size = 15, _font_weight = FontWeightBold }
-    
+    title =
+      setPickFn nullPickFn $
+      label
+        ls
+        HTA_Centre
+        VTA_Centre
+        "Winger surmise compared with eigenvalue splitting of random matrices"
+    ls = def {_font_size = 15, _font_weight = FontWeightBold}
 
 main = do
   g <- newStdGen
-  void $ renderableToFile (def { _fo_format = PDF}) "01.06.pdf" $ fillBackground def $ gridToRenderable $ mkgrid g 1000 50
-
-
+  void $
+    renderableToFile (def {_fo_format = PDF}) "01.06.pdf" $
+    fillBackground def $ gridToRenderable $ mkgrid g 1000 50