generate character variety image

max_slope_picture/colors

@@ -0,0 +1,14 @@
+#a6cee3
+#1f78b4
+#b2df8a
+#33a02c
+#fb9a99
+#e31a1c
+#fdbf6f
+#ff7f00
+#cab2d6
+#6a3d9a
+#ffff99
+#b15928
+#ffff00
+#00ffff

max_slope_picture/combine_images

@@ -0,0 +1,6 @@
+#!/bin/bash
+
+convert -size 100x99 canvas:black combined.png
+for a in partition_*.pnm; do
+	composite -compose plus combined.png $a combined.png
+done

max_slope_picture/generate.hs

@@ -0,0 +1,69 @@
+import Text.Printf
+import System.Environment
+import System.Process
+import Data.List
+
+wordlist = ["abacabacbabcbacbcacbac", "abacbabcbacbac", "abacbabcbacbcacbac", "abacbacbacbacbacbacbac", "abacbacbacbacbac", "abacbacbac", "bacabacbabcbacbcacbcac", "bacabacbabcbacbcac", "baca", "bacbabcbacbcac", "bacbacbacbacbacbacbcac", "bacbacbacbacbcac", "bacbacbcac", "bacbac"]
+
+colors = [(0.651,0.808,0.890), (0.122,0.471,0.706), (0.698,0.875,0.541), (0.200,0.627,0.173), (0.984,0.604,0.600), (0.890,0.102,0.110), (0.992,0.749,0.435), (1.000,0.498,0.000), (0.792,0.698,0.839), (0.416,0.239,0.604), (1.000,1.000,0.600), (0.694,0.349,0.157), (1.000,1.000,0.000), (0.000,1.000,1.000)]
+
+main = sequence $ zipWith (generatePicture "result_20210419_221603.out") wordlist colors
+
+generatePicture :: String -> String -> (Double,Double,Double) -> IO ()
+generatePicture datafile word color = do
+  file1 <- readFile datafile
+  file2 <- readProcess "../special_element" [word] ""
+  let values1 = map (normalize.read.(!!4).words) (lines file1) :: [Double]
+  let values2 = map (normalize.read.(!!3).words) (lines file2) :: [Double]
+  let diff = zipWith (-) values1 values2
+  writeFile (printf "partition_%s.pnm" word) $ drawGrayscalePicture color diff
+  printf "Wrote partition_%s.pnm\n" word
+
+-- kind of a failed experiment
+-- supersample (width, height) to (factor*width - factor + 1, factor*height - factor + 1)
+-- supersample :: Int -> Int -> Int -> [Double] -> [Double]
+-- supersample width height factor orig = [pix x y | x <- [0..(width-1)*factor], y <- [0..(height-1)*factor]]
+--     where
+--       pix x y = xl*yl*a + xl*yr*b + xr*yl*c + xr*yr*d
+--           where
+--             x_ = x`div`factor
+--             y_ = y`div`factor
+--             xr = fromIntegral (x`mod`factor)/fromIntegral factor :: Double
+--             xl = 1 - xr :: Double
+--             yr = fromIntegral (y`mod`factor)/fromIntegral factor :: Double
+--             yl = 1 - yr :: Double
+--             aoffset = x_*height + y_
+--             boffset = x_*height + y_+1
+--             coffset = (x_+1)*height + y_
+--             doffset = (x_+1)*height + y_+1
+--             a = orig!!aoffset
+--             b = if boffset < width*height then orig!!boffset else 0
+--             c = if coffset < width*height then orig!!coffset else 0
+--             d = if doffset < width*height then orig!!doffset else 0
+
+-- xl*yl*a + xl*yr*b + xr*yl*c + xr*yr*d
+
+drawGrayscalePicture :: (Double,Double,Double) -> [Double] -> String
+drawGrayscalePicture (r,g,b) values = drawPicture 100 99 $ map color values
+    where
+      color x = (round (255*r*colorscale x), round (255*g*colorscale x), round (255*b*colorscale x))
+
+drawPicture :: Int -> Int -> [(Int,Int,Int)] -> String
+drawPicture w h values = printf "P3\n%d %d\n255\n%s" w h pixels
+    where
+      pixels = concat [printf "%d %d %d\n" r g b | (r,g,b) <- values] :: String
+
+normalize x = if x < 1 then 1/x else x
+
+readDataFile :: String -> IO [(String,Double)]
+readDataFile filename = do
+  f <- readFile filename
+  return $ map process $ map words $ lines f
+      where
+        process (x:y:_:_:z:rest) = (x++" "++y,read z)
+        normalize x = if x < 1 then 1/x else x
+
+colorscale :: Double -> Double
+colorscale x = if cs x < 0 then 1 else if cs x > 1 then 0 else 1 - cs x
+    where
+      cs x = 1e5*x

special_element.c

@@ -1,3 +1,4 @@
+
 #include "coxeter.h"
 #include "linalg.h"
 #include "mat.h"
@@ -261,7 +262,7 @@ int main(int argc, char *argv[])
 			y = -log(fabs(evs[2]));
 
 //	gmp_printf("%Qd %Qd %f %f %f\n", tr, trinv, x, y, y/x);
-			gmp_printf("%.5f %.5f %.5f %.5f\n", mpq_get_d(t), mpq_get_d(m), s, y/x);
+			gmp_printf("%.5f %.5f %.7f %.9f\n", mpq_get_d(t), mpq_get_d(m), s, y/x);
 
 		}
 	}