From 173d34c0d529830efeab39b7cca9a03856514469 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 1 Sep 2011 20:23:57 -0400
Subject: [PATCH] Use an IArray for the cubes and cube_at functions.

---
 src/Grid.hs | 58 +++++++++++++++++++++++++++--------------------------
 1 file changed, 30 insertions(+), 28 deletions(-)

diff --git a/src/Grid.hs b/src/Grid.hs
index ab698c1..8bf8382 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,6 +4,7 @@
 module Grid
 where
 
+import Data.Array (Array, array, (!))
 import qualified Data.Array.Repa as R
 import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
 
@@ -15,6 +16,9 @@ import Tetrahedron (polynomial)
 import Values (Values3D, dims, empty3d, zoom_shape)
 
 
+type CubeGrid = Array (Int,Int,Int) Cube
+
+
 -- | Our problem is defined on a Grid. The grid size is given by the
 --   positive number h. The function values are the values of the
 --   function at the grid points, which are distance h from one
@@ -44,18 +48,24 @@ empty_grid :: Grid
 empty_grid = Grid 1 empty3d
 
 
--- | Returns a three-dimensional list of cubes centered on the grid
+-- | Returns a three-dimensional array of cubes centered on the grid
 --   points of g with the appropriate 'FunctionValues'.
-cubes :: Grid -> [[[Cube]]]
+cubes :: Grid -> CubeGrid
 cubes g
-    | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]]
-    | otherwise =
-        [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
-              | j <- [0..ysize]]
-              | k <- [0..zsize]]
-    where
-      fvs = function_values g
-      (xsize, ysize, zsize) = dims fvs
+  = array (lbounds, ubounds)
+           [ ((i,j,k), cube_ijk)
+                 | i <- [0..xmax],
+                   j <- [0..ymax],
+                   k <- [0..zmax],
+                   let cube_ijk = Cube (h g) i j k (make_values fvs i j k)]
+     where
+       xmax = xsize - 1
+       ymax = ysize - 1
+       zmax = zsize - 1
+       lbounds = (0, 0, 0)
+       ubounds = (xmax, ymax, zmax)
+       fvs = function_values g
+       (xsize, ysize, zsize) = dims fvs
 
 
 -- | Takes a grid and a position as an argument and returns the cube
@@ -63,24 +73,16 @@ cubes g
 --   position is outside of the grid), it will throw an error.
 cube_at :: Grid -> Int -> Int -> Int -> Cube
 cube_at g i j k
-    | i < 0 = error "i < 0 in cube_at"
-    | j < 0 = error "j < 0 in cube_at"
-    | k < 0 = error "k < 0 in cube_at"
-    | otherwise =
-        let zsize = length (cubes g) in
-          if k >= zsize then
-            error "k >= xsize in cube_at"
-          else
-            let ysize = length ((cubes g) !! k) in
-              if j >= ysize then
-                error "j >= ysize in cube_at"
-              else
-                let xsize = length (((cubes g) !! k) !! j) in
-                  if i >= xsize then
-                    error "i >= xsize in cube_at"
-                  else
-                    (((cubes g) !! k) !! j) !! i
-
+    | i < 0      = error "i < 0 in cube_at"
+    | i >= xsize = error "i >= xsize in cube_at"
+    | j < 0      = error "j < 0 in cube_at"
+    | j >= ysize = error "j >= ysize in cube_at"
+    | k < 0      = error "k < 0 in cube_at"
+    | k >= zsize = error "k >= zsize in cube_at"
+    | otherwise = (cubes g) ! (i,j,k)
+      where
+        fvs = function_values g
+        (xsize, ysize, zsize) = dims fvs
 
 --   The first cube along any axis covers (-h/2, h/2). The second
 --   covers (h/2, 3h/2).  The third, (3h/2, 5h/2), and so on.
-- 
2.43.2