From 8d413191a61d8b444213b0349bfe3df3fd24f35b Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 2 Oct 2011 12:09:50 -0400
Subject: [PATCH] Fix the FunctionValues value_at cases, and update the Grid
 tests to match.

---
 src/FunctionValues.hs | 74 ++++++++++++++++++++-----------------------
 src/Grid.hs           | 12 ++++---
 2 files changed, 42 insertions(+), 44 deletions(-)

diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs
index 9d52323..8400c80 100644
--- a/src/FunctionValues.hs
+++ b/src/FunctionValues.hs
@@ -195,51 +195,37 @@ eval f (Quotient x y) = (eval f x) / (eval f y)
 --   1.0
 --
 --   >>> value_at Examples.trilinear 1 3 0
---   4.0
+--   5.0
 --
 value_at :: Values3D -> Int -> Int -> Int -> Double
 value_at v3d i j k
   -- Put the most common case first!
-  | (i >= 0) && (j >= 0) && (k >= 0) =
+  | (valid_i i) && (valid_j j) && (valid_k k) =
       idx v3d i j k
 
-  -- The next three are from the first line in (7.3).
-  | (i == -1) && (j >= 0) && (k >= 0) =
-      2*(value_at v3d 0 j k) - (value_at v3d 1 j k)
-
-  | (i >= 0) && (j == -1) && (k >= 0) =
-      2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
-
-  | (i >= 0) && (j >= 0) && (k == -1) =
-      2*(value_at v3d i j 0) - (value_at v3d i j 1)
-
-  -- The next two are from the second line in (7.3).
-  | (i == -1) && (j == -1) && (k >= 0) =
-      2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
-
-  | (i == -1) && (j == ysize) && (k >= 0) =
-      2*(value_at v3d i (ysize - 1) k) - (value_at v3d i (ysize - 2) k)
-
-  -- The next two are from the third line in (7.3).
-  | (i == -1) && (j >= 0) && (k == -1) =
-      2*(value_at v3d i j 0) - (value_at v3d i j 1)
-
-  | (i == -1) && (j >= 0) && (k == zsize) =
-      2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2))
-
-  -- Repeat the above (j and k) cases for i >= 0.
-  | (i >= 0) && (j == -1) && (k == -1) =
-      2*(value_at v3d i j 0) - (value_at v3d i j 1)
-
-  | (i == xsize) && (j == -1) && (k >= 0) =
-      2*(value_at v3d (xsize - 1) j k) - (value_at v3d (xsize - 2) j k)
-
-  -- These two cases I made up.
-  | (i == -1) && (j == -1) && (k == -1) =
-      2*(value_at v3d i j 0) - (value_at v3d i j 1)
-
-  | (i == xsize) && (j == ysize) && (k == zsize) =
-      2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2))
+  -- The next three are from the first line in (7.3). Analogous cases
+  -- have been added where the indices are one-too-big. These are the
+  -- "one index is bad" cases.
+  | not (valid_i i) =
+      if (i == -1)
+      then
+        2*(value_at v3d 0 j k) - (value_at v3d 1 j k)
+      else
+        2*(value_at v3d (i-1) j k) - (value_at v3d (i-2) j k)
+
+  | not (valid_j j) =
+      if (j == -1)
+      then
+        2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
+      else
+        2*(value_at v3d i (j-1) k) - (value_at v3d i (j-2) k)
+
+  | not (valid_k k) =
+      if (k == -1)
+      then
+        2*(value_at v3d i j 0) - (value_at v3d i j 1)
+      else
+        2*(value_at v3d i j (k-1)) - (value_at v3d i j (k-2))
 
   | otherwise =
       let istr = show i
@@ -251,6 +237,16 @@ value_at v3d i j k
   where
     (xsize, ysize, zsize) = dims v3d
 
+    valid_i :: Int -> Bool
+    valid_i i' = (i' >= 0) && (i' < xsize)
+
+    valid_j :: Int -> Bool
+    valid_j j' = (j' >= 0) && (j' < ysize)
+
+    valid_k :: Int -> Bool
+    valid_k k' = (k' >= 0) && (k' < zsize)
+
+
 
 -- | Given a three-dimensional list of 'Double' and a set of 3D
 --   coordinates (i,j,k), constructs and returns the 'FunctionValues'
diff --git a/src/Grid.hs b/src/Grid.hs
index 6170d36..db8d4d3 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -291,6 +291,7 @@ test_trilinear_reproduced =
                     | i <- [0..2],
                       j <- [0..2],
                       k <- [0..2],
+                      c0 <- cs,
                       t <- tetrahedra c0,
                       let p = polynomial t,
                       let i' = fromIntegral i,
@@ -298,7 +299,7 @@ test_trilinear_reproduced =
                       let k' = fromIntegral k]
     where
       g = make_grid 1 trilinear
-      c0 = cube_at g 1 1 1
+      cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
 
 
 test_zeros_reproduced :: Assertion
@@ -310,12 +311,13 @@ test_zeros_reproduced =
                       k <- [0..2],
                       let i' = fromIntegral i,
                       let j' = fromIntegral j,
-                      let k' = fromIntegral k]
+                      let k' = fromIntegral k,
+                      c0 <- cs,
+                      t0 <- tetrahedra c0,
+                      let p = polynomial t0 ]
     where
       g = make_grid 1 zeros
-      c0 = cube_at g 1 1 1
-      t0 = tetrahedron c0 0
-      p = polynomial t0
+      cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
 
 
 -- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
-- 
2.43.2