X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=43e60ef2c17948e78e334b2c49847b4c1fa19f50;hb=944668e6c12378c4c179b9b3ada0e4626c3c71e0;hp=a1058d07f2fa4c89d5bcab914e05a428dccb52f8;hpb=1bf996325008f79215a607d765adb042026f7444;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index a1058d0..43e60ef 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -1,63 +1,69 @@
 {-# LANGUAGE BangPatterns #-}
--- | The Grid module just contains the Grid type and two constructors
---   for it. We hide the main Grid constructor because we don't want
---   to allow instantiation of a grid with h <= 0.
+-- | The Grid module contains the Grid type, its tests, and the 'zoom'
+--   function used to build the interpolation.
 module Grid (
   cube_at,
+  grid_properties,
   grid_tests,
-  make_grid,
   slow_tests,
-  zoom
-  )
+  zoom )
 where
 
-import qualified Data.Array.Repa as R
-import Test.HUnit (Assertion, assertEqual)
-import Test.Framework (Test, testGroup)
-import Test.Framework.Providers.HUnit (testCase)
-import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.QuickCheck ((==>),
-                        Arbitrary(..),
-                        Gen,
-                        Positive(..),
-                        Property,
-                        choose)
-import Assertions (assertAlmostEqual, assertTrue)
-import Comparisons ((~=))
-import Cube (Cube(Cube),
-             find_containing_tetrahedron,
-             tetrahedra,
-             tetrahedron)
-import Examples (trilinear, trilinear9x9x9, zeros, naturals_1d)
-import FunctionValues (make_values, value_at)
-import Point (Point(..))
-import ScaleFactor (ScaleFactor)
-import Tetrahedron (Tetrahedron, c, polynomial, v0, v1, v2, v3)
-import ThreeDimensional (ThreeDimensional(..))
-import Values (Values3D, dims, empty3d, zoom_shape)
+import Data.Array.Repa (
+  (:.)( (:.) ),
+  DIM3,
+  Z( Z ),
+  computeUnboxedP,
+  fromListUnboxed )
+import Data.Array.Repa.Operators.Traversal ( unsafeTraverse )
+import Test.Tasty ( TestTree, testGroup )
+import Test.Tasty.HUnit ( Assertion, assertEqual, testCase )
+import Test.Tasty.QuickCheck (
+  Arbitrary( arbitrary ),
+  Gen,
+  Property,
+  (==>),
+  choose,
+  vectorOf,
+  testProperty )
+
+import Assertions ( assertAlmostEqual, assertTrue )
+import Comparisons ( (~=) )
+import Cube (
+  Cube( Cube ),
+  find_containing_tetrahedron,
+  tetrahedra,
+  tetrahedron )
+import Examples ( trilinear, trilinear9x9x9, zeros )
+import FunctionValues ( make_values, value_at )
+import Point ( Point(Point) )
+import ScaleFactor ( ScaleFactor )
+import Tetrahedron (
+  Tetrahedron( v0, v1, v2, v3 ),
+  c,
+  polynomial )
+import Values ( Values3D, dims, empty3d, zoom_shape )
 
 
 -- | 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
---   another in each direction (x,y,z).
-data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
-                   function_values :: Values3D }
-          deriving (Show)
+--   positive number h, which we have defined to always be 1 for
+--   performance reasons (and simplicity). The function values are the
+--   values of the function at the grid points, which are distance h=1
+--   from one another in each direction (x,y,z).
+--
+newtype Grid = Grid { function_values :: Values3D }
+                 deriving (Show)
 
 
 instance Arbitrary Grid where
     arbitrary = do
-      (Positive h') <- arbitrary :: Gen (Positive Double)
-      fvs <- arbitrary :: Gen Values3D
-      return (make_grid h' fvs)
-
-
--- | The constructor that we want people to use.
---   Ignore non-positive grid sizes for performance.
-make_grid :: Double -> Values3D -> Grid
-make_grid grid_size values =
-  Grid grid_size values
+      x_dim <- choose (1, 27)
+      y_dim <- choose (1, 27)
+      z_dim <- choose (1, 27)
+      elements <- vectorOf (x_dim * y_dim * z_dim) (arbitrary :: Gen Double)
+      let new_shape = (Z :. x_dim :. y_dim :. z_dim)
+      let fvs = fromListUnboxed new_shape elements
+      return $ Grid fvs
 
 
 
@@ -67,19 +73,18 @@ make_grid grid_size values =
 --   does improve performance.
 cube_at :: Grid -> Int -> Int -> Int -> Cube
 cube_at !g !i !j !k =
-   Cube delta i j k fvs' tet_vol
+   Cube i j k fvs' tet_vol
    where
      fvs = function_values g
      fvs' = make_values fvs i j k
-     delta = h g
-     tet_vol = (1/24)*(delta^(3::Int))
+     tet_vol = (1/24) :: Double
 
 
---   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.
+--   The first cube along any axis covers (-1/2, 1/2). The second
+--   covers (1/2, 3/2).  The third, (3/2, 5/2), and so on.
 --
---   We translate the (x,y,z) coordinates forward by 'h/2' so that the
---   first covers (0, h), the second covers (h, 2h), etc. This makes
+--   We translate the (x,y,z) coordinates forward by 1/2 so that the
+--   first covers (0, 1), the second covers (1, 2), etc. This makes
 --   it easy to figure out which cube contains the given point.
 calculate_containing_cube_coordinate :: Grid -> Double -> Int
 calculate_containing_cube_coordinate g coord
@@ -88,11 +93,10 @@ calculate_containing_cube_coordinate g coord
     -- exists.
     | coord < offset = 0
     | coord == offset && (xsize > 1 && ysize > 1 && zsize > 1) = 1
-    | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
+    | otherwise = (ceiling (coord + offset)) - 1
     where
       (xsize, ysize, zsize) = dims (function_values g)
-      cube_width = (h g)
-      offset = cube_width / 2
+      offset = (1/2) :: Double
 
 
 -- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
@@ -107,17 +111,17 @@ find_containing_cube g (Point x y z) =
       k = calculate_containing_cube_coordinate g z
 
 
-zoom_lookup :: Values3D -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup :: Values3D -> ScaleFactor -> a -> (DIM3 -> Double)
 zoom_lookup v3d scale_factor _ =
     zoom_result v3d scale_factor
 
 
-zoom_result :: Values3D -> ScaleFactor -> R.DIM3 -> Double
-zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
+zoom_result :: Values3D -> ScaleFactor -> DIM3 -> Double
+zoom_result v3d (sfx, sfy, sfz) (Z :. m :. n :. o) =
   f p
   where
-    g = make_grid 1 v3d
-    offset = (h g)/2
+    g = Grid v3d
+    offset = (1/2) :: Double
     m' = (fromIntegral m) / (fromIntegral sfx) - offset
     n' = (fromIntegral n) / (fromIntegral sfy) - offset
     o' = (fromIntegral o) / (fromIntegral sfz) - offset
@@ -127,15 +131,19 @@ zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
     f = polynomial t
 
 
-zoom :: Values3D -> ScaleFactor -> Values3D
+--
+-- Instead of IO, we could get away with a generic monad 'm'
+-- here. However, /we/ only call this function from within IO.
+--
+zoom :: Values3D -> ScaleFactor -> IO Values3D
 zoom v3d scale_factor
-    | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+    | xsize == 0 || ysize == 0 || zsize == 0 = return empty3d
     | otherwise =
-        R.compute $ R.unsafeTraverse v3d transExtent f
-          where
-            (xsize, ysize, zsize) = dims v3d
-            transExtent = zoom_shape scale_factor
-            f = zoom_lookup v3d scale_factor
+        computeUnboxedP $ unsafeTraverse v3d transExtent f
+        where
+          (xsize, ysize, zsize) = dims v3d
+          transExtent = zoom_shape scale_factor
+          f = zoom_lookup v3d scale_factor :: (DIM3 -> Double) -> DIM3 -> Double
 
 
 -- | Check all coefficients of tetrahedron0 belonging to the cube
@@ -145,7 +153,7 @@ zoom v3d scale_factor
 --   We also verify that the four vertices on face0 of the cube are
 --   in the correct location.
 --
-trilinear_c0_t0_tests :: Test.Framework.Test
+trilinear_c0_t0_tests :: TestTree
 trilinear_c0_t0_tests =
   testGroup "trilinear c0 t0"
     [testGroup "coefficients"
@@ -177,7 +185,7 @@ trilinear_c0_t0_tests =
        testCase "v3 is correct" test_trilinear_f0_t0_v3]
     ]
   where
-    g = make_grid 1 trilinear
+    g = Grid trilinear
     cube = cube_at g 1 1 1
     t = tetrahedron cube 0
 
@@ -288,11 +296,11 @@ test_trilinear_reproduced =
                       c0 <- cs,
                       t <- tetrahedra c0,
                       let p = polynomial t,
-                      let i' = fromIntegral i,
-                      let j' = fromIntegral j,
-                      let k' = fromIntegral k]
+                      let i' = fromIntegral i :: Double,
+                      let j' = fromIntegral j :: Double,
+                      let k' = fromIntegral k :: Double]
     where
-      g = make_grid 1 trilinear
+      g = Grid trilinear
       cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
 
 
@@ -303,14 +311,14 @@ test_zeros_reproduced =
                     | i <- [0..2],
                       j <- [0..2],
                       k <- [0..2],
-                      let i' = fromIntegral i,
-                      let j' = fromIntegral j,
-                      let k' = fromIntegral k,
+                      let i' = fromIntegral i :: Double,
+                      let j' = fromIntegral j :: Double,
+                      let k' = fromIntegral k :: Double,
                       c0 <- cs,
                       t0 <- tetrahedra c0,
                       let p = polynomial t0 ]
     where
-      g = make_grid 1 zeros
+      g = Grid zeros
       cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
 
 
@@ -324,44 +332,24 @@ test_trilinear9x9x9_reproduced =
               k <- [0..8],
               t <- tetrahedra c0,
               let p = polynomial t,
-              let i' = (fromIntegral i) * 0.5,
-              let j' = (fromIntegral j) * 0.5,
-              let k' = (fromIntegral k) * 0.5]
+              let i' = (fromIntegral i) * 0.5 :: Double,
+              let j' = (fromIntegral j) * 0.5 :: Double,
+              let k' = (fromIntegral k) * 0.5 :: Double]
     where
-      g = make_grid 1 trilinear
+      g = Grid trilinear
       c0 = cube_at g 1 1 1
 
 
--- | The point 'p' in this test lies on the boundary of tetrahedra 12 and 15.
---   However, the 'contains_point' test fails due to some numerical innacuracy.
---   This bug should have been fixed by setting a positive tolerance level.
---
---   Example from before the fix:
---
---   b1 (tetrahedron c 20) (0, 17.5, 0.5)
---   -0.0
---
-test_tetrahedra_collision_sensitivity :: Assertion
-test_tetrahedra_collision_sensitivity =
-  assertTrue "tetrahedron collision tests isn't too sensitive" $
-             contains_point t20 p
-  where
-    g = make_grid 1 naturals_1d
-    cube = cube_at g 0 18 0
-    p = Point 0 17.5 0.5
-    t20 = tetrahedron cube 20
-
 
 prop_cube_indices_never_go_out_of_bounds :: Grid -> Gen Bool
 prop_cube_indices_never_go_out_of_bounds g =
   do
-    let delta = Grid.h g
-    let coordmin = negate (delta/2)
+    let coordmin = negate (1/2) :: Double
 
     let (xsize, ysize, zsize) = dims $ function_values g
-    let xmax = delta*(fromIntegral xsize) - (delta/2)
-    let ymax = delta*(fromIntegral ysize) - (delta/2)
-    let zmax = delta*(fromIntegral zsize) - (delta/2)
+    let xmax = (fromIntegral xsize) - (1/2) :: Double
+    let ymax = (fromIntegral ysize) - (1/2) :: Double
+    let zmax = (fromIntegral zsize) - (1/2) :: Double
 
     x <- choose (coordmin, xmax)
     y <- choose (coordmin, ymax)
@@ -387,7 +375,7 @@ prop_cube_indices_never_go_out_of_bounds g =
 --   in opposite directions, one of them has to have negative volume!
 prop_c0120_identity :: Grid -> Property
 prop_c0120_identity g =
-  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+  xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
     c t0 0 1 2 0 ~= (c t0 1 0 2 0 + c t10 1 0 0 2) / 2
   where
     fvs = function_values g
@@ -402,7 +390,7 @@ prop_c0120_identity g =
 --   'prop_c0120_identity'.
 prop_c0111_identity :: Grid -> Property
 prop_c0111_identity g =
-  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+  xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
     c t0 0 1 1 1 ~= (c t0 1 0 1 1 + c t10 1 0 1 1) / 2
   where
     fvs = function_values g
@@ -417,7 +405,7 @@ prop_c0111_identity g =
 --   'prop_c0120_identity'.
 prop_c0201_identity :: Grid -> Property
 prop_c0201_identity g =
-  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+  xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
     c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t10 1 1 1 0) / 2
   where
     fvs = function_values g
@@ -432,7 +420,7 @@ prop_c0201_identity g =
 --   'prop_c0120_identity'.
 prop_c0102_identity :: Grid -> Property
 prop_c0102_identity g =
-  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+  xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
     c t0 0 1 0 2 ~= (c t0 1 0 0 2 + c t10 1 0 2 0) / 2
   where
     fvs = function_values g
@@ -447,7 +435,7 @@ prop_c0102_identity g =
 --   'prop_c0120_identity'.
 prop_c0210_identity :: Grid -> Property
 prop_c0210_identity g =
-  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+  xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
     c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t10 1 1 0 1) / 2
   where
     fvs = function_values g
@@ -462,7 +450,7 @@ prop_c0210_identity g =
 --   'prop_c0120_identity'.
 prop_c0300_identity :: Grid -> Property
 prop_c0300_identity g =
-  and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+  xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
     c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t10 1 2 0 0) / 2
   where
     fvs = function_values g
@@ -475,9 +463,9 @@ prop_c0300_identity g =
 
 -- | All of the properties from Section (2.9), p. 80. These require a
 --   grid since they refer to two adjacent cubes.
-p80_29_properties :: Test.Framework.Test
+p80_29_properties :: TestTree
 p80_29_properties =
-  testGroup "p. 80, Section (2.9) Properties" [
+  testGroup "p. 80, Section (2.9) properties" [
     testProperty "c0120 identity" prop_c0120_identity,
     testProperty "c0111 identity" prop_c0111_identity,
     testProperty "c0201 identity" prop_c0201_identity,
@@ -486,21 +474,22 @@ p80_29_properties =
     testProperty "c0300 identity" prop_c0300_identity ]
 
 
-grid_tests :: Test.Framework.Test
+grid_tests :: TestTree
 grid_tests =
-    testGroup "Grid Tests" [
-      trilinear_c0_t0_tests,
-      p80_29_properties,
-      testCase "tetrahedra collision test isn't too sensitive"
-        test_tetrahedra_collision_sensitivity,
-      testProperty "cube indices within bounds"
-        prop_cube_indices_never_go_out_of_bounds ]
+  testGroup "Grid tests" [ trilinear_c0_t0_tests ]
+
 
+grid_properties :: TestTree
+grid_properties =
+  testGroup "Grid properties"
+    [ p80_29_properties,
+      testProperty "cube indices within bounds"
+                   prop_cube_indices_never_go_out_of_bounds ]
 
 -- Do the slow tests last so we can stop paying attention.
-slow_tests :: Test.Framework.Test
+slow_tests :: TestTree
 slow_tests =
-    testGroup "Slow Tests" [
+    testGroup "Slow tests" [
       testCase "trilinear reproduced" test_trilinear_reproduced,
       testCase "trilinear9x9x9 reproduced" test_trilinear9x9x9_reproduced,
       testCase "zeros reproduced" test_zeros_reproduced ]