src/Examples.hs

   1 module Examples (
   2   naturals,
   3   naturals_1d,
   4   trilinear,
   5   trilinear_zoom_2,
   6   trilinear9x9x9,
   7   zeros )
   8 where
   9
  10 import Data.Array.Repa (
  11   (:.)( (:.) ),
  12   DIM3,
  13   Z( Z ),
  14   fromListUnboxed )
  15 import Misc ( flatten, transpose_xz )
  16 import Values ( Values3D )
  17
  18
  19 -- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at nine
  20 --   points (hi, hj, jk) with h = 1. From example one in the paper.
  21 --   Used in the next bunch of tests.
  22 --
  23 trilinear_list :: [[[Double]]]
  24 trilinear_list = [ [ [ 1, 2, 3 ],
  25                 [ 1, 3, 5 ],
  26                 [ 1, 4, 7 ] ],
  27               [ [ 1, 2, 3 ],
  28                 [ 1, 4, 7 ],
  29                 [ 1, 6, 11 ] ],
  30               [ [ 1, 2, 3 ],
  31                 [ 1, 5, 9 ],
  32                 [ 1, 8, 15 ]]]
  33
  34
  35 n_cube :: Int -> DIM3
  36 n_cube n = (Z :. n :. n :. n)
  37
  38 trilinear :: Values3D
  39 trilinear = fromListUnboxed (n_cube 3) $
  40             flatten $
  41             transpose_xz
  42             trilinear_list
  43
  44
  45 -- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at 5^3
  46 --   points (hi, hj, jk) with h = 0.5. We should be able to reproduce
  47 --   this from splines based on the 3x3x3 trilinear.
  48 trilinear_zoom_2_list :: [[[Double]]]
  49 trilinear_zoom_2_list = [[[1, 3/2, 2, 5/2, 3], [1, 7/4, 5/2, 13/4, 4], [1, 2, 3, 4, 5], [1, 9/4, 7/2, 19/4, 6], [1, 5/2, 4, 11/2, 7]], [[1, 3/2, 2, 5/2, 3], [1, 15/8, 11/4, 29/8, 9/2], [1, 9/4, 7/2, 19/4, 6], [1, 21/8, 17/4, 47/8, 15/2], [1, 3, 5, 7, 9]], [[1, 3/2, 2, 5/2, 3], [1, 2, 3, 4, 5], [1, 5/2, 4, 11/2, 7], [1, 3, 5, 7, 9], [1, 7/2, 6, 17/2, 11]], [[1, 3/2, 2, 5/2, 3], [1, 17/8, 13/4, 35/8, 11/2], [1, 11/4, 9/2, 25/4, 8], [1, 27/8, 23/4, 65/8, 21/2], [1, 4, 7, 10, 13]], [[1, 3/2, 2, 5/2, 3], [1, 9/4, 7/2, 19/4, 6], [1, 3, 5, 7, 9], [1, 15/4, 13/2, 37/4, 12], [1, 9/2, 8, 23/2, 15]]]
  50
  51 trilinear_zoom_2 :: Values3D
  52 trilinear_zoom_2 = fromListUnboxed (n_cube 6) $
  53                    flatten $
  54                    transpose_xz
  55                    trilinear_zoom_2_list
  56
  57
  58 -- | Values of the function f(x,y,z) = 1 + x + xy + xyz taken at nine^3
  59 --   points (hi, hj, jk) with h = 0.5. We should be able to reproduce
  60 --   this from splines based on the 3x3x3 trilinear.
  61 trilinear9x9x9_list :: [[[Double]]]
  62 trilinear9x9x9_list = [[[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 1.75, 2.5, 3.25, 4, 4.75, 5.5, 6.25, 7], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2.25, 3.5, 4.75, 6, 7.25, 8.5, 9.75, 11], [1, 2.5, 4, 5.5, 7, 8.5, 10, 11.5, 13], [1, 2.75, 4.5, 6.25, 8, 9.75, 11.5, 13.25, 15], [1, 3, 5, 7, 9, 11, 13, 15, 17], [1, 3.25, 5.5, 7.75, 10, 12.25, 14.5, 16.75, 19], [1, 3.5, 6, 8.5, 11, 13.5, 16, 18.5, 21]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 1.875, 2.75, 3.625, 4.5, 5.375, 6.25, 7.125, 8], [1, 2.25, 3.5, 4.75, 6, 7.25, 8.5, 9.75, 11], [1, 2.625, 4.25, 5.875, 7.5, 9.125, 10.75, 12.375, 14], [1, 3, 5, 7, 9, 11, 13, 15, 17], [1, 3.375, 5.75, 8.125, 10.5, 12.875, 15.25, 17.625, 20], [1, 3.75, 6.5, 9.25, 12, 14.75, 17.5, 20.25, 23], [1, 4.125, 7.25, 10.375, 13.5, 16.625, 19.75, 22.875, 26], [1, 4.5, 8, 11.5, 15, 18.5, 22, 25.5, 29]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2, 3, 4, 5, 6, 7, 8, 9], [1, 2.5, 4, 5.5, 7, 8.5, 10, 11.5, 13], [1, 3, 5, 7, 9, 11, 13, 15, 17], [1, 3.5, 6, 8.5, 11, 13.5, 16, 18.5, 21], [1, 4, 7, 10, 13, 16, 19, 22, 25], [1, 4.5, 8, 11.5, 15, 18.5, 22, 25.5, 29], [1, 5, 9, 13, 17, 21, 25, 29, 33], [1, 5.5, 10, 14.5, 19, 23.5, 28, 32.5, 37]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2.125, 3.25, 4.375, 5.5, 6.625, 7.75, 8.875, 10], [1, 2.75, 4.5, 6.25, 8, 9.75, 11.5, 13.25, 15], [1, 3.375, 5.75, 8.125, 10.5, 12.875, 15.25, 17.625, 20], [1, 4, 7, 10, 13, 16, 19, 22, 25], [1, 4.625, 8.25, 11.875, 15.5, 19.125, 22.75, 26.375, 30], [1, 5.25, 9.5, 13.75, 18, 22.25, 26.5, 30.75, 35], [1, 5.875, 10.75, 15.625, 20.5, 25.375, 30.25, 35.125, 40], [1, 6.5, 12, 17.5, 23, 28.5, 34, 39.5, 45]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2.25, 3.5, 4.75, 6, 7.25, 8.5, 9.75, 11], [1, 3, 5, 7, 9, 11, 13, 15, 17], [1, 3.75, 6.5, 9.25, 12, 14.75, 17.5, 20.25, 23], [1, 4.5, 8, 11.5, 15, 18.5, 22, 25.5, 29], [1, 5.25, 9.5, 13.75, 18, 22.25, 26.5, 30.75, 35], [1, 6, 11, 16, 21, 26, 31, 36, 41], [1, 6.75, 12.5, 18.25, 24, 29.75, 35.5, 41.25, 47], [1, 7.5, 14, 20.5, 27, 33.5, 40, 46.5, 53]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2.375, 3.75, 5.125, 6.5, 7.875, 9.25, 10.625, 12], [1, 3.25, 5.5, 7.75, 10, 12.25, 14.5, 16.75, 19], [1, 4.125, 7.25, 10.375, 13.5, 16.625, 19.75, 22.875, 26], [1, 5, 9, 13, 17, 21, 25, 29, 33], [1, 5.875, 10.75, 15.625, 20.5, 25.375, 30.25, 35.125, 40], [1, 6.75, 12.5, 18.25, 24, 29.75, 35.5, 41.25, 47], [1, 7.625, 14.25, 20.875, 27.5, 34.125, 40.75, 47.375, 54], [1, 8.5, 16, 23.5, 31, 38.5, 46, 53.5, 61]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2.5, 4, 5.5, 7, 8.5, 10, 11.5, 13], [1, 3.5, 6, 8.5, 11, 13.5, 16, 18.5, 21], [1, 4.5, 8, 11.5, 15, 18.5, 22, 25.5, 29], [1, 5.5, 10, 14.5, 19, 23.5, 28, 32.5, 37], [1, 6.5, 12, 17.5, 23, 28.5, 34, 39.5, 45], [1, 7.5, 14, 20.5, 27, 33.5, 40, 46.5, 53], [1, 8.5, 16, 23.5, 31, 38.5, 46, 53.5, 61], [1, 9.5, 18, 26.5, 35, 43.5, 52, 60.5, 69]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2.625, 4.25, 5.875, 7.5, 9.125, 10.75, 12.375, 14], [1, 3.75, 6.5, 9.25, 12, 14.75, 17.5, 20.25, 23], [1, 4.875, 8.75, 12.625, 16.5, 20.375, 24.25, 28.125, 32], [1, 6, 11, 16, 21, 26, 31, 36, 41], [1, 7.125, 13.25, 19.375, 25.5, 31.625, 37.75, 43.875, 50], [1, 8.25, 15.5, 22.75, 30, 37.25, 44.5, 51.75, 59], [1, 9.375, 17.75, 26.125, 34.5, 42.875, 51.25, 59.625, 68], [1, 10.5, 20, 29.5, 39, 48.5, 58, 67.5, 77]], [[1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5], [1, 2.75, 4.5, 6.25, 8, 9.75, 11.5, 13.25, 15], [1, 4, 7, 10, 13, 16, 19, 22, 25], [1, 5.25, 9.5, 13.75, 18, 22.25, 26.5, 30.75, 35], [1, 6.5, 12, 17.5, 23, 28.5, 34, 39.5, 45], [1, 7.75, 14.5, 21.25, 28, 34.75, 41.5, 48.25, 55], [1, 9, 17, 25, 33, 41, 49, 57, 65], [1, 10.25, 19.5, 28.75, 38, 47.25, 56.5, 65.75, 75], [1, 11.5, 22, 32.5, 43, 53.5, 64, 74.5, 85]]]
  63
  64
  65 trilinear9x9x9 :: Values3D
  66 trilinear9x9x9 = fromListUnboxed (n_cube 9) $
  67                  flatten $
  68                  transpose_xz
  69                  trilinear9x9x9_list
  70
  71
  72 -- | A 3x3x3 array of zeros.
  73 zeros_list :: [[[Double]]]
  74 zeros_list = [ [ [ 0, 0, 0 ],
  75             [ 0, 0, 0 ],
  76             [ 0, 0, 0 ] ],
  77
  78           [ [ 0, 0, 0 ],
  79             [ 0, 0, 0 ],
  80             [ 0, 0, 0 ] ],
  81
  82           [ [ 0, 0, 0 ],
  83             [ 0, 0, 0 ],
  84             [ 0, 0, 0 ]]]
  85
  86
  87 -- No need to transpose_xz this one.
  88 zeros :: Values3D
  89 zeros = fromListUnboxed (n_cube 3) $ flatten zeros_list
  90
  91
  92 -- | A 3x3x3 array of numbers, starting at (0,0,0) == 0 and counting
  93 --   up to (2,2,2) == 26 in x,y,z order.
  94 naturals_list :: [[[Double]]]
  95 naturals_list = [ [ [ 0, 1, 2 ],
  96                [ 3, 4, 5 ],
  97                [ 6, 7, 8 ] ],
  98
  99              [ [ 9, 10, 11 ],
 100                [ 12, 13, 14 ],
 101                [ 15, 16, 17 ] ],
 102
 103              [ [ 18, 19, 20 ],
 104                [ 21, 22, 23 ],
 105                [ 24, 25, 26 ]]]
 106
 107 naturals :: Values3D
 108 naturals = fromListUnboxed (n_cube 3) $
 109            flatten $
 110            transpose_xz
 111            naturals_list
 112
 113
 114
 115 naturals_1d_list :: [[[Double]]]
 116 naturals_1d_list =[[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
 117                      11, 12, 13, 14, 15, 16, 17, 18, 19, 20]]]
 118
 119
 120 twenty_vector :: DIM3
 121 twenty_vector = (Z :. 1 :. 20 :. 1)
 122
 123 -- | Used in at least one test where we need a 1x20x1 array.
 124 naturals_1d :: Values3D
 125 naturals_1d = fromListUnboxed twenty_vector (flatten naturals_1d_list)