import Test.QuickCheck (Arbitrary(..), choose)
import Cardinal
+import Values (Values3D, dims, idx)
-- | The FunctionValues type represents the value of our function f at
-- the 27 points surrounding (and including) the center of a
-- | Takes a three-dimensional list of 'Double' and a set of 3D
-- coordinates (i,j,k), and returns the value at (i,j,k) in the
-- supplied list. If there is no such value, zero is returned.
-value_at :: [[[Double]]] -> Int -> Int -> Int -> Double
+value_at :: Values3D -> Int -> Int -> Int -> Double
value_at values i j k
| i < 0 = 0
| j < 0 = 0
| k < 0 = 0
- | length values <= k = 0
- | length (values !! k) <= j = 0
- | length ((values !! k) !! j) <= i = 0
- | otherwise = ((values !! k) !! j) !! i
+ | xsize <= i = 0
+ | ysize <= j = 0
+ | zsize <= k = 0
+ | otherwise = idx values i j k
+ where
+ (xsize, ysize, zsize) = dims values
-- | Given a three-dimensional list of 'Double' and a set of 3D
-- coordinates (i,j,k), constructs and returns the 'FunctionValues'
-- object centered at (i,j,k)
-make_values :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues
+make_values :: Values3D -> Int -> Int -> Int -> FunctionValues
make_values values i j k =
empty_values { front = value_at values (i-1) j k,
back = value_at values (i+1) j k,
import Point (Point)
import Tetrahedron (polynomial)
import ThreeDimensional (contains_point)
-
+import Values (Values3D, dims, empty3d)
-- | 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 :: [[[Double]]] }
+ function_values :: Values3D }
deriving (Eq, Show)
instance Arbitrary Grid where
arbitrary = do
(Positive h') <- arbitrary :: Gen (Positive Double)
- fvs <- arbitrary :: Gen [[[Double]]]
+ fvs <- arbitrary :: Gen Values3D
return (make_grid h' fvs)
-- | The constructor that we want people to use. If we're passed a
-- non-positive grid size, we throw an error.
-make_grid :: Double -> [[[Double]]] -> Grid
+make_grid :: Double -> Values3D -> Grid
make_grid grid_size values
| grid_size <= 0 = error "grid size must be positive"
| otherwise = Grid grid_size values
-- | Creates an empty grid with grid size 1.
empty_grid :: Grid
-empty_grid = Grid 1 [[[]]]
+empty_grid = Grid 1 empty3d
-- | Returns a three-dimensional list of cubes centered on the grid
-- points of g with the appropriate 'FunctionValues'.
cubes :: Grid -> [[[Cube]]]
cubes g
- | fvs == [[[]]] = [[[]]]
- | head fvs == [[]] = [[[]]]
+ | 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
- zsize = (length fvs) - 1
- ysize = length (head fvs) - 1
- xsize = length (head $ head fvs) - 1
+ (xsize, ysize, zsize) = dims fvs
-- | Takes a grid and a position as an argument and returns the cube
zoom :: Grid -> Int -> [[[Double]]]
zoom g scale_factor
- | fvs == [[[]]] = []
- | head fvs == [[]] = []
+ | xsize == 0 || ysize == 0 || zsize == 0 = []
| otherwise =
[[[f p | i <- [0..scaled_zsize],
let i' = scale_dimension i,
scale_dimension x = (fromIntegral x) / (fromIntegral scale_factor)
fvs = function_values g
- scaled_zsize = ((length fvs) - 1) * scale_factor
- scaled_ysize = (length (head fvs) - 1) * scale_factor
- scaled_xsize = (length (head $ head fvs) - 1) * scale_factor
+ (xsize, ysize, zsize) = dims fvs
+ scaled_xsize = xsize * scale_factor
+ scaled_ysize = ysize * scale_factor
+ scaled_zsize = zsize * scale_factor
+
DIM3,
Z(..),
(:.)(..),
- toList
)
import Values
---import Grid(make_grid, zoom)
+import Grid(make_grid, zoom)
mri_shape :: DIM3
mri_shape = (Z :. 256 :. 256 :. 109)
main :: IO ()
main = do
mridata <- read_values_3d mri_shape "./data/mridata.txt"
- let tmp = Data.Array.Repa.toList mridata
- print tmp
--- let g = make_grid 1 (Data.Array.Repa.toList mridata2)
--- let output = zoom g 2
--- print "Hello, world."
+ let g = make_grid 1 mridata
+ let output = zoom g 1
+ print output
+{-# LANGUAGE TypeSynonymInstances #-}
+
module Values
where
import Data.Array.Repa (
Array,
+ Z(..),
+ (:.)(..),
DIM1,
+ DIM2,
DIM3,
+ extent,
+ fromList,
+ index,
reshape,
)
import Data.Array.Repa.IO.Vector (readVectorFromTextFile)
import System.FilePath ()
+import Test.QuickCheck (Arbitrary(..), Gen)
type Values1D = Array DIM1 Double
+type Values2D = Array DIM2 Double
type Values3D = Array DIM3 Double
+
+instance Arbitrary Values3D where
+ arbitrary = do
+ x_dim <- arbitrary :: Gen Int
+ y_dim <- arbitrary :: Gen Int
+ z_dim <- arbitrary :: Gen Int
+ one_d <- arbitrary :: Gen Values1D
+ let new_shape = (Z :. x_dim :. y_dim :. z_dim)
+ let three_d = reshape new_shape one_d
+ return three_d
+
+
+instance Arbitrary Values1D where
+ arbitrary = do
+ x <- arbitrary :: Gen [Double]
+ let shape = (Z :. (length x))
+ let one_d = Data.Array.Repa.fromList shape x
+ return one_d
+
+
read_values_1d :: FilePath -> IO Values1D
read_values_1d path = readVectorFromTextFile path
+
read_values_3d :: DIM3 -> FilePath -> IO Values3D
read_values_3d sh path = do
one_d <- read_values_1d path
return $ reshape sh one_d
+
+
+empty3d :: Values3D
+empty3d = Data.Array.Repa.fromList (Z :. 0 :. 0 :. 0) []
+
+
+dims :: Values3D -> (Int, Int, Int)
+dims v3d =
+ let (Z :. x :. y :. z) = extent v3d
+ in
+ (x,y,z)
+
+
+idx :: Values3D -> Int -> Int -> Int -> Double
+idx v3d i j k =
+ index v3d shape
+ where
+ shape :: DIM3
+ shape = (Z :. i :. j :. k)
projects / spline3.git / commitdiff