import Numeric.LinearAlgebra hiding (i, scale)
import Prelude hiding (LT)
+import Test.QuickCheck (Arbitrary(..), Gen)
import Cardinal
import FunctionValues
v3 :: Point }
deriving (Eq)
+
+instance Arbitrary Tetrahedron where
+ arbitrary = do
+ rnd_v0 <- arbitrary :: Gen Point
+ rnd_v1 <- arbitrary :: Gen Point
+ rnd_v2 <- arbitrary :: Gen Point
+ rnd_v3 <- arbitrary :: Gen Point
+ rnd_fv <- arbitrary :: Gen FunctionValues
+ return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
+
+
instance Show Tetrahedron where
show t = "Tetrahedron:\n" ++
" fv: " ++ (show (fv t)) ++ "\n" ++
b3_term = (b3 t) `fexp` l
+-- | The coefficient function. c t i j k l returns the coefficient
+-- c_ijkl with respect to the tetrahedron t. The definition uses
+-- pattern matching to mimic the definitions given in Sorokina and
+-- Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
+-- function will simply error.
c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
c t 0 0 3 0 = eval (fv t) $
(1/8) * (I + F + L + T + LT + FL + FT + FLT)
+-- | The matrix used in the tetrahedron volume calculation as given in
+-- Lai & Schumaker, Definition 15.4, page 436.
vol_matrix :: Tetrahedron -> Matrix Double
vol_matrix t = (4><4)
[1, 1, 1, 1,