X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FFEM%2FR1.hs;h=dd5c11b023b9f267ddf2ac70479e2b4c6a004f85;hb=3274b18a2fb48f26e6582d9dcee11b4067230911;hp=f99b3dcace7be32ee7df3ba07a488dc012285ae2;hpb=d0056767bcf231e1d5cce78a85f6be0688770cc3;p=numerical-analysis.git

diff --git a/src/FEM/R1.hs b/src/FEM/R1.hs
index f99b3dc..dd5c11b 100644
--- a/src/FEM/R1.hs
+++ b/src/FEM/R1.hs
@@ -35,7 +35,7 @@ import qualified Algebra.RealField as RealField ( C )
 import qualified Algebra.ToRational as ToRational ( C )
 import Data.Vector.Fixed ( Arity, S )
 import NumericPrelude hiding ( abs )
-import qualified Prelude as P
+import Prelude ()
 
 import Integration.Gaussian ( gaussian )
 import Linear.Matrix (
@@ -583,33 +583,11 @@ solution pde params =
             combine ci ni = ci*(ni xi)
 
 
--- energy_true :: (Arity m, Arity n, Arity l,
---                 Algebraic.C a, Eq a, RealField.C a, ToRational.C a)
---             => PDE a
---             -> Params m n (S l) a
---             -> (a -> a) -- ^ True solution @u@
---             -> (a -> a) -- ^ Derivative of true solution @u'@
---             -> a
--- energy_true pde params u u' =
---   case (bdy pde) of
---     Left (Dirichlet (x1,x2)) ->
---       sqrt $ bilinear_form u u' u u'
---       where
---         two = fromInteger 2
---         q = affine_inv (x1,x2)
---         bilinear_form w w' v v' = (x2 - x1)*(gaussian integrand)/two
---           where
---             integrand x = ((big_A pde) (q x))*(w' (q x))*(v' (q x))
---                             + ((c pde) (q x))*(w (q x))*(v (q x))
-
---     _ -> error "Neumann BCs not implemented."
-
-
 energy_fem :: (Arity m, Arity n, Arity l,
                 Algebraic.C a, Eq a, RealField.C a, ToRational.C a)
-            => PDE a
-            -> Params m n (S l) a
-            -> a
+           => PDE a
+           -> Params m n (S l) a
+           -> a
 energy_fem pde params =
   (coefficients pde params) `dot` (big_F pde params)
 
@@ -637,8 +615,7 @@ relative_error_pointwise :: forall m n l a.
                          -> a -- ^ The point @x@ at which to compute the error.
                          -> a
 relative_error_pointwise pde params u x =
-  cent * ( u_exact - u_fem ) / u_exact
+  cent * ( abs $ (u x) - u_fem ) / ( abs $ u x )
   where
-    u_exact = abs $ u x
     u_fem = evaluate' (solution pde params) x
     cent = fromInteger 100