Laplace equation using linear relations in hmatrix

laplace.hs

type HLinRel2D u d l r = HLinRel (Either u l) (Either d r)


{-
A stencil  of 2d resistors for tiling


          u
          /
          \
          /
         |
l -/\/\/----/\/\/\-  r
         |
         /
         \
         /
         |
         d


        -}
stencil :: HLinRel2D IV IV IV IV
stencil = (hpar r10 r10) <<< short <<< (hpar r10 r10) where r10 = resistor 10

horicomp :: forall w w' w'' w''' a b c. (BEnum w, BEnum w', BEnum a, BEnum w''', BEnum b, BEnum w'', BEnum c ) => HLinRel2D w' w'' b c -> HLinRel2D w w''' a b -> HLinRel2D (Either w' w) (Either w'' w''') a c
horicomp f g = hcompose f' g' where 
               f' :: HLinRel (Either (Either w' w''') b) (Either (Either w'' w''') c)
               f' = (first hswap) <<< hassoc' <<< (hpar hid f) <<< hassoc <<<  (first hswap) 
               g' :: HLinRel (Either (Either w' w) a) (Either (Either w' w''') b)
               g' = hassoc' <<< (hpar hid g) <<< hassoc


rotate :: (BEnum w, BEnum w', BEnum a, BEnum b) => HLinRel2D w w' a b -> HLinRel2D a b w w'                                      
rotate f = hswap <<< f <<< hswap

vertcomp :: (BEnum w, BEnum w', BEnum a, BEnum d, BEnum b, BEnum w'', BEnum c ) => HLinRel2D w'  w'' c d -> HLinRel2D w w' a b -> HLinRel2D w w'' (Either c a) (Either d b)
vertcomp f g = rotate (horicomp (rotate f)  (rotate g) )