Improve haddock

2 files changed, 124 insertions, 67 deletions

diff --git a/packages/sundials/src/Main.hs b/packages/sundials/src/Main.hs
index d22fafa..b65d668 100644
--- a/packages/sundials/src/Main.hs
+++ b/packages/sundials/src/Main.hs
@@ -94,44 +94,39 @@ kSaxis :: [(Double, Double)] -> P.Axis B D.V2 Double
 kSaxis xs = P.r2Axis &~ do
   P.linePlot' xs
 
-butcherTableauTex :: (Show a, Element a) => Matrix a -> String
-butcherTableauTex m = render $
-                    vcat [ text ("\n\\begin{array}{c|" ++ (concat $ replicate n "c") ++ "}")
-                         , us
-                         , text "\\end{array}"
-                         ]
+butcherTableauTex :: ButcherTable -> String
+butcherTableauTex (ButcherTable m c b b2) =
+  render $
+  vcat [ text ("\n\\begin{array}{c|" ++ (concat $ replicate n "c") ++ "}")
+       , us
+       , text "\\hline"
+       , text bs <+> text "\\\\"
+       , text b2s <+> text "\\\\"
+       , text "\\end{array}"
+       ]
   where
     n = rows m
     rs = toLists m
     ss = map (\r -> intercalate " & " $ map show r) rs
-    ts = zipWith (\i r -> "c_" ++ show i ++ " & " ++ r) [1..n] ss
+    ts = zipWith (\i r -> show i ++ " & " ++ r) (toList c) ss
     us = vcat $ map (\r -> text r <+> text "\\\\") ts
+    bs  = " & " ++ (intercalate " & " $ map show $ toList b)
+    b2s = " & " ++ (intercalate " & " $ map show $ toList b2)
 
 main :: IO ()
 main = do
-  -- $$
-  -- \begin{array}{c|cccc}
-  -- c_1    & a_{11} & a_{12}& \dots & a_{1s}\\
-  -- c_2    & a_{21} & a_{22}& \dots & a_{2s}\\
-  -- \vdots & \vdots & \vdots& \ddots& \vdots\\
-  -- c_s    & a_{s1} & a_{s2}& \dots & a_{ss} \\
-  -- \hline
-  --        & b_1    & b_2   & \dots & b_s\\
-  --        & b^*_1  & b^*_2 & \dots & b^*_s\\
-  -- \end{array}
-  -- $$
-
-  let res = btGet (SDIRK_2_1_2 undefined)
+
+  let res = butcherTable (SDIRK_2_1_2 undefined)
   putStrLn $ show res
-  putStrLn $ butcherTableauTex $ fst res
+  putStrLn $ butcherTableauTex res
 
-  let res = btGet (KVAERNO_4_2_3 undefined)
+  let res = butcherTable (KVAERNO_4_2_3 undefined)
   putStrLn $ show res
-  putStrLn $ butcherTableauTex $ fst res
+  putStrLn $ butcherTableauTex res
 
-  let res = btGet (SDIRK_5_3_4 undefined)
+  let res = butcherTable (SDIRK_5_3_4 undefined)
   putStrLn $ show res
-  putStrLn $ butcherTableauTex $ fst res
+  putStrLn $ butcherTableauTex res
 
   let res1 = odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0])
   renderRasterific "diagrams/brusselator.png"
diff --git a/packages/sundials/src/Numeric/Sundials/ARKode/ODE.hs b/packages/sundials/src/Numeric/Sundials/ARKode/ODE.hs
index b6a59e2..67378cc 100644
--- a/packages/sundials/src/Numeric/Sundials/ARKode/ODE.hs
+++ b/packages/sundials/src/Numeric/Sundials/ARKode/ODE.hs
@@ -21,30 +21,57 @@
 --
 -- A simple example:
 --
+-- <<diagrams/brusselator.png#diagram=brusselator&height=400&width=500>>
+--
 -- @
--- import Numeric.Sundials.ARKode
--- import Numeric.LinearAlgebra
--- import Graphics.Plot(mplot)
+-- import           Numeric.Sundials.ARKode.ODE
+-- import           Numeric.LinearAlgebra
 --
--- xdot t [x,v] = [v, -0.95*x - 0.1*v]
+-- import           Plots as P
+-- import qualified Diagrams.Prelude as D
+-- import           Diagrams.Backend.Rasterific
 --
--- ts = linspace 100 (0,20 :: Double)
+-- brusselator :: Double -> [Double] -> [Double]
+-- brusselator _t x = [ a - (w + 1) * u + v * u * u
+--                    , w * u - v * u * u
+--                    , (b - w) / eps - w * u
+--                    ]
+--   where
+--     a = 1.0
+--     b = 3.5
+--     eps = 5.0e-6
+--     u = x !! 0
+--     v = x !! 1
+--     w = x !! 2
 --
--- sol = odeSolve xdot [10,0] ts
+-- lSaxis :: [[Double]] -> P.Axis B D.V2 Double
+-- lSaxis xs = P.r2Axis &~ do
+--   let ts = xs!!0
+--       us = xs!!1
+--       vs = xs!!2
+--       ws = xs!!3
+--   P.linePlot' $ zip ts us
+--   P.linePlot' $ zip ts vs
+--   P.linePlot' $ zip ts ws
 --
--- main = mplot (ts : toColumns sol)
+-- main = do
+--   let res1 = odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0])
+--   renderRasterific "diagrams/brusselator.png"
+--                    (D.dims2D 500.0 500.0)
+--                    (renderAxis $ lSaxis $ [0.0, 0.1 .. 10.0]:(toLists $ tr res1))
 -- @
 --
--- <<diagrams/brusselator.png#diagram=brusselator&height=400&width=500>>
---
 -- KVAERNO_4_2_3
 --
 -- \[
 -- \begin{array}{c|cccc}
--- c_1 & 0.0 & 0.0 & 0.0 & 0.0 \\
--- c_2 & 0.4358665215 & 0.4358665215 & 0.0 & 0.0 \\
--- c_3 & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
--- c_4 & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
+-- 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
+-- 0.871733043 & 0.4358665215 & 0.4358665215 & 0.0 & 0.0 \\
+-- 1.0 & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
+-- 1.0 & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
+-- \hline
+--  & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
+--  & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
 -- \end{array}
 -- \]
 --
@@ -52,8 +79,11 @@
 --
 -- \[
 -- \begin{array}{c|cc}
--- c_1 & 1.0 & 0.0 \\
--- c_2 & -1.0 & 1.0 \\
+-- 1.0 & 1.0 & 0.0 \\
+-- 0.0 & -1.0 & 1.0 \\
+-- \hline
+--  & 0.5 & 0.5 \\
+--  & 1.0 & 0.0 \\
 -- \end{array}
 -- \]
 --
@@ -61,20 +91,22 @@
 --
 -- \[
 -- \begin{array}{c|ccccc}
--- c_1 & 0.25 & 0.0 & 0.0 & 0.0 & 0.0 \\
--- c_2 & 0.5 & 0.25 & 0.0 & 0.0 & 0.0 \\
--- c_3 & 0.34 & -4.0e-2 & 0.25 & 0.0 & 0.0 \\
--- c_4 & 0.2727941176470588 & -5.036764705882353e-2 & 2.7573529411764705e-2 & 0.25 & 0.0 \\
--- c_5 & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
+-- 0.25 & 0.25 & 0.0 & 0.0 & 0.0 & 0.0 \\
+-- 0.75 & 0.5 & 0.25 & 0.0 & 0.0 & 0.0 \\
+-- 0.55 & 0.34 & -4.0e-2 & 0.25 & 0.0 & 0.0 \\
+-- 0.5 & 0.2727941176470588 & -5.036764705882353e-2 & 2.7573529411764705e-2 & 0.25 & 0.0 \\
+-- 1.0 & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
+-- \hline
+--  & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
+--  & 1.2291666666666667 & -0.17708333333333334 & 7.03125 & -7.083333333333333 & 0.0 \\
 -- \end{array}
 -- \]
 -----------------------------------------------------------------------------
 module Numeric.Sundials.ARKode.ODE ( odeSolve
                                    , odeSolveV
                                    , odeSolveVWith
-                                   , getButcherTable
-                                   , getBT
-                                   , btGet
+                                   , ButcherTable(..)
+                                   , butcherTable
                                    , ODEMethod(..)
                                    , StepControl(..)
                                    , SundialsDiagnostics(..)
@@ -457,10 +489,11 @@ solveOdeC method jacH (absTols, relTol) fun f0 ts = unsafePerformIO $ do
                          ($vec-ptr:(long int *diagMut))[9] = ncfn;
 
                          /* Clean up and return */
-                         N_VDestroy(y);            /* Free y vector */
+                         N_VDestroy(y);            /* Free y vector          */
+                         N_VDestroy(tv);           /* Free tv vector         */
                          ARKodeFree(&arkode_mem);  /* Free integrator memory */
-                         SUNLinSolFree(LS);        /* Free linear solver */
-                         SUNMatDestroy(A);         /* Free A matrix */
+                         SUNLinSolFree(LS);        /* Free linear solver     */
+                         SUNMatDestroy(A);         /* Free A matrix          */
 
                          return flag;
                        } |]
@@ -482,22 +515,43 @@ solveOdeC method jacH (absTols, relTol) fun f0 ts = unsafePerformIO $ do
     else do
       return $ Left res
 
-btGet :: ODEMethod -> (Matrix Double, Vector Double)
-btGet method = case getBT method of
-                 Left c -> error $ show c -- FIXME
-                 Right ((v, w), sqp) -> ( subMatrix (0, 0) (s, s) $
-                                          (B.arkSMax >< B.arkSMax) (V.toList v)
-                                        , subVector 0 s w)
-                   where
-                     s = fromIntegral $ sqp V.! 0
+data ButcherTable = ButcherTable { am  :: Matrix Double
+                                 , cv  :: Vector Double
+                                 , bv  :: Vector Double
+                                 , b2v :: Vector Double
+                                 }
+  deriving Show
+
+data ButcherTable' a = ButcherTable' { am'  :: V.Vector a
+                                     , cv'  :: V.Vector a
+                                     , bv'  :: V.Vector a
+                                     , b2v' :: V.Vector a
+                                     }
+  deriving Show
+
+butcherTable :: ODEMethod -> ButcherTable
+butcherTable method =
+  case getBT method of
+    Left c -> error $ show c -- FIXME
+    Right (ButcherTable' v w x y, sqp) ->
+      ButcherTable { am = subMatrix (0, 0) (s, s) $ (B.arkSMax >< B.arkSMax) (V.toList v)
+                   , cv = subVector 0 s w
+                   , bv = subVector 0 s x
+                   , b2v = subVector 0 s y
+                   }
+      where
+        s = fromIntegral $ sqp V.! 0
 
-getBT :: ODEMethod -> Either Int ((V.Vector Double, V.Vector Double), V.Vector Int)
+getBT :: ODEMethod -> Either Int (ButcherTable' Double, V.Vector Int)
 getBT method = case getButcherTable method of
-                 Left c -> Left $ fromIntegral c
-                 Right ((v, w), sqp) -> Right $ ((coerce v, coerce w), V.map fromIntegral sqp)
+                 Left c ->
+                   Left $ fromIntegral c
+                 Right (ButcherTable' a b c d, sqp) ->
+                   Right $ ( ButcherTable' (coerce a) (coerce b) (coerce c) (coerce d)
+                           , V.map fromIntegral sqp )
 
 getButcherTable :: ODEMethod
-                -> Either CInt ((V.Vector CDouble, V.Vector CDouble), V.Vector CInt)
+                -> Either CInt (ButcherTable' CDouble, V.Vector CInt)
 getButcherTable method = unsafePerformIO $ do
   -- ARKode seems to want an ODE in order to set and then get the
   -- Butcher tableau so here's one to keep it happy
@@ -515,8 +569,12 @@ getButcherTable method = unsafePerformIO $ do
   btSQPMut <- V.thaw btSQP
   btAs :: V.Vector CDouble <- createVector (B.arkSMax * B.arkSMax)
   btAsMut <- V.thaw btAs
-  btCs :: V.Vector CDouble <- createVector B.arkSMax
-  btCsMut <- V.thaw btCs
+  btCs  :: V.Vector CDouble <- createVector B.arkSMax
+  btBs  :: V.Vector CDouble <- createVector B.arkSMax
+  btB2s :: V.Vector CDouble <- createVector B.arkSMax
+  btCsMut  <- V.thaw btCs
+  btBsMut  <- V.thaw btBs
+  btB2sMut <- V.thaw btB2s
   let funIO :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt
       funIO x y f _ptr = do
         fImm <- fun x <$> getDataFromContents dim y
@@ -576,7 +634,9 @@ getButcherTable method = unsafePerformIO $ do
                          }
 
                          for (i = 0; i < s; i++) {
-                           ($vec-ptr:(double *btCsMut))[i] = ci[i];
+                           ($vec-ptr:(double *btCsMut))[i]  = ci[i];
+                           ($vec-ptr:(double *btBsMut))[i]  = bi[i];
+                           ($vec-ptr:(double *btB2sMut))[i] = b2i[i];
                          }
 
                          /* Clean up and return */
@@ -590,7 +650,9 @@ getButcherTable method = unsafePerformIO $ do
       x <- V.freeze btAsMut
       y <- V.freeze btSQPMut
       z <- V.freeze btCsMut
-      return $ Right ((x, z), y)
+      u <- V.freeze btBsMut
+      v <- V.freeze btB2sMut
+      return $ Right (ButcherTable' { am' = x, cv' = z, bv' = u, b2v' = v }, y)
     else do
       return $ Left res