Start of support for CVODE

1 files changed, 456 insertions, 0 deletions

diff --git a/packages/sundials/src/Numeric/Sundials/CVode/ODE.hs b/packages/sundials/src/Numeric/Sundials/CVode/ODE.hs
new file mode 100644
index 0000000..f75d91f
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+++ b/packages/sundials/src/Numeric/Sundials/CVode/ODE.hs
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+{-# OPTIONS_GHC -Wall #-}
+
+{-# LANGUAGE QuasiQuotes #-}
+{-# LANGUAGE TemplateHaskell #-}
+{-# LANGUAGE MultiWayIf #-}
+{-# LANGUAGE OverloadedStrings #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Numeric.Sundials.CVode.ODE
+-- Copyright   :  Dominic Steinitz 2018,
+--                Novadiscovery 2018
+-- License     :  BSD
+-- Maintainer  :  Dominic Steinitz
+-- Stability   :  provisional
+--
+-- Solution of ordinary differential equation (ODE) initial value problems.
+--
+-- <https://computation.llnl.gov/projects/sundials/sundials-software>
+--
+-- A simple example:
+--
+-- <<diagrams/brusselator.png#diagram=brusselator&height=400&width=500>>
+--
+-- @
+-- import           Numeric.Sundials.CVode.ODE
+-- import           Numeric.LinearAlgebra
+--
+-- import           Plots as P
+-- import qualified Diagrams.Prelude as D
+-- import           Diagrams.Backend.Rasterific
+--
+-- 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
+--
+-- 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 = 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))
+-- @
+--
+-- KVAERNO_4_2_3
+--
+-- \[
+-- \begin{array}{c|cccc}
+-- 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
+-- 0.871733043 & 0.4358665215 & 0.4358665215 & 0.0 & 0.0 \\
+-- 1.0 & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
+-- 1.0 & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
+-- \hline
+--  & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
+--  & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
+-- \end{array}
+-- \]
+--
+-- SDIRK_2_1_2
+--
+-- \[
+-- \begin{array}{c|cc}
+-- 1.0 & 1.0 & 0.0 \\
+-- 0.0 & -1.0 & 1.0 \\
+-- \hline
+--  & 0.5 & 0.5 \\
+--  & 1.0 & 0.0 \\
+-- \end{array}
+-- \]
+--
+-- SDIRK_5_3_4
+--
+-- \[
+-- \begin{array}{c|ccccc}
+-- 0.25 & 0.25 & 0.0 & 0.0 & 0.0 & 0.0 \\
+-- 0.75 & 0.5 & 0.25 & 0.0 & 0.0 & 0.0 \\
+-- 0.55 & 0.34 & -4.0e-2 & 0.25 & 0.0 & 0.0 \\
+-- 0.5 & 0.2727941176470588 & -5.036764705882353e-2 & 2.7573529411764705e-2 & 0.25 & 0.0 \\
+-- 1.0 & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
+-- \hline
+--  & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
+--  & 1.2291666666666667 & -0.17708333333333334 & 7.03125 & -7.083333333333333 & 0.0 \\
+-- \end{array}
+-- \]
+-----------------------------------------------------------------------------
+module Numeric.Sundials.CVode.ODE ( odeSolve
+                                   , odeSolveV
+                                   , odeSolveVWith
+                                   , odeSolveVWith'
+                                   , ODEMethod(..)
+                                   , StepControl(..)
+                                   , Jacobian
+                                   , SundialsDiagnostics(..)
+                                   ) where
+
+import qualified Language.C.Inline as C
+import qualified Language.C.Inline.Unsafe as CU
+
+import           Data.Monoid ((<>))
+import           Data.Maybe (isJust)
+
+import           Foreign.C.Types
+import           Foreign.Ptr (Ptr)
+import           Foreign.ForeignPtr (newForeignPtr_)
+import           Foreign.Storable (Storable)
+
+import qualified Data.Vector.Storable as V
+import qualified Data.Vector.Storable.Mutable as VM
+
+import           Data.Coerce (coerce)
+import           System.IO.Unsafe (unsafePerformIO)
+
+import           Numeric.LinearAlgebra.Devel (createVector)
+
+import           Numeric.LinearAlgebra.HMatrix (Vector, Matrix, toList, (><),
+                                                subMatrix, rows, cols, toLists,
+                                                size, subVector)
+
+import qualified Types as T
+import           Arkode (cV_ADAMS, cV_BDF)
+import qualified Arkode as B
+
+
+C.context (C.baseCtx <> C.vecCtx <> C.funCtx <> T.sunCtx)
+
+C.include "<stdlib.h>"
+C.include "<stdio.h>"
+C.include "<math.h>"
+C.include "<cvode/cvode.h>"               -- prototypes for CVODE fcts., consts.
+C.include "<nvector/nvector_serial.h>"    -- serial N_Vector types, fcts., macros
+C.include "<sunmatrix/sunmatrix_dense.h>" -- access to dense SUNMatrix
+C.include "<sunlinsol/sunlinsol_dense.h>" -- access to dense SUNLinearSolver
+C.include "<cvode/cvode_direct.h>"        -- access to CVDls interface
+C.include "<sundials/sundials_types.h>"   -- definition of type realtype
+C.include "<sundials/sundials_math.h>"
+C.include "../../../helpers.h"
+C.include "Arkode_hsc.h"
+
+
+getDataFromContents :: Int -> Ptr T.SunVector -> IO (V.Vector CDouble)
+getDataFromContents len ptr = do
+  qtr <- B.getContentPtr ptr
+  rtr <- B.getData qtr
+  vectorFromC len rtr
+
+-- FIXME: Potentially an instance of Storable
+_getMatrixDataFromContents :: Ptr T.SunMatrix -> IO T.SunMatrix
+_getMatrixDataFromContents ptr = do
+  qtr <- B.getContentMatrixPtr ptr
+  rs  <- B.getNRows qtr
+  cs  <- B.getNCols qtr
+  rtr <- B.getMatrixData qtr
+  vs  <- vectorFromC (fromIntegral $ rs * cs) rtr
+  return $ T.SunMatrix { T.rows = rs, T.cols = cs, T.vals = vs }
+
+putMatrixDataFromContents :: T.SunMatrix -> Ptr T.SunMatrix -> IO ()
+putMatrixDataFromContents mat ptr = do
+  let rs = T.rows mat
+      cs = T.cols mat
+      vs = T.vals mat
+  qtr <- B.getContentMatrixPtr ptr
+  B.putNRows rs qtr
+  B.putNCols cs qtr
+  rtr <- B.getMatrixData qtr
+  vectorToC vs (fromIntegral $ rs * cs) rtr
+-- FIXME: END
+
+putDataInContents :: Storable a => V.Vector a -> Int -> Ptr b -> IO ()
+putDataInContents vec len ptr = do
+  qtr <- B.getContentPtr ptr
+  rtr <- B.getData qtr
+  vectorToC vec len rtr
+
+-- Utils
+
+vectorFromC :: Storable a => Int -> Ptr a -> IO (V.Vector a)
+vectorFromC len ptr = do
+  ptr' <- newForeignPtr_ ptr
+  V.freeze $ VM.unsafeFromForeignPtr0 ptr' len
+
+vectorToC :: Storable a => V.Vector a -> Int -> Ptr a -> IO ()
+vectorToC vec len ptr = do
+  ptr' <- newForeignPtr_ ptr
+  V.copy (VM.unsafeFromForeignPtr0 ptr' len) vec
+
+data SundialsDiagnostics = SundialsDiagnostics {
+    aRKodeGetNumSteps               :: Int
+  , aRKodeGetNumStepAttempts        :: Int
+  , aRKodeGetNumRhsEvals_fe         :: Int
+  , aRKodeGetNumRhsEvals_fi         :: Int
+  , aRKodeGetNumLinSolvSetups       :: Int
+  , aRKodeGetNumErrTestFails        :: Int
+  , aRKodeGetNumNonlinSolvIters     :: Int
+  , aRKodeGetNumNonlinSolvConvFails :: Int
+  , aRKDlsGetNumJacEvals            :: Int
+  , aRKDlsGetNumRhsEvals            :: Int
+  } deriving Show
+
+type Jacobian = Double -> Vector Double -> Matrix Double
+
+-- | Stepping functions
+data ODEMethod = ADAMS
+               | BDF
+
+getMethod :: ODEMethod -> Int
+getMethod (ADAMS) = cV_ADAMS
+getMethod (BDF)   = cV_BDF
+
+getJacobian :: ODEMethod -> Maybe Jacobian
+getJacobian _ = Nothing
+
+-- | A version of 'odeSolveVWith' with reasonable default step control.
+odeSolveV
+    :: ODEMethod
+    -> Maybe Double      -- ^ initial step size - by default, ARKode
+                         -- estimates the initial step size to be the
+                         -- solution \(h\) of the equation
+                         -- \(\|\frac{h^2\ddot{y}}{2}\| = 1\), where
+                         -- \(\ddot{y}\) is an estimated value of the
+                         -- second derivative of the solution at \(t_0\)
+    -> Double            -- ^ absolute tolerance for the state vector
+    -> Double            -- ^ relative tolerance for the state vector
+    -> (Double -> Vector Double -> Vector Double) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
+    -> Vector Double     -- ^ initial conditions
+    -> Vector Double     -- ^ desired solution times
+    -> Matrix Double     -- ^ solution
+odeSolveV meth hi epsAbs epsRel f y0 ts =
+  case odeSolveVWith meth (X epsAbs epsRel) hi g y0 ts of
+    Left c -> error $ show c -- FIXME
+    -- FIXME: Can we do better than using lists?
+    Right (v, d) -> (nR >< nC) (V.toList v)
+  where
+    us = toList ts
+    nR = length us
+    nC = size y0
+    g t x0 = coerce $ f t x0
+
+-- | A version of 'odeSolveV' with reasonable default parameters and
+-- system of equations defined using lists. FIXME: we should say
+-- something about the fact we could use the Jacobian but don't for
+-- compatibility with hmatrix-gsl.
+odeSolve :: (Double -> [Double] -> [Double]) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
+         -> [Double]                         -- ^ initial conditions
+         -> Vector Double                    -- ^ desired solution times
+         -> Matrix Double                    -- ^ solution
+odeSolve f y0 ts =
+  -- FIXME: These tolerances are different from the ones in GSL
+  case odeSolveVWith BDF (XX' 1.0e-6 1.0e-10 1 1)  Nothing g (V.fromList y0) (V.fromList $ toList ts) of
+    Left c -> error $ show c -- FIXME
+    Right (v, d) -> (nR >< nC) (V.toList v)
+  where
+    us = toList ts
+    nR = length us
+    nC = length y0
+    g t x0 = V.fromList $ f t (V.toList x0)
+
+odeSolveVWith' ::
+  ODEMethod
+  -> StepControl
+  -> Maybe Double -- ^ initial step size - by default, ARKode
+                  -- estimates the initial step size to be the
+                  -- solution \(h\) of the equation
+                  -- \(\|\frac{h^2\ddot{y}}{2}\| = 1\), where
+                  -- \(\ddot{y}\) is an estimated value of the second
+                  -- derivative of the solution at \(t_0\)
+  -> (Double -> V.Vector Double -> V.Vector Double) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
+  -> V.Vector Double                     -- ^ Initial conditions
+  -> V.Vector Double                     -- ^ Desired solution times
+  -> Matrix Double                       -- ^ Error code or solution
+odeSolveVWith' method control initStepSize f y0 tt =
+  case odeSolveVWith method control initStepSize f y0 tt of
+    Left c        -> error $ show c -- FIXME
+    Right (v, _d) -> (nR >< nC) (V.toList v)
+  where
+    nR = V.length tt
+    nC = V.length y0
+
+odeSolveVWith ::
+  ODEMethod
+  -> StepControl
+  -> Maybe Double -- ^ initial step size - by default, ARKode
+                  -- estimates the initial step size to be the
+                  -- solution \(h\) of the equation
+                  -- \(\|\frac{h^2\ddot{y}}{2}\| = 1\), where
+                  -- \(\ddot{y}\) is an estimated value of the second
+                  -- derivative of the solution at \(t_0\)
+  -> (Double -> V.Vector Double -> V.Vector Double) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
+  -> V.Vector Double                     -- ^ Initial conditions
+  -> V.Vector Double                     -- ^ Desired solution times
+  -> Either Int ((V.Vector Double), SundialsDiagnostics) -- ^ Error code or solution
+odeSolveVWith method control initStepSize f y0 tt =
+  case solveOdeC (fromIntegral $ getMethod method) (coerce initStepSize) jacH (scise control)
+                 (coerce f) (coerce y0) (coerce tt) of
+    Left c -> Left $ fromIntegral c
+    Right (v, d) -> Right (coerce v, d)
+  where
+    l = size y0
+    scise (X absTol relTol)                          = coerce (V.replicate l absTol, relTol)
+    scise (X' absTol relTol)                         = coerce (V.replicate l absTol, relTol)
+    scise (XX' absTol relTol yScale _yDotScale)      = coerce (V.replicate l absTol, yScale * relTol)
+    -- FIXME; Should we check that the length of ss is correct?
+    scise (ScXX' absTol relTol yScale _yDotScale ss) = coerce (V.map (* absTol) ss, yScale * relTol)
+    jacH = fmap (\g t v -> matrixToSunMatrix $ g (coerce t) (coerce v)) $
+           getJacobian method
+    matrixToSunMatrix m = T.SunMatrix { T.rows = nr, T.cols = nc, T.vals = vs }
+      where
+        nr = fromIntegral $ rows m
+        nc = fromIntegral $ cols m
+        -- FIXME: efficiency
+        vs = V.fromList $ map coerce $ concat $ toLists m
+
+solveOdeC ::
+  CInt ->
+  Maybe CDouble ->
+  (Maybe (CDouble -> V.Vector CDouble -> T.SunMatrix)) ->
+  (V.Vector CDouble, CDouble) ->
+  (CDouble -> V.Vector CDouble -> V.Vector CDouble) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
+  -> V.Vector CDouble -- ^ Initial conditions
+  -> V.Vector CDouble -- ^ Desired solution times
+  -> Either CInt ((V.Vector CDouble), SundialsDiagnostics) -- ^ Error code or solution
+solveOdeC method initStepSize jacH (absTols, relTol) fun f0 ts = unsafePerformIO $ do
+
+  let isInitStepSize :: CInt
+      isInitStepSize = fromIntegral $ fromEnum $ isJust initStepSize
+      ss :: CDouble
+      ss = case initStepSize of
+             -- It would be better to put an error message here but
+             -- inline-c seems to evaluate this even if it is never
+             -- used :(
+             Nothing -> 0.0
+             Just x  -> x
+  let dim = V.length f0
+      nEq :: CLong
+      nEq = fromIntegral dim
+      nTs :: CInt
+      nTs = fromIntegral $ V.length ts
+  -- FIXME: fMut is not actually mutatated
+  fMut <- V.thaw f0
+  tMut <- V.thaw ts
+  -- FIXME: I believe this gets taken from the ghc heap and so should
+  -- be subject to garbage collection.
+  -- quasiMatrixRes <- createVector ((fromIntegral dim) * (fromIntegral nTs))
+  -- qMatMut <- V.thaw quasiMatrixRes
+  diagnostics :: V.Vector CLong <- createVector 10 -- FIXME
+  diagMut <- V.thaw diagnostics
+  -- We need the types that sundials expects. These are tied together
+  -- in 'Types'. FIXME: The Haskell type is currently empty!
+  let funIO :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt
+      funIO x y f _ptr = do
+        -- Convert the pointer we get from C (y) to a vector, and then
+        -- apply the user-supplied function.
+        fImm <- fun x <$> getDataFromContents dim y
+        -- Fill in the provided pointer with the resulting vector.
+        putDataInContents fImm dim f
+        -- FIXME: I don't understand what this comment means
+        -- Unsafe since the function will be called many times.
+        [CU.exp| int{ 0 } |]
+  let isJac :: CInt
+      isJac = fromIntegral $ fromEnum $ isJust jacH
+      jacIO :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr T.SunMatrix ->
+               Ptr () -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr T.SunVector ->
+               IO CInt
+      jacIO t y _fy jacS _ptr _tmp1 _tmp2 _tmp3 = do
+        case jacH of
+          Nothing   -> error "Numeric.Sundials.ARKode.ODE: Jacobian not defined"
+          Just jacI -> do j <- jacI t <$> getDataFromContents dim y
+                          putMatrixDataFromContents j jacS
+                          -- FIXME: I don't understand what this comment means
+                          -- Unsafe since the function will be called many times.
+                          [CU.exp| int{ 0 } |]
+
+  res <- [C.block| int {
+                         /* general problem variables */
+
+                         int flag;                  /* reusable error-checking flag                 */
+                         int i, j;                  /* reusable loop indices                        */
+                         N_Vector y = NULL;         /* empty vector for storing solution            */
+                         void *cvode_mem = NULL;    /* empty CVODE memory structure                 */
+
+                         /* general problem parameters */
+
+                         realtype T0 = RCONST(($vec-ptr:(double *ts))[0]); /* initial time              */
+                         sunindextype NEQ = $(sunindextype nEq);           /* number of dependent vars. */
+
+                         /* Initialize data structures */
+
+                         y = N_VNew_Serial(NEQ); /* Create serial vector for solution */
+                         if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
+                         /* Specify initial condition */
+                         for (i = 0; i < NEQ; i++) {
+                           NV_Ith_S(y,i) = ($vec-ptr:(double *f0))[i];
+                         };
+
+                         cvode_mem = CVodeCreate(CV_BDF, CV_NEWTON);
+                         if (check_flag((void *)cvode_mem, "CVodeCreate", 0)) return(1);
+
+                         /* Call CVodeInit to initialize the integrator memory and specify the
+                          * user's right hand side function in y'=f(t,y), the inital time T0, and
+                          * the initial dependent variable vector y. */
+                         flag = CVodeInit(cvode_mem,   $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y);
+                         if (check_flag(&flag, "CVodeInit", 1)) return(1);
+
+                         /* Clean up and return */
+
+                         N_VDestroy(y);          /* Free y vector          */
+                         CVodeFree(&cvode_mem);  /* Free integrator memory */
+
+                         return flag;
+                       } |]
+  if res == 0
+    then do
+      return $ Left res
+    else do
+      return $ Left res
+
+-- | Adaptive step-size control
+-- functions.
+--
+-- [GSL](https://www.gnu.org/software/gsl/doc/html/ode-initval.html#adaptive-step-size-control)
+-- allows the user to control the step size adjustment using
+-- \(D_i = \epsilon^{abs}s_i + \epsilon^{rel}(a_{y} |y_i| + a_{dy/dt} h |\dot{y}_i|)\) where
+-- \(\epsilon^{abs}\) is the required absolute error, \(\epsilon^{rel}\)
+-- is the required relative error, \(s_i\) is a vector of scaling
+-- factors, \(a_{y}\) is a scaling factor for the solution \(y\) and
+-- \(a_{dydt}\) is a scaling factor for the derivative of the solution \(dy/dt\).
+--
+-- [ARKode](https://computation.llnl.gov/projects/sundials/arkode)
+-- allows the user to control the step size adjustment using
+-- \(\eta^{rel}|y_i| + \eta^{abs}_i\). For compatibility with
+-- [hmatrix-gsl](https://hackage.haskell.org/package/hmatrix-gsl),
+-- tolerances for \(y\) and \(\dot{y}\) can be specified but the latter have no
+-- effect.
+data StepControl = X     Double Double -- ^ absolute and relative tolerance for \(y\); in GSL terms, \(a_{y} = 1\) and \(a_{dy/dt} = 0\); in ARKode terms, the \(\eta^{abs}_i\) are identical
+                 | X'    Double Double -- ^ absolute and relative tolerance for \(\dot{y}\); in GSL terms, \(a_{y} = 0\) and \(a_{dy/dt} = 1\); in ARKode terms, the latter is treated as the relative tolerance for \(y\) so this is the same as specifying 'X' which may be entirely incorrect for the given problem
+                 | XX'   Double Double Double Double -- ^ include both via relative tolerance
+                                                     -- scaling factors \(a_y\), \(a_{{dy}/{dt}}\); in ARKode terms, the latter is ignored and \(\eta^{rel} = a_{y}\epsilon^{rel}\)
+                 | ScXX' Double Double Double Double (Vector Double) -- ^ scale absolute tolerance of \(y_i\); in ARKode terms, \(a_{{dy}/{dt}}\) is ignored, \(\eta^{abs}_i = s_i \epsilon^{abs}\) and \(\eta^{rel} = a_{y}\epsilon^{rel}\)