{-# OPTIONS_GHC -Wall #-}

{-# LANGUAGE QuasiQuotes #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}

module Numeric.Sundials.Arkode.ODE ( solveOde
                                   , odeSolve
                                   ) where

import qualified Language.C.Inline as C
import qualified Language.C.Inline.Unsafe as CU

import           Data.Monoid ((<>))

import           Foreign.C.Types
import           Foreign.Ptr (Ptr)
import           Foreign.ForeignPtr (newForeignPtr_)
import           Foreign.Storable (Storable, peekByteOff)

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, (><))

import qualified Types as T

C.context (C.baseCtx <> C.vecCtx <> C.funCtx <> T.sunCtx)

-- C includes
C.include "<stdlib.h>"
C.include "<stdio.h>"
C.include "<math.h>"
C.include "<arkode/arkode.h>"                 -- prototypes for ARKODE 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 "<arkode/arkode_direct.h>"          -- access to ARKDls interface          
C.include "<sundials/sundials_types.h>"       -- definition of type realtype         
C.include "<sundials/sundials_math.h>"
C.include "../../../helpers.h"


-- These were semi-generated using hsc2hs with Bar.hsc as the
-- template. They are probably very fragile and could easily break on
-- different architectures and / or changes in the sundials package.

getContentPtr :: Storable a => Ptr b -> IO a
getContentPtr ptr = ((\hsc_ptr -> peekByteOff hsc_ptr 0)) ptr

getData :: Storable a => Ptr b -> IO a
getData ptr = ((\hsc_ptr -> peekByteOff hsc_ptr 16)) ptr

getDataFromContents :: Storable b => Int -> Ptr a -> IO (V.Vector b)
getDataFromContents len ptr = do
  qtr <- getContentPtr ptr
  rtr <- getData qtr
  vectorFromC len rtr

putDataInContents :: Storable a => V.Vector a -> Int -> Ptr b -> IO ()
putDataInContents vec len ptr = do
  qtr <- getContentPtr ptr
  rtr <- 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

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 = case solveOde g (V.fromList y0) (V.fromList $ toList ts) of
                     Left c -> error $ show c -- FIXME
                     Right (v, _) -> (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)

solveOde :: 
  (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
solveOde f y0 tt = case solveOdeC (coerce f) (coerce y0) (coerce tt) of
                     Left c -> Left $ fromIntegral c
                     Right (v, d) -> Right (coerce v, d)
                        
solveOdeC ::
  (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 fun f0 ts = unsafePerformIO $ do
  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.BarType -> Ptr T.BarType -> 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
        -- 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 */
                         N_Vector y = NULL;              /* empty vector for storing solution */
                         SUNMatrix A = NULL;             /* empty matrix for linear solver */
                         SUNLinearSolver LS = NULL;      /* empty linear solver object */
                         void *arkode_mem = NULL;        /* empty ARKode memory structure */
                         realtype t;
                         long int nst, nst_a, nfe, nfi, nsetups, nje, nfeLS, nni, ncfn, netf;

                         /* general problem parameters */
                         realtype T0 = RCONST(($vec-ptr:(double *tMut))[0]);    /* initial time */

                         sunindextype NEQ = $(sunindextype nEq); /* number of dependent vars. */
                         realtype reltol = 1.0e-6;     /* tolerances */
                         realtype abstol = 1.0e-10;

                         /* Initial diagnostics output */
                         printf("\nAnalytical ODE test problem:\n");
                         printf("   reltol = %.1"ESYM"\n",  reltol);
                         printf("   abstol = %.1"ESYM"\n\n",abstol);

                         /* Initialize data structures */
                         y = N_VNew_Serial(NEQ);      /* Create serial vector for solution */
                         if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
                         int i, j;
                         for (i = 0; i < NEQ; i++) {
                           NV_Ith_S(y,i) = ($vec-ptr:(double *fMut))[i];
                         }; /* Specify initial condition */
                         arkode_mem = ARKodeCreate(); /* Create the solver memory */
                         if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1;

                         /* Call ARKodeInit to initialize the integrator memory and specify the */
                         /*    right-hand side function in y'=f(t,y), the inital time T0, and */
                         /*    the initial dependent variable vector y.  Note: since this */
                         /*    problem is fully implicit, we set f_E to NULL and f_I to f. */

                         /* Here we use the C types defined in helpers.h which tie up with */
                         /* the Haskell types defined in Types                             */
                         flag = ARKodeInit(arkode_mem, NULL, $fun:(int (* funIO) (double t, BarType y[], BarType dydt[], void * params)), T0, y);
                         if (check_flag(&flag, "ARKodeInit", 1)) return 1;

                         /* Set routines */
                         flag = ARKodeSStolerances(arkode_mem, reltol, abstol);  /* Specify tolerances */
                         if (check_flag(&flag, "ARKodeSStolerances", 1)) return 1;

                         /* Initialize dense matrix data structure and solver */
                         A = SUNDenseMatrix(NEQ, NEQ);
                         if (check_flag((void *)A, "SUNDenseMatrix", 0)) return 1;
                         LS = SUNDenseLinearSolver(y, A);
                         if (check_flag((void *)LS, "SUNDenseLinearSolver", 0)) return 1;

                         /* Linear solver interface */
                         flag = ARKDlsSetLinearSolver(arkode_mem, LS, A);        /* Attach matrix and linear solver */
                         /* Store initial conditions */
                         for (j = 0; j < NEQ; j++) {
                           ($vec-ptr:(double *qMatMut))[0 * $(int nTs) + j] = NV_Ith_S(y,j);
                         }

                         flag = ARKodeSetIRKTableNum(arkode_mem, KVAERNO_4_2_3);
                         if (check_flag(&flag, "ARKode", 1)) return 1;

                         int s, q, p;
                         realtype *ai = (realtype *)malloc(ARK_S_MAX * ARK_S_MAX * sizeof(realtype));
                         realtype *ae = (realtype *)malloc(ARK_S_MAX * ARK_S_MAX * sizeof(realtype));
                         realtype *ci = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
                         realtype *ce = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
                         realtype *bi = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
                         realtype *be = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
                         realtype *b2i = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
                         realtype *b2e = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
                         flag = ARKodeGetCurrentButcherTables(arkode_mem, &s, &q, &p, ai, ae, ci, ce, bi, be, b2i, b2e);
                         if (check_flag(&flag, "ARKode", 1)) return 1;
                         fprintf(stderr, "s = %d, q = %d, p = %d\n", s, q, p);
                         for (i = 0; i < s; i++) {
                           for (j = 0; j < s; j++) {
                             fprintf(stderr, "ai[%d,%d] = %f", i, j, ai[i * ARK_S_MAX + j]);
                           }
                           fprintf(stderr, "\n");
                         }

                         /* Main time-stepping loop: calls ARKode to perform the integration */
                         /* Stops when the final time has been reached */
                         for (i = 1; i < $(int nTs); i++) {

                           flag = ARKode(arkode_mem, ($vec-ptr:(double *tMut))[i], y, &t, ARK_NORMAL); /* call integrator */
                           if (check_flag(&flag, "ARKode", 1)) break;

                           /* Store the results for Haskell */
                           for (j = 0; j < NEQ; j++) {
                             ($vec-ptr:(double *qMatMut))[i * NEQ + j] = NV_Ith_S(y,j);
                           }

                           if (flag < 0) {                                                 /* unsuccessful solve: break */
                             fprintf(stderr,"Solver failure, stopping integration\n");
                             break;
                           }
                         }

                         /* Get some final statistics on how the solve progressed */
                         flag = ARKodeGetNumSteps(arkode_mem, &nst);
                         check_flag(&flag, "ARKodeGetNumSteps", 1);
                         ($vec-ptr:(long int *diagMut))[0] = nst;

                         flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a);
                         check_flag(&flag, "ARKodeGetNumStepAttempts", 1);
                         ($vec-ptr:(long int *diagMut))[1] = nst_a;

                         flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
                         check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
                         ($vec-ptr:(long int *diagMut))[2] = nfe;
                         ($vec-ptr:(long int *diagMut))[3] = nfi;

                         flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
                         check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
                         ($vec-ptr:(long int *diagMut))[4] = nsetups;

                         flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
                         check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
                         ($vec-ptr:(long int *diagMut))[5] = netf;

                         flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
                         check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
                         ($vec-ptr:(long int *diagMut))[6] = nni;

                         flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
                         check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
                         ($vec-ptr:(long int *diagMut))[7] = ncfn;

                         flag = ARKDlsGetNumJacEvals(arkode_mem, &nje);
                         check_flag(&flag, "ARKDlsGetNumJacEvals", 1);
                         ($vec-ptr:(long int *diagMut))[8] = ncfn;

                         flag = ARKDlsGetNumRhsEvals(arkode_mem, &nfeLS);
                         check_flag(&flag, "ARKDlsGetNumRhsEvals", 1);
                         ($vec-ptr:(long int *diagMut))[9] = ncfn;
                         
                         /* Clean up and return */
                         N_VDestroy(y);            /* Free y vector */
                         ARKodeFree(&arkode_mem);  /* Free integrator memory */
                         SUNLinSolFree(LS);        /* Free linear solver */
                         SUNMatDestroy(A);         /* Free A matrix */
 
                         return flag;
                       } |]
  if res == 0
    then do
      preD <- V.freeze diagMut
      let d = SundialsDiagnostics (fromIntegral $ preD V.!0)
                                  (fromIntegral $ preD V.!1)
                                  (fromIntegral $ preD V.!2)
                                  (fromIntegral $ preD V.!3)
                                  (fromIntegral $ preD V.!4)
                                  (fromIntegral $ preD V.!5)
                                  (fromIntegral $ preD V.!6)
                                  (fromIntegral $ preD V.!7)
                                  (fromIntegral $ preD V.!8)
                                  (fromIntegral $ preD V.!9)
      m <- V.freeze qMatMut
      return $ Right (m, d)
    else do
      return $ Left res