{-# LANGUAGE QuasiQuotes #-} {-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE MultiWayIf #-} {-# LANGUAGE OverloadedStrings #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE KindSignatures #-} {-# LANGUAGE TypeSynonymInstances #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE FlexibleContexts #-} ----------------------------------------------------------------------------- -- | -- Module : Numeric.Sundials.ARKode.ODE -- Copyright : Dominic Steinitz 2018, -- Novadiscovery 2018 -- License : BSD -- Maintainer : Dominic Steinitz -- Stability : provisional -- -- Solution of ordinary differential equation (ODE) initial value problems. -- See for more detail. -- -- A simple example: -- -- <> -- -- @ -- import Numeric.Sundials.ARKode.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)) -- @ -- -- With Sundials ARKode, it is possible to retrieve the Butcher tableau for the solver. -- -- @ -- import Numeric.Sundials.ARKode.ODE -- import Numeric.LinearAlgebra -- -- import Data.List (intercalate) -- -- import Text.PrettyPrint.HughesPJClass -- -- -- 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 -> 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 -- -- let res = butcherTable (SDIRK_2_1_2 undefined) -- putStrLn $ show res -- putStrLn $ butcherTableauTex res -- -- let resA = butcherTable (KVAERNO_4_2_3 undefined) -- putStrLn $ show resA -- putStrLn $ butcherTableauTex resA -- -- let resB = butcherTable (SDIRK_5_3_4 undefined) -- putStrLn $ show resB -- putStrLn $ butcherTableauTex resB -- @ -- -- Using the code above from the examples gives -- -- 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.ARKode.ODE ( odeSolve , odeSolveV , odeSolveVWith , odeSolveVWith' , ButcherTable(..) , butcherTable , ODEMethod(..) , StepControl(..) ) 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 (CDouble, CInt, CLong) import Foreign.Ptr (Ptr) import Foreign.Storable (poke) import qualified Data.Vector.Storable as V import Data.Coerce (coerce) import System.IO.Unsafe (unsafePerformIO) import GHC.Generics (C1, Constructor, (:+:)(..), D1, Rep, Generic, M1(..), from, conName) import Numeric.LinearAlgebra.Devel (createVector) import Numeric.LinearAlgebra.HMatrix (Vector, Matrix, toList, rows, cols, toLists, size, reshape, subVector, subMatrix, (><)) import Numeric.Sundials.ODEOpts (ODEOpts(..), Jacobian, SundialsDiagnostics(..)) import qualified Numeric.Sundials.Arkode as T import Numeric.Sundials.Arkode (getDataFromContents, putDataInContents, arkSMax, sDIRK_2_1_2, bILLINGTON_3_3_2, tRBDF2_3_3_2, kVAERNO_4_2_3, aRK324L2SA_DIRK_4_2_3, cASH_5_2_4, cASH_5_3_4, sDIRK_5_3_4, kVAERNO_5_3_4, aRK436L2SA_DIRK_6_3_4, kVAERNO_7_4_5, aRK548L2SA_DIRK_8_4_5, hEUN_EULER_2_1_2, bOGACKI_SHAMPINE_4_2_3, aRK324L2SA_ERK_4_2_3, zONNEVELD_5_3_4, aRK436L2SA_ERK_6_3_4, sAYFY_ABURUB_6_3_4, cASH_KARP_6_4_5, fEHLBERG_6_4_5, dORMAND_PRINCE_7_4_5, aRK548L2SA_ERK_8_4_5, vERNER_8_5_6, fEHLBERG_13_7_8) C.context (C.baseCtx <> C.vecCtx <> C.funCtx <> T.sunCtx) C.include "" C.include "" C.include "" C.include "" -- prototypes for ARKODE fcts., consts. C.include "" -- serial N_Vector types, fcts., macros C.include "" -- access to dense SUNMatrix C.include "" -- access to dense SUNLinearSolver C.include "" -- access to ARKDls interface C.include "" -- definition of type realtype C.include "" C.include "../../../helpers.h" C.include "Numeric/Sundials/Arkode_hsc.h" -- | Stepping functions data ODEMethod = SDIRK_2_1_2 Jacobian | SDIRK_2_1_2' | BILLINGTON_3_3_2 Jacobian | BILLINGTON_3_3_2' | TRBDF2_3_3_2 Jacobian | TRBDF2_3_3_2' | KVAERNO_4_2_3 Jacobian | KVAERNO_4_2_3' | ARK324L2SA_DIRK_4_2_3 Jacobian | ARK324L2SA_DIRK_4_2_3' | CASH_5_2_4 Jacobian | CASH_5_2_4' | CASH_5_3_4 Jacobian | CASH_5_3_4' | SDIRK_5_3_4 Jacobian | SDIRK_5_3_4' | KVAERNO_5_3_4 Jacobian | KVAERNO_5_3_4' | ARK436L2SA_DIRK_6_3_4 Jacobian | ARK436L2SA_DIRK_6_3_4' | KVAERNO_7_4_5 Jacobian | KVAERNO_7_4_5' | ARK548L2SA_DIRK_8_4_5 Jacobian | ARK548L2SA_DIRK_8_4_5' | HEUN_EULER_2_1_2 Jacobian | HEUN_EULER_2_1_2' | BOGACKI_SHAMPINE_4_2_3 Jacobian | BOGACKI_SHAMPINE_4_2_3' | ARK324L2SA_ERK_4_2_3 Jacobian | ARK324L2SA_ERK_4_2_3' | ZONNEVELD_5_3_4 Jacobian | ZONNEVELD_5_3_4' | ARK436L2SA_ERK_6_3_4 Jacobian | ARK436L2SA_ERK_6_3_4' | SAYFY_ABURUB_6_3_4 Jacobian | SAYFY_ABURUB_6_3_4' | CASH_KARP_6_4_5 Jacobian | CASH_KARP_6_4_5' | FEHLBERG_6_4_5 Jacobian | FEHLBERG_6_4_5' | DORMAND_PRINCE_7_4_5 Jacobian | DORMAND_PRINCE_7_4_5' | ARK548L2SA_ERK_8_4_5 Jacobian | ARK548L2SA_ERK_8_4_5' | VERNER_8_5_6 Jacobian | VERNER_8_5_6' | FEHLBERG_13_7_8 Jacobian | FEHLBERG_13_7_8' deriving Generic constrName :: (HasConstructor (Rep a), Generic a)=> a -> String constrName = genericConstrName . from class HasConstructor (f :: * -> *) where genericConstrName :: f x -> String instance HasConstructor f => HasConstructor (D1 c f) where genericConstrName (M1 x) = genericConstrName x instance (HasConstructor x, HasConstructor y) => HasConstructor (x :+: y) where genericConstrName (L1 l) = genericConstrName l genericConstrName (R1 r) = genericConstrName r instance Constructor c => HasConstructor (C1 c f) where genericConstrName x = conName x instance Show ODEMethod where show x = constrName x -- FIXME: We can probably do better here with generics getMethod :: ODEMethod -> Int getMethod (SDIRK_2_1_2 _) = sDIRK_2_1_2 getMethod (SDIRK_2_1_2') = sDIRK_2_1_2 getMethod (BILLINGTON_3_3_2 _) = bILLINGTON_3_3_2 getMethod (BILLINGTON_3_3_2') = bILLINGTON_3_3_2 getMethod (TRBDF2_3_3_2 _) = tRBDF2_3_3_2 getMethod (TRBDF2_3_3_2') = tRBDF2_3_3_2 getMethod (KVAERNO_4_2_3 _) = kVAERNO_4_2_3 getMethod (KVAERNO_4_2_3') = kVAERNO_4_2_3 getMethod (ARK324L2SA_DIRK_4_2_3 _) = aRK324L2SA_DIRK_4_2_3 getMethod (ARK324L2SA_DIRK_4_2_3') = aRK324L2SA_DIRK_4_2_3 getMethod (CASH_5_2_4 _) = cASH_5_2_4 getMethod (CASH_5_2_4') = cASH_5_2_4 getMethod (CASH_5_3_4 _) = cASH_5_3_4 getMethod (CASH_5_3_4') = cASH_5_3_4 getMethod (SDIRK_5_3_4 _) = sDIRK_5_3_4 getMethod (SDIRK_5_3_4') = sDIRK_5_3_4 getMethod (KVAERNO_5_3_4 _) = kVAERNO_5_3_4 getMethod (KVAERNO_5_3_4') = kVAERNO_5_3_4 getMethod (ARK436L2SA_DIRK_6_3_4 _) = aRK436L2SA_DIRK_6_3_4 getMethod (ARK436L2SA_DIRK_6_3_4') = aRK436L2SA_DIRK_6_3_4 getMethod (KVAERNO_7_4_5 _) = kVAERNO_7_4_5 getMethod (KVAERNO_7_4_5') = kVAERNO_7_4_5 getMethod (ARK548L2SA_DIRK_8_4_5 _) = aRK548L2SA_DIRK_8_4_5 getMethod (ARK548L2SA_DIRK_8_4_5') = aRK548L2SA_DIRK_8_4_5 getMethod (HEUN_EULER_2_1_2 _) = hEUN_EULER_2_1_2 getMethod (HEUN_EULER_2_1_2') = hEUN_EULER_2_1_2 getMethod (BOGACKI_SHAMPINE_4_2_3 _) = bOGACKI_SHAMPINE_4_2_3 getMethod (BOGACKI_SHAMPINE_4_2_3') = bOGACKI_SHAMPINE_4_2_3 getMethod (ARK324L2SA_ERK_4_2_3 _) = aRK324L2SA_ERK_4_2_3 getMethod (ARK324L2SA_ERK_4_2_3') = aRK324L2SA_ERK_4_2_3 getMethod (ZONNEVELD_5_3_4 _) = zONNEVELD_5_3_4 getMethod (ZONNEVELD_5_3_4') = zONNEVELD_5_3_4 getMethod (ARK436L2SA_ERK_6_3_4 _) = aRK436L2SA_ERK_6_3_4 getMethod (ARK436L2SA_ERK_6_3_4') = aRK436L2SA_ERK_6_3_4 getMethod (SAYFY_ABURUB_6_3_4 _) = sAYFY_ABURUB_6_3_4 getMethod (SAYFY_ABURUB_6_3_4') = sAYFY_ABURUB_6_3_4 getMethod (CASH_KARP_6_4_5 _) = cASH_KARP_6_4_5 getMethod (CASH_KARP_6_4_5') = cASH_KARP_6_4_5 getMethod (FEHLBERG_6_4_5 _) = fEHLBERG_6_4_5 getMethod (FEHLBERG_6_4_5' ) = fEHLBERG_6_4_5 getMethod (DORMAND_PRINCE_7_4_5 _) = dORMAND_PRINCE_7_4_5 getMethod (DORMAND_PRINCE_7_4_5') = dORMAND_PRINCE_7_4_5 getMethod (ARK548L2SA_ERK_8_4_5 _) = aRK548L2SA_ERK_8_4_5 getMethod (ARK548L2SA_ERK_8_4_5') = aRK548L2SA_ERK_8_4_5 getMethod (VERNER_8_5_6 _) = vERNER_8_5_6 getMethod (VERNER_8_5_6') = vERNER_8_5_6 getMethod (FEHLBERG_13_7_8 _) = fEHLBERG_13_7_8 getMethod (FEHLBERG_13_7_8') = fEHLBERG_13_7_8 getJacobian :: ODEMethod -> Maybe Jacobian getJacobian (SDIRK_2_1_2 j) = Just j getJacobian (BILLINGTON_3_3_2 j) = Just j getJacobian (TRBDF2_3_3_2 j) = Just j getJacobian (KVAERNO_4_2_3 j) = Just j getJacobian (ARK324L2SA_DIRK_4_2_3 j) = Just j getJacobian (CASH_5_2_4 j) = Just j getJacobian (CASH_5_3_4 j) = Just j getJacobian (SDIRK_5_3_4 j) = Just j getJacobian (KVAERNO_5_3_4 j) = Just j getJacobian (ARK436L2SA_DIRK_6_3_4 j) = Just j getJacobian (KVAERNO_7_4_5 j) = Just j getJacobian (ARK548L2SA_DIRK_8_4_5 j) = Just j getJacobian (HEUN_EULER_2_1_2 j) = Just j getJacobian (BOGACKI_SHAMPINE_4_2_3 j) = Just j getJacobian (ARK324L2SA_ERK_4_2_3 j) = Just j getJacobian (ZONNEVELD_5_3_4 j) = Just j getJacobian (ARK436L2SA_ERK_6_3_4 j) = Just j getJacobian (SAYFY_ABURUB_6_3_4 j) = Just j getJacobian (CASH_KARP_6_4_5 j) = Just j getJacobian (FEHLBERG_6_4_5 j) = Just j getJacobian (DORMAND_PRINCE_7_4_5 j) = Just j getJacobian (ARK548L2SA_ERK_8_4_5 j) = Just j getJacobian (VERNER_8_5_6 j) = Just j getJacobian (FEHLBERG_13_7_8 j) = Just j 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 = odeSolveVWith meth (X epsAbs epsRel) hi g y0 ts where 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 odeSolveVWith SDIRK_5_3_4' (XX' 1.0e-6 1.0e-10 1 1) Nothing g (V.fromList y0) (V.fromList $ toList ts) where 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' opts method control initStepSize f y0 tt of Left (c, _v) -> error $ show c -- FIXME Right (v, _d) -> v where opts = ODEOpts { maxNumSteps = 10000 , minStep = 1.0e-12 , relTol = error "relTol" , absTols = error "absTol" , initStep = error "initStep" , maxFail = 10 } odeSolveVWith' :: ODEOpts -> 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 (Matrix Double, Int) (Matrix Double, SundialsDiagnostics) -- ^ Error code or solution odeSolveVWith' opts method control initStepSize f y0 tt = case solveOdeC (fromIntegral $ maxFail opts) (fromIntegral $ maxNumSteps opts) (coerce $ minStep opts) (fromIntegral $ getMethod method) (coerce initStepSize) jacH (scise control) (coerce f) (coerce y0) (coerce tt) of Left (v, c) -> Left (reshape l (coerce v), fromIntegral c) Right (v, d) -> Right (reshape l (coerce v), d) where l = size y0 scise (X aTol rTol) = coerce (V.replicate l aTol, rTol) scise (X' aTol rTol) = coerce (V.replicate l aTol, rTol) scise (XX' aTol rTol yScale _yDotScale) = coerce (V.replicate l aTol, yScale * rTol) -- FIXME; Should we check that the length of ss is correct? scise (ScXX' aTol rTol yScale _yDotScale ss) = coerce (V.map (* aTol) ss, yScale * rTol) 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 -> CLong -> CDouble -> 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 (V.Vector CDouble, CInt) (V.Vector CDouble, SundialsDiagnostics) -- ^ Partial solution and error code or -- solution and diagnostics solveOdeC maxErrTestFails maxNumSteps_ minStep_ method initStepSize jacH (aTols, rTol) 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 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 'CLangToHaskellTypes'. 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 <$> getDataFromContents dim y poke jacS j -- FIXME: I don't understand what this comment means -- Unsafe since the function will be called many times. [CU.exp| int{ 0 } |] res <- [C.block| int { /* general problem variables */ int flag; /* reusable error-checking flag */ int i, j; /* reusable loop indices */ N_Vector y = NULL; /* empty vector for storing solution */ N_Vector tv = NULL; /* empty vector for storing absolute tolerances */ SUNMatrix A = NULL; /* empty matrix for linear solver */ SUNLinearSolver LS = NULL; /* empty linear solver object */ void *arkode_mem = NULL; /* empty ARKode memory structure */ realtype t; long int nst, nst_a, nfe, nfi, nsetups, nje, nfeLS, nni, ncfn, netf; /* general problem parameters */ realtype T0 = RCONST(($vec-ptr:(double *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]; }; tv = N_VNew_Serial(NEQ); /* Create serial vector for absolute tolerances */ if (check_flag((void *)tv, "N_VNew_Serial", 0)) return 1; /* Specify tolerances */ for (i = 0; i < NEQ; i++) { NV_Ith_S(tv,i) = ($vec-ptr:(double *aTols))[i]; }; arkode_mem = ARKodeCreate(); /* Create the solver memory */ if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1; /* Call ARKodeInit to initialize the integrator memory and specify the */ /* right-hand side function in y'=f(t,y), the inital time T0, and */ /* the initial dependent variable vector y. Note: we treat the */ /* problem as fully implicit and set f_E to NULL and f_I to f. */ /* Here we use the C types defined in helpers.h which tie up with */ /* the Haskell types defined in CLangToHaskellTypes */ if ($(int method) < MIN_DIRK_NUM) { flag = ARKodeInit(arkode_mem, $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), NULL, T0, y); if (check_flag(&flag, "ARKodeInit", 1)) return 1; } else { flag = ARKodeInit(arkode_mem, NULL, $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y); if (check_flag(&flag, "ARKodeInit", 1)) return 1; } flag = ARKodeSetMinStep(arkode_mem, $(double minStep_)); if (check_flag(&flag, "ARKodeSetMinStep", 1)) return 1; flag = ARKodeSetMaxNumSteps(arkode_mem, $(long int maxNumSteps_)); if (check_flag(&flag, "ARKodeSetMaxNumSteps", 1)) return 1; flag = ARKodeSetMaxErrTestFails(arkode_mem, $(int maxErrTestFails)); if (check_flag(&flag, "ARKodeSetMaxErrTestFails", 1)) return 1; /* Set routines */ flag = ARKodeSVtolerances(arkode_mem, $(double rTol), tv); if (check_flag(&flag, "ARKodeSVtolerances", 1)) return 1; /* Initialize dense matrix data structure and solver */ A = SUNDenseMatrix(NEQ, NEQ); if (check_flag((void *)A, "SUNDenseMatrix", 0)) return 1; LS = SUNDenseLinearSolver(y, A); if (check_flag((void *)LS, "SUNDenseLinearSolver", 0)) return 1; /* Attach matrix and linear solver */ flag = ARKDlsSetLinearSolver(arkode_mem, LS, A); if (check_flag(&flag, "ARKDlsSetLinearSolver", 1)) return 1; /* Set the initial step size if there is one */ if ($(int isInitStepSize)) { /* FIXME: We could check if the initial step size is 0 */ /* or even NaN and then throw an error */ flag = ARKodeSetInitStep(arkode_mem, $(double ss)); if (check_flag(&flag, "ARKodeSetInitStep", 1)) return 1; } /* Set the Jacobian if there is one */ if ($(int isJac)) { flag = ARKDlsSetJacFn(arkode_mem, $fun:(int (* jacIO) (double t, SunVector y[], SunVector fy[], SunMatrix Jac[], void * params, SunVector tmp1[], SunVector tmp2[], SunVector tmp3[]))); if (check_flag(&flag, "ARKDlsSetJacFn", 1)) return 1; } /* Store initial conditions */ for (j = 0; j < NEQ; j++) { ($vec-ptr:(double *qMatMut))[0 * $(int nTs) + j] = NV_Ith_S(y,j); } /* Explicitly set the method */ if ($(int method) >= MIN_DIRK_NUM) { flag = ARKodeSetIRKTableNum(arkode_mem, $(int method)); if (check_flag(&flag, "ARKodeSetIRKTableNum", 1)) return 1; } else { flag = ARKodeSetERKTableNum(arkode_mem, $(int method)); if (check_flag(&flag, "ARKodeSetERKTableNum", 1)) return 1; } /* 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 *ts))[i], y, &t, ARK_NORMAL); /* call integrator */ if (check_flag(&flag, "ARKode solver failure, stopping integration", 1)) return 1; /* Store the results for Haskell */ for (j = 0; j < NEQ; j++) { ($vec-ptr:(double *qMatMut))[i * NEQ + j] = NV_Ith_S(y,j); } } /* Get some final statistics on how the solve progressed */ flag = ARKodeGetNumSteps(arkode_mem, &nst); check_flag(&flag, "ARKodeGetNumSteps", 1); ($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 */ N_VDestroy(tv); /* Free tv vector */ ARKodeFree(&arkode_mem); /* Free integrator memory */ SUNLinSolFree(LS); /* Free linear solver */ SUNMatDestroy(A); /* Free A matrix */ return flag; } |] 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 if res == 0 then do return $ Right (m, d) else do return $ Left (m, res) 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) $ (arkSMax >< 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 (ButcherTable' Double, V.Vector Int) getBT method = case getButcherTable method of 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 (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 let funI :: CDouble -> V.Vector CDouble -> V.Vector CDouble funI _t ys = V.fromList [ ys V.! 0 ] let funE :: CDouble -> V.Vector CDouble -> V.Vector CDouble funE _t ys = V.fromList [ ys V.! 0 ] f0 = V.fromList [ 1.0 ] ts = V.fromList [ 0.0 ] dim = V.length f0 nEq :: CLong nEq = fromIntegral dim mN :: CInt mN = fromIntegral $ getMethod method btSQP :: V.Vector CInt <- createVector 3 btSQPMut <- V.thaw btSQP btAs :: V.Vector CDouble <- createVector (arkSMax * arkSMax) btAsMut <- V.thaw btAs btCs :: V.Vector CDouble <- createVector arkSMax btBs :: V.Vector CDouble <- createVector arkSMax btB2s :: V.Vector CDouble <- createVector arkSMax btCsMut <- V.thaw btCs btBsMut <- V.thaw btBs btB2sMut <- V.thaw btB2s let funIOI :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt funIOI x y f _ptr = do fImm <- funI x <$> getDataFromContents dim y putDataInContents fImm dim f -- FIXME: I don't understand what this comment means -- Unsafe since the function will be called many times. [CU.exp| int{ 0 } |] let funIOE :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt funIOE x y f _ptr = do fImm <- funE x <$> getDataFromContents dim y 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 } |] res <- [C.block| int { /* general problem variables */ int flag; /* reusable error-checking flag */ N_Vector y = NULL; /* empty vector for storing solution */ void *arkode_mem = NULL; /* empty ARKode memory structure */ int i, j; /* reusable loop indices */ /* 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]; }; arkode_mem = ARKodeCreate(); /* Create the solver memory */ if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1; flag = ARKodeInit(arkode_mem, $fun:(int (* funIOE) (double t, SunVector y[], SunVector dydt[], void * params)), $fun:(int (* funIOI) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y); if (check_flag(&flag, "ARKodeInit", 1)) return 1; if ($(int mN) >= MIN_DIRK_NUM) { flag = ARKodeSetIRKTableNum(arkode_mem, $(int mN)); if (check_flag(&flag, "ARKodeSetIRKTableNum", 1)) return 1; } else { flag = ARKodeSetERKTableNum(arkode_mem, $(int mN)); if (check_flag(&flag, "ARKodeSetERKTableNum", 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; $vec-ptr:(int *btSQPMut)[0] = s; $vec-ptr:(int *btSQPMut)[1] = q; $vec-ptr:(int *btSQPMut)[2] = p; for (i = 0; i < s; i++) { for (j = 0; j < s; j++) { /* FIXME: double should be realtype */ ($vec-ptr:(double *btAsMut))[i * ARK_S_MAX + j] = ai[i * ARK_S_MAX + j]; } } for (i = 0; i < s; 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 */ N_VDestroy(y); /* Free y vector */ ARKodeFree(&arkode_mem); /* Free integrator memory */ return flag; } |] if res == 0 then do x <- V.freeze btAsMut y <- V.freeze btSQPMut z <- V.freeze btCsMut 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 -- | 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 \(\eta^{rel} = a_{y}\epsilon^{rel}\)