hmatrix-sundials-0.19.1.0: src/Numeric/Sundials/ARKode/ODE.hs
{-# 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 <https://computation.llnl.gov/projects/sundials/sundials-software> for more detail.
--
-- A simple example:
--
-- <<diagrams/brusselator.png#diagram=brusselator&height=400&width=500>>
--
-- @
-- 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 "<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"
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 \(\eta^{rel} = a_{y}\epsilon^{rel}\)