diff --git a/ChangeLog.md b/ChangeLog.md --- a/ChangeLog.md +++ b/ChangeLog.md @@ -1,5 +1,13 @@ # Revision history for hmatrix-sundials -## 0.1.0.0 -- 2018-04-21 +## 0.19.0.0 -- 2018-04-21 -* First version. Released on an unsuspecting world. Just Runge-Kutta methods to start with. +* First version. Released on an unsuspecting world. Just Runge-Kutta + methods to start with. + +## 0.19.1.0 -- 2018-08-14 + +* Methods in CVODE: Adams-Moulton and Backward Differentiation + Formulas (BDFs). +* An experimental interface for finding when a variable has crossed a + certain value. diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -1,5 +1,7 @@ -Currently only an interface to the Runge-Kutta methods: -[ARKode](https://computation.llnl.gov/projects/sundials/arkode) +An interface to the Runge-Kutta methods: +[ARKode](https://computation.llnl.gov/projects/sundials/arkode) and +the methods in +[CVode](https://computation.llnl.gov/projects/sundials/cvode) The interface is almost certainly going to change. Sundials gives a rich set of "combinators" for controlling the solution of your problem diff --git a/diagrams/lorenzA.png b/diagrams/lorenzA.png deleted file mode 100644 Binary files a/diagrams/lorenzA.png and /dev/null differ diff --git a/diagrams/predatorPrey.png b/diagrams/predatorPrey.png new file mode 100644 Binary files /dev/null and b/diagrams/predatorPrey.png differ diff --git a/diagrams/predatorPrey1.png b/diagrams/predatorPrey1.png new file mode 100644 Binary files /dev/null and b/diagrams/predatorPrey1.png differ diff --git a/diagrams/predatorPrey2.png b/diagrams/predatorPrey2.png new file mode 100644 Binary files /dev/null and b/diagrams/predatorPrey2.png differ diff --git a/hmatrix-sundials.cabal b/hmatrix-sundials.cabal --- a/hmatrix-sundials.cabal +++ b/hmatrix-sundials.cabal @@ -1,5 +1,5 @@ name: hmatrix-sundials -version: 0.19.0.0 +version: 0.19.1.0 synopsis: hmatrix interface to sundials description: An interface to the solving suite SUNDIALS. Currently, it mimics the solving interface in hmstrix-gsl but @@ -25,21 +25,24 @@ template-haskell >=2.12 && <2.13, containers >=0.5 && <0.6, hmatrix>=0.18 - extra-libraries: sundials_arkode + extra-libraries: sundials_arkode, + sundials_cvode other-extensions: QuasiQuotes hs-source-dirs: src - exposed-modules: Numeric.Sundials.ARKode.ODE - other-modules: Types, - Arkode + exposed-modules: Numeric.Sundials.ODEOpts, + Numeric.Sundials.ARKode.ODE, + Numeric.Sundials.CVode.ODE + other-modules: Numeric.Sundials.Arkode c-sources: src/helpers.c src/helpers.h default-language: Haskell2010 test-suite hmatrix-sundials-testsuite type: exitcode-stdio-1.0 main-is: Main.hs - other-modules: Types, + other-modules: Numeric.Sundials.ODEOpts, Numeric.Sundials.ARKode.ODE, - Arkode + Numeric.Sundials.CVode.ODE, + Numeric.Sundials.Arkode build-depends: base >=4.10 && <4.11, inline-c >=0.6 && <0.7, vector >=0.12 && <0.13, @@ -52,6 +55,7 @@ lens, hspec hs-source-dirs: src - extra-libraries: sundials_arkode + extra-libraries: sundials_arkode, + sundials_cvode c-sources: src/helpers.c src/helpers.h default-language: Haskell2010 diff --git a/src/Arkode.hsc b/src/Arkode.hsc deleted file mode 100644 --- a/src/Arkode.hsc +++ /dev/null @@ -1,114 +0,0 @@ -module Arkode where - -import Foreign -import Foreign.C.Types - - -#include -#include -#include -#include -#include -#include - - -#def typedef struct _generic_N_Vector SunVector; -#def typedef struct _N_VectorContent_Serial SunContent; - -#def typedef struct _generic_SUNMatrix SunMatrix; -#def typedef struct _SUNMatrixContent_Dense SunMatrixContent; - -getContentMatrixPtr :: Storable a => Ptr b -> IO a -getContentMatrixPtr ptr = (#peek SunMatrix, content) ptr - -getNRows :: Ptr b -> IO CInt -getNRows ptr = (#peek SunMatrixContent, M) ptr -putNRows :: CInt -> Ptr b -> IO () -putNRows nr ptr = (#poke SunMatrixContent, M) ptr nr - -getNCols :: Ptr b -> IO CInt -getNCols ptr = (#peek SunMatrixContent, N) ptr -putNCols :: CInt -> Ptr b -> IO () -putNCols nc ptr = (#poke SunMatrixContent, N) ptr nc - -getMatrixData :: Storable a => Ptr b -> IO a -getMatrixData ptr = (#peek SunMatrixContent, data) ptr - -getContentPtr :: Storable a => Ptr b -> IO a -getContentPtr ptr = (#peek SunVector, content) ptr - -getData :: Storable a => Ptr b -> IO a -getData ptr = (#peek SunContent, data) ptr - -arkSMax :: Int -arkSMax = #const ARK_S_MAX - -mIN_DIRK_NUM, mAX_DIRK_NUM :: Int -mIN_DIRK_NUM = #const MIN_DIRK_NUM -mAX_DIRK_NUM = #const MAX_DIRK_NUM - --- FIXME: We could just use inline-c instead - --- Butcher table accessors -- implicit -sDIRK_2_1_2 :: Int -sDIRK_2_1_2 = #const SDIRK_2_1_2 -bILLINGTON_3_3_2 :: Int -bILLINGTON_3_3_2 = #const BILLINGTON_3_3_2 -tRBDF2_3_3_2 :: Int -tRBDF2_3_3_2 = #const TRBDF2_3_3_2 -kVAERNO_4_2_3 :: Int -kVAERNO_4_2_3 = #const KVAERNO_4_2_3 -aRK324L2SA_DIRK_4_2_3 :: Int -aRK324L2SA_DIRK_4_2_3 = #const ARK324L2SA_DIRK_4_2_3 -cASH_5_2_4 :: Int -cASH_5_2_4 = #const CASH_5_2_4 -cASH_5_3_4 :: Int -cASH_5_3_4 = #const CASH_5_3_4 -sDIRK_5_3_4 :: Int -sDIRK_5_3_4 = #const SDIRK_5_3_4 -kVAERNO_5_3_4 :: Int -kVAERNO_5_3_4 = #const KVAERNO_5_3_4 -aRK436L2SA_DIRK_6_3_4 :: Int -aRK436L2SA_DIRK_6_3_4 = #const ARK436L2SA_DIRK_6_3_4 -kVAERNO_7_4_5 :: Int -kVAERNO_7_4_5 = #const KVAERNO_7_4_5 -aRK548L2SA_DIRK_8_4_5 :: Int -aRK548L2SA_DIRK_8_4_5 = #const ARK548L2SA_DIRK_8_4_5 - --- #define DEFAULT_DIRK_2 SDIRK_2_1_2 --- #define DEFAULT_DIRK_3 ARK324L2SA_DIRK_4_2_3 --- #define DEFAULT_DIRK_4 SDIRK_5_3_4 --- #define DEFAULT_DIRK_5 ARK548L2SA_DIRK_8_4_5 - --- Butcher table accessors -- explicit -hEUN_EULER_2_1_2 :: Int -hEUN_EULER_2_1_2 = #const HEUN_EULER_2_1_2 -bOGACKI_SHAMPINE_4_2_3 :: Int -bOGACKI_SHAMPINE_4_2_3 = #const BOGACKI_SHAMPINE_4_2_3 -aRK324L2SA_ERK_4_2_3 :: Int -aRK324L2SA_ERK_4_2_3 = #const ARK324L2SA_ERK_4_2_3 -zONNEVELD_5_3_4 :: Int -zONNEVELD_5_3_4 = #const ZONNEVELD_5_3_4 -aRK436L2SA_ERK_6_3_4 :: Int -aRK436L2SA_ERK_6_3_4 = #const ARK436L2SA_ERK_6_3_4 -sAYFY_ABURUB_6_3_4 :: Int -sAYFY_ABURUB_6_3_4 = #const SAYFY_ABURUB_6_3_4 -cASH_KARP_6_4_5 :: Int -cASH_KARP_6_4_5 = #const CASH_KARP_6_4_5 -fEHLBERG_6_4_5 :: Int -fEHLBERG_6_4_5 = #const FEHLBERG_6_4_5 -dORMAND_PRINCE_7_4_5 :: Int -dORMAND_PRINCE_7_4_5 = #const DORMAND_PRINCE_7_4_5 -aRK548L2SA_ERK_8_4_5 :: Int -aRK548L2SA_ERK_8_4_5 = #const ARK548L2SA_ERK_8_4_5 -vERNER_8_5_6 :: Int -vERNER_8_5_6 = #const VERNER_8_5_6 -fEHLBERG_13_7_8 :: Int -fEHLBERG_13_7_8 = #const FEHLBERG_13_7_8 - --- #define DEFAULT_ERK_2 HEUN_EULER_2_1_2 --- #define DEFAULT_ERK_3 BOGACKI_SHAMPINE_4_2_3 --- #define DEFAULT_ERK_4 ZONNEVELD_5_3_4 --- #define DEFAULT_ERK_5 CASH_KARP_6_4_5 --- #define DEFAULT_ERK_6 VERNER_8_5_6 --- #define DEFAULT_ERK_8 FEHLBERG_13_7_8 diff --git a/src/Main.hs b/src/Main.hs --- a/src/Main.hs +++ b/src/Main.hs @@ -1,6 +1,7 @@ {-# OPTIONS_GHC -Wall #-} -import Numeric.Sundials.ARKode.ODE +import qualified Numeric.Sundials.ARKode.ODE as ARK +import qualified Numeric.Sundials.CVode.ODE as CV import Numeric.LinearAlgebra import Plots as P @@ -80,6 +81,23 @@ where lamda = -100.0 +predatorPrey :: Double -> [Double] -> [Double] +predatorPrey _t v = [ x * a - b * x * y + , d * x * y - c * y - e * y * z + , (-f) * z + g * y * z + ] + where + x = v!!0 + y = v!!1 + z = v!!2 + a = 1.0 + b = 1.0 + c = 1.0 + d = 1.0 + e = 1.0 + f = 1.0 + g = 1.0 + lSaxis :: [[Double]] -> P.Axis B D.V2 Double lSaxis xs = P.r2Axis &~ do let ts = xs!!0 @@ -97,34 +115,38 @@ main :: IO () main = do - let res1 = odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0]) + let res1 = ARK.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)) - let res1a = odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0]) + let res1a = ARK.odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0]) renderRasterific "diagrams/brusselatorA.png" (D.dims2D 500.0 500.0) (renderAxis $ lSaxis $ [0.0, 0.1 .. 10.0]:(toLists $ tr res1a)) - let res2 = odeSolve stiffish [0.0] (fromList [0.0, 0.1 .. 10.0]) + let res2 = ARK.odeSolve stiffish [0.0] (fromList [0.0, 0.1 .. 10.0]) renderRasterific "diagrams/stiffish.png" (D.dims2D 500.0 500.0) (renderAxis $ kSaxis $ zip [0.0, 0.1 .. 10.0] (concat $ toLists res2)) - let res2a = odeSolveV (SDIRK_5_3_4') Nothing 1e-6 1e-10 stiffishV (fromList [0.0]) (fromList [0.0, 0.1 .. 10.0]) + let res2a = ARK.odeSolveV (ARK.SDIRK_5_3_4') Nothing 1e-6 1e-10 stiffishV (fromList [0.0]) (fromList [0.0, 0.1 .. 10.0]) - let res2b = odeSolveV (TRBDF2_3_3_2') Nothing 1e-6 1e-10 stiffishV (fromList [0.0]) (fromList [0.0, 0.1 .. 10.0]) + let res2b = ARK.odeSolveV (ARK.TRBDF2_3_3_2') Nothing 1e-6 1e-10 stiffishV (fromList [0.0]) (fromList [0.0, 0.1 .. 10.0]) - let maxDiff = maximum $ map abs $ - zipWith (-) ((toLists $ tr res2a)!!0) ((toLists $ tr res2b)!!0) + let maxDiffA = maximum $ map abs $ + zipWith (-) ((toLists $ tr res2a)!!0) ((toLists $ tr res2b)!!0) - hspec $ describe "Compare results" $ do - it "for two different RK methods" $ - maxDiff < 1.0e-6 + let res2c = CV.odeSolveV (CV.BDF) Nothing 1e-6 1e-10 stiffishV (fromList [0.0]) (fromList [0.0, 0.1 .. 10.0]) - let res3 = odeSolve lorenz [-5.0, -5.0, 1.0] (fromList [0.0, 0.01 .. 10.0]) + let maxDiffB = maximum $ map abs $ + zipWith (-) ((toLists $ tr res2a)!!0) ((toLists $ tr res2c)!!0) + let maxDiffC = maximum $ map abs $ + zipWith (-) ((toLists $ tr res2b)!!0) ((toLists $ tr res2c)!!0) + + let res3 = ARK.odeSolve lorenz [-5.0, -5.0, 1.0] (fromList [0.0, 0.01 .. 10.0]) + renderRasterific "diagrams/lorenz.png" (D.dims2D 500.0 500.0) (renderAxis $ kSaxis $ zip ((toLists $ tr res3)!!0) ((toLists $ tr res3)!!1)) @@ -136,3 +158,29 @@ renderRasterific "diagrams/lorenz2.png" (D.dims2D 500.0 500.0) (renderAxis $ kSaxis $ zip ((toLists $ tr res3)!!1) ((toLists $ tr res3)!!2)) + + let res4 = CV.odeSolve predatorPrey [0.5, 1.0, 2.0] (fromList [0.0, 0.01 .. 10.0]) + + renderRasterific "diagrams/predatorPrey.png" + (D.dims2D 500.0 500.0) + (renderAxis $ kSaxis $ zip ((toLists $ tr res4)!!0) ((toLists $ tr res4)!!1)) + + renderRasterific "diagrams/predatorPrey1.png" + (D.dims2D 500.0 500.0) + (renderAxis $ kSaxis $ zip ((toLists $ tr res4)!!0) ((toLists $ tr res4)!!2)) + + renderRasterific "diagrams/predatorPrey2.png" + (D.dims2D 500.0 500.0) + (renderAxis $ kSaxis $ zip ((toLists $ tr res4)!!1) ((toLists $ tr res4)!!2)) + + let res4a = ARK.odeSolve predatorPrey [0.5, 1.0, 2.0] (fromList [0.0, 0.01 .. 10.0]) + + let maxDiffPpA = maximum $ map abs $ + zipWith (-) ((toLists $ tr res4)!!0) ((toLists $ tr res4a)!!0) + + hspec $ describe "Compare results" $ do + it "for SDIRK_5_3_4' and TRBDF2_3_3_2'" $ maxDiffA < 1.0e-6 + it "for SDIRK_5_3_4' and BDF" $ maxDiffB < 1.0e-6 + it "for TRBDF2_3_3_2' and BDF" $ maxDiffC < 1.0e-6 + it "for CV and ARK for the Predator Prey model" $ maxDiffPpA < 1.0e-3 + diff --git a/src/Numeric/Sundials/ARKode/ODE.hs b/src/Numeric/Sundials/ARKode/ODE.hs --- a/src/Numeric/Sundials/ARKode/ODE.hs +++ b/src/Numeric/Sundials/ARKode/ODE.hs @@ -1,5 +1,3 @@ -{-# OPTIONS_GHC -Wall #-} - {-# LANGUAGE QuasiQuotes #-} {-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE MultiWayIf #-} @@ -22,8 +20,7 @@ -- Stability : provisional -- -- Solution of ordinary differential equation (ODE) initial value problems. --- --- +-- See for more detail. -- -- A simple example: -- @@ -67,6 +64,54 @@ -- (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 -- -- \[ @@ -116,8 +161,6 @@ , butcherTable , ODEMethod(..) , StepControl(..) - , Jacobian - , SundialsDiagnostics(..) ) where import qualified Language.C.Inline as C @@ -126,27 +169,50 @@ import Data.Monoid ((<>)) import Data.Maybe (isJust) -import Foreign.C.Types +import Foreign.C.Types (CDouble, CInt, CLong) import Foreign.Ptr (Ptr) -import Foreign.ForeignPtr (newForeignPtr_) -import Foreign.Storable (Storable) +import Foreign.Storable (poke) 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 GHC.Generics +import GHC.Generics (C1, Constructor, (:+:)(..), D1, Rep, Generic, M1(..), + from, conName) import Numeric.LinearAlgebra.Devel (createVector) -import Numeric.LinearAlgebra.HMatrix (Vector, Matrix, toList, (><), - subMatrix, rows, cols, toLists, - size, subVector) +import Numeric.LinearAlgebra.HMatrix (Vector, Matrix, toList, rows, + cols, toLists, size, reshape, + subVector, subMatrix, (><)) -import qualified Types as T -import Arkode -import qualified Arkode as B +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) @@ -162,70 +228,9 @@ C.include "" -- definition of type realtype C.include "" C.include "../../../helpers.h" -C.include "Arkode_hsc.h" +C.include "Numeric/Sundials/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 = SDIRK_2_1_2 Jacobian | SDIRK_2_1_2' @@ -390,15 +395,9 @@ -> 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 + 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 @@ -410,16 +409,11 @@ -> Matrix Double -- ^ solution odeSolve f y0 ts = -- FIXME: These tolerances are different from the ones in GSL - case odeSolveVWith SDIRK_5_3_4' (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) + odeSolveVWith SDIRK_5_3_4' (XX' 1.0e-6 1.0e-10 1 1) Nothing g (V.fromList y0) (V.fromList $ toList ts) where - us = toList ts - nR = length us - nC = length y0 g t x0 = V.fromList $ f t (V.toList x0) -odeSolveVWith' :: +odeSolveVWith :: ODEMethod -> StepControl -> Maybe Double -- ^ initial step size - by default, ARKode @@ -432,16 +426,22 @@ -> 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) +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 - nR = V.length tt - nC = V.length y0 + opts = ODEOpts { maxNumSteps = 10000 + , minStep = 1.0e-12 + , relTol = error "relTol" + , absTols = error "absTol" + , initStep = error "initStep" + , maxFail = 10 + } -odeSolveVWith :: - ODEMethod +odeSolveVWith' :: + ODEOpts + -> ODEMethod -> StepControl -> Maybe Double -- ^ initial step size - by default, ARKode -- estimates the initial step size to be the @@ -452,19 +452,21 @@ -> (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) + -> 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 c -> Left $ fromIntegral c - Right (v, d) -> Right (coerce v, d) + 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 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) + 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' absTol relTol yScale _yDotScale ss) = coerce (V.map (* absTol) ss, yScale * relTol) + 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 } @@ -476,14 +478,19 @@ 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 CInt ((V.Vector CDouble), SundialsDiagnostics) -- ^ Error code or solution -solveOdeC method initStepSize jacH (absTols, relTol) fun f0 ts = unsafePerformIO $ do + -> 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 @@ -494,22 +501,18 @@ -- 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! + -- 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 @@ -529,7 +532,7 @@ case jacH of Nothing -> error "Numeric.Sundials.ARKode.ODE: Jacobian not defined" Just jacI -> do j <- jacI t <$> getDataFromContents dim y - putMatrixDataFromContents j jacS + poke jacS j -- FIXME: I don't understand what this comment means -- Unsafe since the function will be called many times. [CU.exp| int{ 0 } |] @@ -549,7 +552,7 @@ /* general problem parameters */ - realtype T0 = RCONST(($vec-ptr:(double *tMut))[0]); /* initial time */ + realtype T0 = RCONST(($vec-ptr:(double *ts))[0]); /* initial time */ sunindextype NEQ = $(sunindextype nEq); /* number of dependent vars. */ /* Initialize data structures */ @@ -558,14 +561,14 @@ if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1; /* Specify initial condition */ for (i = 0; i < NEQ; i++) { - NV_Ith_S(y,i) = ($vec-ptr:(double *fMut))[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 *absTols))[i]; + NV_Ith_S(tv,i) = ($vec-ptr:(double *aTols))[i]; }; arkode_mem = ARKodeCreate(); /* Create the solver memory */ @@ -577,7 +580,7 @@ /* problem as fully implicit and set f_E to NULL and f_I to f. */ /* Here we use the C types defined in helpers.h which tie up with */ - /* the Haskell types defined in Types */ + /* the Haskell types defined in CLangToHaskellTypes */ if ($(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; @@ -586,14 +589,15 @@ if (check_flag(&flag, "ARKodeInit", 1)) return 1; } - /* FIXME: A hack for initial testing */ - flag = ARKodeSetMinStep(arkode_mem, 1.0e-12); + flag = ARKodeSetMinStep(arkode_mem, $(double minStep_)); if (check_flag(&flag, "ARKodeSetMinStep", 1)) return 1; - flag = ARKodeSetMaxNumSteps(arkode_mem, 10000); + 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 relTol), tv); + flag = ARKodeSVtolerances(arkode_mem, $(double rTol), tv); if (check_flag(&flag, "ARKodeSVtolerances", 1)) return 1; /* Initialize dense matrix data structure and solver */ @@ -638,19 +642,13 @@ /* 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; + 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); } - - /* unsuccessful solve: break */ - if (flag < 0) { - fprintf(stderr,"Solver failure, stopping integration\n"); - break; - } } /* Get some final statistics on how the solve progressed */ @@ -701,23 +699,23 @@ 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 - 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 + return $ Left (m, res) data ButcherTable = ButcherTable { am :: Matrix Double , cv :: Vector Double @@ -738,7 +736,7 @@ case getBT method of Left c -> error $ show c -- FIXME Right (ButcherTable' v w x y, sqp) -> - ButcherTable { am = subMatrix (0, 0) (s, s) $ (B.arkSMax >< B.arkSMax) (V.toList v) + 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 @@ -773,11 +771,11 @@ btSQP :: V.Vector CInt <- createVector 3 btSQPMut <- V.thaw btSQP - btAs :: V.Vector CDouble <- createVector (B.arkSMax * B.arkSMax) + btAs :: V.Vector CDouble <- createVector (arkSMax * arkSMax) btAsMut <- V.thaw btAs - btCs :: V.Vector CDouble <- createVector B.arkSMax - btBs :: V.Vector CDouble <- createVector B.arkSMax - btB2s :: V.Vector CDouble <- createVector B.arkSMax + 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 diff --git a/src/Numeric/Sundials/Arkode.hsc b/src/Numeric/Sundials/Arkode.hsc new file mode 100644 --- /dev/null +++ b/src/Numeric/Sundials/Arkode.hsc @@ -0,0 +1,209 @@ +{-# LANGUAGE QuasiQuotes #-} +{-# LANGUAGE TemplateHaskell #-} +{-# LANGUAGE OverloadedStrings #-} +{-# LANGUAGE EmptyDataDecls #-} + +module Numeric.Sundials.Arkode where + +import Foreign +import Foreign.C.Types + +import Language.C.Types as CT + +import qualified Data.Vector.Storable as VS +import qualified Data.Vector.Storable.Mutable as VM + +import qualified Language.Haskell.TH as TH +import qualified Data.Map as Map +import Language.C.Inline.Context + +import qualified Data.Vector.Storable as V + + +#include +#include +#include +#include +#include +#include +#include + + +data SunVector +data SunMatrix = SunMatrix { rows :: CInt + , cols :: CInt + , vals :: V.Vector CDouble + } + +-- | This is true only if configured/ built as 64 bits +type SunIndexType = CLong + +sunTypesTable :: Map.Map TypeSpecifier TH.TypeQ +sunTypesTable = Map.fromList + [ + (TypeName "sunindextype", [t| SunIndexType |] ) + , (TypeName "SunVector", [t| SunVector |] ) + , (TypeName "SunMatrix", [t| SunMatrix |] ) + ] + +sunCtx :: Context +sunCtx = mempty {ctxTypesTable = sunTypesTable} + +getMatrixDataFromContents :: Ptr SunMatrix -> IO SunMatrix +getMatrixDataFromContents ptr = do + qtr <- getContentMatrixPtr ptr + rs <- getNRows qtr + cs <- getNCols qtr + rtr <- getMatrixData qtr + vs <- vectorFromC (fromIntegral $ rs * cs) rtr + return $ SunMatrix { rows = rs, cols = cs, vals = vs } + +putMatrixDataFromContents :: SunMatrix -> Ptr SunMatrix -> IO () +putMatrixDataFromContents mat ptr = do + let rs = rows mat + cs = cols mat + vs = vals mat + qtr <- getContentMatrixPtr ptr + putNRows rs qtr + putNCols cs qtr + rtr <- getMatrixData qtr + vectorToC vs (fromIntegral $ rs * cs) rtr + +instance Storable SunMatrix where + poke = flip putMatrixDataFromContents + peek = getMatrixDataFromContents + sizeOf _ = error "sizeOf not supported for SunMatrix" + alignment _ = error "alignment not supported for SunMatrix" + +vectorFromC :: Storable a => Int -> Ptr a -> IO (VS.Vector a) +vectorFromC len ptr = do + ptr' <- newForeignPtr_ ptr + VS.freeze $ VM.unsafeFromForeignPtr0 ptr' len + +vectorToC :: Storable a => VS.Vector a -> Int -> Ptr a -> IO () +vectorToC vec len ptr = do + ptr' <- newForeignPtr_ ptr + VS.copy (VM.unsafeFromForeignPtr0 ptr' len) vec + +getDataFromContents :: Int -> Ptr SunVector -> IO (VS.Vector CDouble) +getDataFromContents len ptr = do + qtr <- getContentPtr ptr + rtr <- getData qtr + vectorFromC len rtr + +putDataInContents :: Storable a => VS.Vector a -> Int -> Ptr b -> IO () +putDataInContents vec len ptr = do + qtr <- getContentPtr ptr + rtr <- getData qtr + vectorToC vec len rtr + +#def typedef struct _generic_N_Vector SunVector; +#def typedef struct _N_VectorContent_Serial SunContent; + +#def typedef struct _generic_SUNMatrix SunMatrix; +#def typedef struct _SUNMatrixContent_Dense SunMatrixContent; + +getContentMatrixPtr :: Storable a => Ptr b -> IO a +getContentMatrixPtr ptr = (#peek SunMatrix, content) ptr + +getNRows :: Ptr b -> IO CInt +getNRows ptr = (#peek SunMatrixContent, M) ptr +putNRows :: CInt -> Ptr b -> IO () +putNRows nr ptr = (#poke SunMatrixContent, M) ptr nr + +getNCols :: Ptr b -> IO CInt +getNCols ptr = (#peek SunMatrixContent, N) ptr +putNCols :: CInt -> Ptr b -> IO () +putNCols nc ptr = (#poke SunMatrixContent, N) ptr nc + +getMatrixData :: Storable a => Ptr b -> IO a +getMatrixData ptr = (#peek SunMatrixContent, data) ptr + +getContentPtr :: Storable a => Ptr b -> IO a +getContentPtr ptr = (#peek SunVector, content) ptr + +getData :: Storable a => Ptr b -> IO a +getData ptr = (#peek SunContent, data) ptr + +cV_SUCCESS :: Int +cV_SUCCESS = #const CV_SUCCESS +cV_ROOT_RETURN :: Int +cV_ROOT_RETURN = #const CV_ROOT_RETURN + +cV_ADAMS :: Int +cV_ADAMS = #const CV_ADAMS +cV_BDF :: Int +cV_BDF = #const CV_BDF + +arkSMax :: Int +arkSMax = #const ARK_S_MAX + +mIN_DIRK_NUM, mAX_DIRK_NUM :: Int +mIN_DIRK_NUM = #const MIN_DIRK_NUM +mAX_DIRK_NUM = #const MAX_DIRK_NUM + +-- FIXME: We could just use inline-c instead + +-- Butcher table accessors -- implicit +sDIRK_2_1_2 :: Int +sDIRK_2_1_2 = #const SDIRK_2_1_2 +bILLINGTON_3_3_2 :: Int +bILLINGTON_3_3_2 = #const BILLINGTON_3_3_2 +tRBDF2_3_3_2 :: Int +tRBDF2_3_3_2 = #const TRBDF2_3_3_2 +kVAERNO_4_2_3 :: Int +kVAERNO_4_2_3 = #const KVAERNO_4_2_3 +aRK324L2SA_DIRK_4_2_3 :: Int +aRK324L2SA_DIRK_4_2_3 = #const ARK324L2SA_DIRK_4_2_3 +cASH_5_2_4 :: Int +cASH_5_2_4 = #const CASH_5_2_4 +cASH_5_3_4 :: Int +cASH_5_3_4 = #const CASH_5_3_4 +sDIRK_5_3_4 :: Int +sDIRK_5_3_4 = #const SDIRK_5_3_4 +kVAERNO_5_3_4 :: Int +kVAERNO_5_3_4 = #const KVAERNO_5_3_4 +aRK436L2SA_DIRK_6_3_4 :: Int +aRK436L2SA_DIRK_6_3_4 = #const ARK436L2SA_DIRK_6_3_4 +kVAERNO_7_4_5 :: Int +kVAERNO_7_4_5 = #const KVAERNO_7_4_5 +aRK548L2SA_DIRK_8_4_5 :: Int +aRK548L2SA_DIRK_8_4_5 = #const ARK548L2SA_DIRK_8_4_5 + +-- #define DEFAULT_DIRK_2 SDIRK_2_1_2 +-- #define DEFAULT_DIRK_3 ARK324L2SA_DIRK_4_2_3 +-- #define DEFAULT_DIRK_4 SDIRK_5_3_4 +-- #define DEFAULT_DIRK_5 ARK548L2SA_DIRK_8_4_5 + +-- Butcher table accessors -- explicit +hEUN_EULER_2_1_2 :: Int +hEUN_EULER_2_1_2 = #const HEUN_EULER_2_1_2 +bOGACKI_SHAMPINE_4_2_3 :: Int +bOGACKI_SHAMPINE_4_2_3 = #const BOGACKI_SHAMPINE_4_2_3 +aRK324L2SA_ERK_4_2_3 :: Int +aRK324L2SA_ERK_4_2_3 = #const ARK324L2SA_ERK_4_2_3 +zONNEVELD_5_3_4 :: Int +zONNEVELD_5_3_4 = #const ZONNEVELD_5_3_4 +aRK436L2SA_ERK_6_3_4 :: Int +aRK436L2SA_ERK_6_3_4 = #const ARK436L2SA_ERK_6_3_4 +sAYFY_ABURUB_6_3_4 :: Int +sAYFY_ABURUB_6_3_4 = #const SAYFY_ABURUB_6_3_4 +cASH_KARP_6_4_5 :: Int +cASH_KARP_6_4_5 = #const CASH_KARP_6_4_5 +fEHLBERG_6_4_5 :: Int +fEHLBERG_6_4_5 = #const FEHLBERG_6_4_5 +dORMAND_PRINCE_7_4_5 :: Int +dORMAND_PRINCE_7_4_5 = #const DORMAND_PRINCE_7_4_5 +aRK548L2SA_ERK_8_4_5 :: Int +aRK548L2SA_ERK_8_4_5 = #const ARK548L2SA_ERK_8_4_5 +vERNER_8_5_6 :: Int +vERNER_8_5_6 = #const VERNER_8_5_6 +fEHLBERG_13_7_8 :: Int +fEHLBERG_13_7_8 = #const FEHLBERG_13_7_8 + +-- #define DEFAULT_ERK_2 HEUN_EULER_2_1_2 +-- #define DEFAULT_ERK_3 BOGACKI_SHAMPINE_4_2_3 +-- #define DEFAULT_ERK_4 ZONNEVELD_5_3_4 +-- #define DEFAULT_ERK_5 CASH_KARP_6_4_5 +-- #define DEFAULT_ERK_6 VERNER_8_5_6 +-- #define DEFAULT_ERK_8 FEHLBERG_13_7_8 diff --git a/src/Numeric/Sundials/CVode/ODE.hs b/src/Numeric/Sundials/CVode/ODE.hs new file mode 100644 --- /dev/null +++ b/src/Numeric/Sundials/CVode/ODE.hs @@ -0,0 +1,793 @@ +{-# 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. +-- +-- +-- +-- A simple example: +-- +-- <> +-- +-- @ +-- 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)) +-- @ +-- +----------------------------------------------------------------------------- +module Numeric.Sundials.CVode.ODE ( odeSolve + , odeSolveV + , odeSolveVWith + , odeSolveVWith' + , odeSolveRootVWith' + , ODEMethod(..) + , StepControl(..) + , SolverResult(..) + ) 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 Numeric.LinearAlgebra.Devel (createVector) + +import Numeric.LinearAlgebra.HMatrix (Vector, Matrix, toList, rows, + cols, toLists, size, reshape) + +import Numeric.Sundials.Arkode (cV_ADAMS, cV_BDF, + getDataFromContents, putDataInContents, + vectorToC, cV_SUCCESS, cV_ROOT_RETURN) +import qualified Numeric.Sundials.Arkode as T +import Numeric.Sundials.ODEOpts (ODEOpts(..), Jacobian, SundialsDiagnostics(..)) + + +C.context (C.baseCtx <> C.vecCtx <> C.funCtx <> T.sunCtx) + +C.include "" +C.include "" +C.include "" +C.include "" -- prototypes for CVODE 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 CVDls interface +C.include "" -- definition of type realtype +C.include "" +C.include "../../../helpers.h" +C.include "Numeric/Sundials/Arkode_hsc.h" + + +-- | 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, CVode + -- 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 BDF (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, CVode + -- 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, CVode + -- 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.CVode.ODE: Jacobian not defined" + Just jacI -> do j <- jacI t <$> getDataFromContents dim y + poke jacS j + -- FIXME: I don't understand what this comment means + -- Unsafe since the function will be called many times. + [CU.exp| int{ 0 } |] + + res <- [C.block| int { + /* general problem variables */ + + int flag; /* reusable error-checking flag */ + int i, j; /* reusable loop indices */ + N_Vector y = NULL; /* empty vector for storing solution */ + N_Vector tv = NULL; /* empty vector for storing absolute tolerances */ + + SUNMatrix A = NULL; /* empty matrix for linear solver */ + SUNLinearSolver LS = NULL; /* empty linear solver object */ + void *cvode_mem = NULL; /* empty CVODE memory structure */ + realtype t; + long int nst, nfe, nsetups, nje, nfeLS, nni, ncfn, netf, nge; + + /* general problem parameters */ + + realtype T0 = RCONST(($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($(int method), 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, $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y); + if (check_flag(&flag, "CVodeInit", 1)) return(1); + + tv = N_VNew_Serial(NEQ); /* Create serial vector for absolute tolerances */ + if (check_flag((void *)tv, "N_VNew_Serial", 0)) return 1; + /* Specify tolerances */ + for (i = 0; i < NEQ; i++) { + NV_Ith_S(tv,i) = ($vec-ptr:(double *aTols))[i]; + }; + + flag = CVodeSetMinStep(cvode_mem, $(double minStep_)); + if (check_flag(&flag, "CVodeSetMinStep", 1)) return 1; + flag = CVodeSetMaxNumSteps(cvode_mem, $(long int maxNumSteps_)); + if (check_flag(&flag, "CVodeSetMaxNumSteps", 1)) return 1; + flag = CVodeSetMaxErrTestFails(cvode_mem, $(int maxErrTestFails)); + if (check_flag(&flag, "CVodeSetMaxErrTestFails", 1)) return 1; + + /* Call CVodeSVtolerances to specify the scalar relative tolerance + * and vector absolute tolerances */ + flag = CVodeSVtolerances(cvode_mem, $(double rTol), tv); + if (check_flag(&flag, "CVodeSVtolerances", 1)) return(1); + + /* Initialize dense matrix data structure and solver */ + A = SUNDenseMatrix(NEQ, NEQ); + if (check_flag((void *)A, "SUNDenseMatrix", 0)) return 1; + LS = SUNDenseLinearSolver(y, A); + if (check_flag((void *)LS, "SUNDenseLinearSolver", 0)) return 1; + + /* Attach matrix and linear solver */ + flag = CVDlsSetLinearSolver(cvode_mem, LS, A); + if (check_flag(&flag, "CVDlsSetLinearSolver", 1)) return 1; + + /* Set the initial step size if there is one */ + if ($(int isInitStepSize)) { + /* FIXME: We could check if the initial step size is 0 */ + /* or even NaN and then throw an error */ + flag = CVodeSetInitStep(cvode_mem, $(double ss)); + if (check_flag(&flag, "CVodeSetInitStep", 1)) return 1; + } + + /* Set the Jacobian if there is one */ + if ($(int isJac)) { + flag = CVDlsSetJacFn(cvode_mem, $fun:(int (* jacIO) (double t, SunVector y[], SunVector fy[], SunMatrix Jac[], void * params, SunVector tmp1[], SunVector tmp2[], SunVector tmp3[]))); + if (check_flag(&flag, "CVDlsSetJacFn", 1)) return 1; + } + + /* Store initial conditions */ + for (j = 0; j < NEQ; j++) { + ($vec-ptr:(double *qMatMut))[0 * $(int nTs) + j] = NV_Ith_S(y,j); + } + + /* Main time-stepping loop: calls CVode to perform the integration */ + /* Stops when the final time has been reached */ + for (i = 1; i < $(int nTs); i++) { + + flag = CVode(cvode_mem, ($vec-ptr:(double *ts))[i], y, &t, CV_NORMAL); /* call integrator */ + if (check_flag(&flag, "CVode solver failure, stopping integration", 1)) return 1; + + /* Store the results for Haskell */ + for (j = 0; j < NEQ; j++) { + ($vec-ptr:(double *qMatMut))[i * NEQ + j] = NV_Ith_S(y,j); + } + } + + /* Get some final statistics on how the solve progressed */ + + flag = CVodeGetNumSteps(cvode_mem, &nst); + check_flag(&flag, "CVodeGetNumSteps", 1); + ($vec-ptr:(long int *diagMut))[0] = nst; + + /* FIXME */ + ($vec-ptr:(long int *diagMut))[1] = 0; + + flag = CVodeGetNumRhsEvals(cvode_mem, &nfe); + check_flag(&flag, "CVodeGetNumRhsEvals", 1); + ($vec-ptr:(long int *diagMut))[2] = nfe; + /* FIXME */ + ($vec-ptr:(long int *diagMut))[3] = 0; + + flag = CVodeGetNumLinSolvSetups(cvode_mem, &nsetups); + check_flag(&flag, "CVodeGetNumLinSolvSetups", 1); + ($vec-ptr:(long int *diagMut))[4] = nsetups; + + flag = CVodeGetNumErrTestFails(cvode_mem, &netf); + check_flag(&flag, "CVodeGetNumErrTestFails", 1); + ($vec-ptr:(long int *diagMut))[5] = netf; + + flag = CVodeGetNumNonlinSolvIters(cvode_mem, &nni); + check_flag(&flag, "CVodeGetNumNonlinSolvIters", 1); + ($vec-ptr:(long int *diagMut))[6] = nni; + + flag = CVodeGetNumNonlinSolvConvFails(cvode_mem, &ncfn); + check_flag(&flag, "CVodeGetNumNonlinSolvConvFails", 1); + ($vec-ptr:(long int *diagMut))[7] = ncfn; + + flag = CVDlsGetNumJacEvals(cvode_mem, &nje); + check_flag(&flag, "CVDlsGetNumJacEvals", 1); + ($vec-ptr:(long int *diagMut))[8] = ncfn; + + flag = CVDlsGetNumRhsEvals(cvode_mem, &nfeLS); + check_flag(&flag, "CVDlsGetNumRhsEvals", 1); + ($vec-ptr:(long int *diagMut))[9] = ncfn; + + /* Clean up and return */ + + N_VDestroy(y); /* Free y vector */ + N_VDestroy(tv); /* Free tv vector */ + CVodeFree(&cvode_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) + +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 + -> CInt -- ^ FIXME + -> (CDouble -> V.Vector CDouble -> V.Vector CDouble) -- ^ FIXME + -> V.Vector CDouble -- ^ Desired solution times + -> SolverResult V.Vector V.Vector CInt CDouble +solveOdeC' maxErrTestFails maxNumSteps_ minStep_ method initStepSize + jacH (aTols, rTol) fun f0 nr g 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. + -- FIXME: The Haskell type is currently empty! + let funIO :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt + funIO t y f _ptr = do + -- Convert the pointer we get from C (y) to a vector, and then + -- apply the user-supplied function. + fImm <- fun t <$> getDataFromContents dim y + -- Fill in the provided pointer with the resulting vector. + putDataInContents fImm dim f + -- FIXME: I don't understand what this comment means + -- Unsafe since the function will be called many times. + [CU.exp| int{ 0 } |] + + let nrPre = fromIntegral nr + gResults :: V.Vector CInt <- createVector nrPre + gResMut <- V.thaw gResults + tRoot :: V.Vector CDouble <- createVector 1 + tRootMut <- V.thaw tRoot + + let gIO :: CDouble -> Ptr T.SunVector -> Ptr CDouble -> Ptr () -> IO CInt + gIO x y f _ptr = do + -- Convert the pointer we get from C (y) to a vector, and then + -- apply the user-supplied function. + gImm <- g x <$> getDataFromContents dim y + -- Fill in the provided pointer with the resulting vector. + vectorToC gImm nrPre 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.CVode.ODE: Jacobian not defined" + Just jacI -> do j <- jacI t <$> getDataFromContents dim y + poke jacS j + -- FIXME: I don't understand what this comment means + -- Unsafe since the function will be called many times. + [CU.exp| int{ 0 } |] + + res <- [C.block| int { + /* general problem variables */ + + int flag; /* reusable error-checking flag */ + int flagr; /* root finding flag */ + + int i, j; /* reusable loop indices */ + N_Vector y = NULL; /* empty vector for storing solution */ + N_Vector tv = NULL; /* empty vector for storing absolute tolerances */ + + SUNMatrix A = NULL; /* empty matrix for linear solver */ + SUNLinearSolver LS = NULL; /* empty linear solver object */ + void *cvode_mem = NULL; /* empty CVODE memory structure */ + realtype t; + long int nst, nfe, nsetups, nje, nfeLS, nni, ncfn, netf, nge; + + realtype tout; + + /* general problem parameters */ + + realtype T0 = RCONST(($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($(int method), 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, $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y); + if (check_flag(&flag, "CVodeInit", 1)) return(1); + + tv = N_VNew_Serial(NEQ); /* Create serial vector for absolute tolerances */ + if (check_flag((void *)tv, "N_VNew_Serial", 0)) return 1; + /* Specify tolerances */ + for (i = 0; i < NEQ; i++) { + NV_Ith_S(tv,i) = ($vec-ptr:(double *aTols))[i]; + }; + + flag = CVodeSetMinStep(cvode_mem, $(double minStep_)); + if (check_flag(&flag, "CVodeSetMinStep", 1)) return 1; + flag = CVodeSetMaxNumSteps(cvode_mem, $(long int maxNumSteps_)); + if (check_flag(&flag, "CVodeSetMaxNumSteps", 1)) return 1; + flag = CVodeSetMaxErrTestFails(cvode_mem, $(int maxErrTestFails)); + if (check_flag(&flag, "CVodeSetMaxErrTestFails", 1)) return 1; + + /* Call CVodeSVtolerances to specify the scalar relative tolerance + * and vector absolute tolerances */ + flag = CVodeSVtolerances(cvode_mem, $(double rTol), tv); + if (check_flag(&flag, "CVodeSVtolerances", 1)) return(1); + + /* Call CVodeRootInit to specify the root function g with nr components */ + flag = CVodeRootInit(cvode_mem, $(int nr), $fun:(int (* gIO) (double t, SunVector y[], double gout[], void * params))); + + if (check_flag(&flag, "CVodeRootInit", 1)) return(1); + + /* Initialize dense matrix data structure and solver */ + A = SUNDenseMatrix(NEQ, NEQ); + if (check_flag((void *)A, "SUNDenseMatrix", 0)) return 1; + LS = SUNDenseLinearSolver(y, A); + if (check_flag((void *)LS, "SUNDenseLinearSolver", 0)) return 1; + + /* Attach matrix and linear solver */ + flag = CVDlsSetLinearSolver(cvode_mem, LS, A); + if (check_flag(&flag, "CVDlsSetLinearSolver", 1)) return 1; + + /* Set the initial step size if there is one */ + if ($(int isInitStepSize)) { + /* FIXME: We could check if the initial step size is 0 */ + /* or even NaN and then throw an error */ + flag = CVodeSetInitStep(cvode_mem, $(double ss)); + if (check_flag(&flag, "CVodeSetInitStep", 1)) return 1; + } + + /* Set the Jacobian if there is one */ + if ($(int isJac)) { + flag = CVDlsSetJacFn(cvode_mem, $fun:(int (* jacIO) (double t, SunVector y[], SunVector fy[], SunMatrix Jac[], void * params, SunVector tmp1[], SunVector tmp2[], SunVector tmp3[]))); + if (check_flag(&flag, "CVDlsSetJacFn", 1)) return 1; + } + + /* Store initial conditions */ + for (j = 0; j < NEQ; j++) { + ($vec-ptr:(double *qMatMut))[0 * $(int nTs) + j] = NV_Ith_S(y,j); + } + + /* Main time-stepping loop: calls CVode to perform the integration */ + /* Stops when the final time has been reached */ + for (i = 1; i < $(int nTs); i++) { + + flag = CVode(cvode_mem, ($vec-ptr:(double *ts))[i], y, &t, CV_NORMAL); /* call integrator */ + if (check_flag(&flag, "CVode solver failure, stopping integration", 1)) return 1; + + /* Store the results for Haskell */ + for (j = 0; j < NEQ; j++) { + ($vec-ptr:(double *qMatMut))[i * NEQ + j] = NV_Ith_S(y,j); + } + + if (flag == CV_ROOT_RETURN) { + flagr = CVodeGetRootInfo(cvode_mem, ($vec-ptr:(int *gResMut))); + if (check_flag(&flagr, "CVodeGetRootInfo", 1)) return(1); + ($vec-ptr:(double *tRootMut))[0] = t; + flagr = flag; + break; + } + } + + /* Get some final statistics on how the solve progressed */ + + flag = CVodeGetNumSteps(cvode_mem, &nst); + check_flag(&flag, "CVodeGetNumSteps", 1); + ($vec-ptr:(long int *diagMut))[0] = nst; + + /* FIXME */ + ($vec-ptr:(long int *diagMut))[1] = 0; + + flag = CVodeGetNumRhsEvals(cvode_mem, &nfe); + check_flag(&flag, "CVodeGetNumRhsEvals", 1); + ($vec-ptr:(long int *diagMut))[2] = nfe; + /* FIXME */ + ($vec-ptr:(long int *diagMut))[3] = 0; + + flag = CVodeGetNumLinSolvSetups(cvode_mem, &nsetups); + check_flag(&flag, "CVodeGetNumLinSolvSetups", 1); + ($vec-ptr:(long int *diagMut))[4] = nsetups; + + flag = CVodeGetNumErrTestFails(cvode_mem, &netf); + check_flag(&flag, "CVodeGetNumErrTestFails", 1); + ($vec-ptr:(long int *diagMut))[5] = netf; + + flag = CVodeGetNumNonlinSolvIters(cvode_mem, &nni); + check_flag(&flag, "CVodeGetNumNonlinSolvIters", 1); + ($vec-ptr:(long int *diagMut))[6] = nni; + + flag = CVodeGetNumNonlinSolvConvFails(cvode_mem, &ncfn); + check_flag(&flag, "CVodeGetNumNonlinSolvConvFails", 1); + ($vec-ptr:(long int *diagMut))[7] = ncfn; + + flag = CVDlsGetNumJacEvals(cvode_mem, &nje); + check_flag(&flag, "CVDlsGetNumJacEvals", 1); + ($vec-ptr:(long int *diagMut))[8] = ncfn; + + flag = CVDlsGetNumRhsEvals(cvode_mem, &nfeLS); + check_flag(&flag, "CVDlsGetNumRhsEvals", 1); + ($vec-ptr:(long int *diagMut))[9] = ncfn; + + /* Clean up and return */ + + N_VDestroy(y); /* Free y vector */ + N_VDestroy(tv); /* Free tv vector */ + CVodeFree(&cvode_mem); /* Free integrator memory */ + SUNLinSolFree(LS); /* Free linear solver */ + SUNMatDestroy(A); /* Free A matrix */ + + if (flag == CV_SUCCESS && flagr == CV_ROOT_RETURN) { + return CV_ROOT_RETURN; + } + else { + 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 + t <- V.freeze tRootMut + rs <- V.freeze gResMut + putStrLn $ show rs + let f r | r == cV_SUCCESS = SolverSuccess m d + | r == cV_ROOT_RETURN = SolverRoot (t V.!0) rs m d + | otherwise = SolverError m res + return $ f $ fromIntegral res + +data SolverResult f g a b = + SolverError (f b) a -- ^ Partial results and error code + | SolverSuccess (f b) SundialsDiagnostics -- ^ Results and diagnostics + | SolverRoot b (g a) (f b) SundialsDiagnostics -- ^ Time at which the root was found, the root itself and the + -- results and diagnostics. NB the final result will be at the time + -- at which the root was found not as specified by the times given + -- to the solver. + deriving Show + +odeSolveRootVWith' :: + ODEOpts + -> ODEMethod + -> StepControl + -> Maybe Double -- ^ initial step size - by default, CVode + -- 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 + -> Int -- ^ Dimension of the range of the roots function + -> (Double -> V.Vector Double -> V.Vector Double) -- ^ Roots function + -> V.Vector Double -- ^ Desired solution times + -> SolverResult Matrix Vector Int Double +odeSolveRootVWith' opts method control initStepSize f y0 is gg tt = + case solveOdeC' (fromIntegral $ maxFail opts) + (fromIntegral $ maxNumSteps opts) (coerce $ minStep opts) + (fromIntegral $ getMethod method) (coerce initStepSize) jacH (scise control) + (coerce f) (coerce y0) (fromIntegral is) (coerce gg) (coerce tt) of + SolverError v c -> SolverError (reshape l (coerce v)) (fromIntegral c) + SolverSuccess v d -> SolverSuccess (reshape l (coerce v)) d + SolverRoot t rs v d -> SolverRoot (coerce t) (V.map fromIntegral rs) (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 + +-- | 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 \(\eta^{rel} = a_{y}\epsilon^{rel}\) diff --git a/src/Numeric/Sundials/ODEOpts.hs b/src/Numeric/Sundials/ODEOpts.hs new file mode 100644 --- /dev/null +++ b/src/Numeric/Sundials/ODEOpts.hs @@ -0,0 +1,32 @@ +module Numeric.Sundials.ODEOpts where + +import Data.Word (Word32) +import qualified Data.Vector.Storable as VS + +import Numeric.LinearAlgebra.HMatrix (Vector, Matrix) + + +type Jacobian = Double -> Vector Double -> Matrix Double + +data ODEOpts = ODEOpts { + maxNumSteps :: Word32 + , minStep :: Double + , relTol :: Double + , absTols :: VS.Vector Double + , initStep :: Maybe Double + , maxFail :: Word32 + } deriving (Read, Show, Eq, Ord) + +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 + diff --git a/src/Types.hs b/src/Types.hs deleted file mode 100644 --- a/src/Types.hs +++ /dev/null @@ -1,40 +0,0 @@ -{-# OPTIONS_GHC -Wall #-} - -{-# LANGUAGE QuasiQuotes #-} -{-# LANGUAGE TemplateHaskell #-} -{-# LANGUAGE MultiWayIf #-} -{-# LANGUAGE OverloadedStrings #-} -{-# LANGUAGE EmptyDataDecls #-} - -module Types where - -import Foreign.C.Types - -import qualified Language.Haskell.TH as TH -import qualified Language.C.Types as CT -import qualified Data.Map as Map -import Language.C.Inline.Context - -import qualified Data.Vector.Storable as V - - -data SunVector -data SunMatrix = SunMatrix { rows :: CInt - , cols :: CInt - , vals :: V.Vector CDouble - } - --- FIXME: Is this true? -type SunIndexType = CLong - -sunTypesTable :: Map.Map CT.TypeSpecifier TH.TypeQ -sunTypesTable = Map.fromList - [ - (CT.TypeName "sunindextype", [t| SunIndexType |] ) - , (CT.TypeName "SunVector", [t| SunVector |] ) - , (CT.TypeName "SunMatrix", [t| SunMatrix |] ) - ] - -sunCtx :: Context -sunCtx = mempty {ctxTypesTable = sunTypesTable} -