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1{-# LANGUAGE QuasiQuotes #-}
2{-# LANGUAGE TemplateHaskell #-}
3{-# LANGUAGE MultiWayIf #-}
4{-# LANGUAGE OverloadedStrings #-}
5{-# LANGUAGE ScopedTypeVariables #-}
6{-# LANGUAGE DeriveGeneric #-}
7{-# LANGUAGE TypeOperators #-}
8{-# LANGUAGE KindSignatures #-}
9{-# LANGUAGE TypeSynonymInstances #-}
10{-# LANGUAGE FlexibleInstances #-}
11{-# LANGUAGE FlexibleContexts #-}
12
13-----------------------------------------------------------------------------
14-- |
15-- Module : Numeric.Sundials.ARKode.ODE
16-- Copyright : Dominic Steinitz 2018,
17-- Novadiscovery 2018
18-- License : BSD
19-- Maintainer : Dominic Steinitz
20-- Stability : provisional
21--
22-- Solution of ordinary differential equation (ODE) initial value problems.
23-- See <https://computation.llnl.gov/projects/sundials/sundials-software> for more detail.
24--
25-- A simple example:
26--
27-- <<diagrams/brusselator.png#diagram=brusselator&height=400&width=500>>
28--
29-- @
30-- import Numeric.Sundials.ARKode.ODE
31-- import Numeric.LinearAlgebra
32--
33-- import Plots as P
34-- import qualified Diagrams.Prelude as D
35-- import Diagrams.Backend.Rasterific
36--
37-- brusselator :: Double -> [Double] -> [Double]
38-- brusselator _t x = [ a - (w + 1) * u + v * u * u
39-- , w * u - v * u * u
40-- , (b - w) / eps - w * u
41-- ]
42-- where
43-- a = 1.0
44-- b = 3.5
45-- eps = 5.0e-6
46-- u = x !! 0
47-- v = x !! 1
48-- w = x !! 2
49--
50-- lSaxis :: [[Double]] -> P.Axis B D.V2 Double
51-- lSaxis xs = P.r2Axis &~ do
52-- let ts = xs!!0
53-- us = xs!!1
54-- vs = xs!!2
55-- ws = xs!!3
56-- P.linePlot' $ zip ts us
57-- P.linePlot' $ zip ts vs
58-- P.linePlot' $ zip ts ws
59--
60-- main = do
61-- let res1 = odeSolve brusselator [1.2, 3.1, 3.0] (fromList [0.0, 0.1 .. 10.0])
62-- renderRasterific "diagrams/brusselator.png"
63-- (D.dims2D 500.0 500.0)
64-- (renderAxis $ lSaxis $ [0.0, 0.1 .. 10.0]:(toLists $ tr res1))
65-- @
66--
67-- With Sundials ARKode, it is possible to retrieve the Butcher tableau for the solver.
68--
69-- @
70-- import Numeric.Sundials.ARKode.ODE
71-- import Numeric.LinearAlgebra
72--
73-- import Data.List (intercalate)
74--
75-- import Text.PrettyPrint.HughesPJClass
76--
77--
78-- butcherTableauTex :: ButcherTable -> String
79-- butcherTableauTex (ButcherTable m c b b2) =
80-- render $
81-- vcat [ text ("\n\\begin{array}{c|" ++ (concat $ replicate n "c") ++ "}")
82-- , us
83-- , text "\\hline"
84-- , text bs <+> text "\\\\"
85-- , text b2s <+> text "\\\\"
86-- , text "\\end{array}"
87-- ]
88-- where
89-- n = rows m
90-- rs = toLists m
91-- ss = map (\r -> intercalate " & " $ map show r) rs
92-- ts = zipWith (\i r -> show i ++ " & " ++ r) (toList c) ss
93-- us = vcat $ map (\r -> text r <+> text "\\\\") ts
94-- bs = " & " ++ (intercalate " & " $ map show $ toList b)
95-- b2s = " & " ++ (intercalate " & " $ map show $ toList b2)
96--
97-- main :: IO ()
98-- main = do
99--
100-- let res = butcherTable (SDIRK_2_1_2 undefined)
101-- putStrLn $ show res
102-- putStrLn $ butcherTableauTex res
103--
104-- let resA = butcherTable (KVAERNO_4_2_3 undefined)
105-- putStrLn $ show resA
106-- putStrLn $ butcherTableauTex resA
107--
108-- let resB = butcherTable (SDIRK_5_3_4 undefined)
109-- putStrLn $ show resB
110-- putStrLn $ butcherTableauTex resB
111-- @
112--
113-- Using the code above from the examples gives
114--
115-- KVAERNO_4_2_3
116--
117-- \[
118-- \begin{array}{c|cccc}
119-- 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\
120-- 0.871733043 & 0.4358665215 & 0.4358665215 & 0.0 & 0.0 \\
121-- 1.0 & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
122-- 1.0 & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
123-- \hline
124-- & 0.308809969973036 & 1.490563388254106 & -1.235239879727145 & 0.4358665215 \\
125-- & 0.490563388419108 & 7.3570090080892e-2 & 0.4358665215 & 0.0 \\
126-- \end{array}
127-- \]
128--
129-- SDIRK_2_1_2
130--
131-- \[
132-- \begin{array}{c|cc}
133-- 1.0 & 1.0 & 0.0 \\
134-- 0.0 & -1.0 & 1.0 \\
135-- \hline
136-- & 0.5 & 0.5 \\
137-- & 1.0 & 0.0 \\
138-- \end{array}
139-- \]
140--
141-- SDIRK_5_3_4
142--
143-- \[
144-- \begin{array}{c|ccccc}
145-- 0.25 & 0.25 & 0.0 & 0.0 & 0.0 & 0.0 \\
146-- 0.75 & 0.5 & 0.25 & 0.0 & 0.0 & 0.0 \\
147-- 0.55 & 0.34 & -4.0e-2 & 0.25 & 0.0 & 0.0 \\
148-- 0.5 & 0.2727941176470588 & -5.036764705882353e-2 & 2.7573529411764705e-2 & 0.25 & 0.0 \\
149-- 1.0 & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
150-- \hline
151-- & 1.0416666666666667 & -1.0208333333333333 & 7.8125 & -7.083333333333333 & 0.25 \\
152-- & 1.2291666666666667 & -0.17708333333333334 & 7.03125 & -7.083333333333333 & 0.0 \\
153-- \end{array}
154-- \]
155-----------------------------------------------------------------------------
156module Numeric.Sundials.ARKode.ODE ( odeSolve
157 , odeSolveV
158 , odeSolveVWith
159 , odeSolveVWith'
160 , ButcherTable(..)
161 , butcherTable
162 , ODEMethod(..)
163 , StepControl(..)
164 ) where
165
166import qualified Language.C.Inline as C
167import qualified Language.C.Inline.Unsafe as CU
168
169import Data.Monoid ((<>))
170import Data.Maybe (isJust)
171
172import Foreign.C.Types (CDouble, CInt, CLong)
173import Foreign.Ptr (Ptr)
174import Foreign.Storable (poke)
175
176import qualified Data.Vector.Storable as V
177
178import Data.Coerce (coerce)
179import System.IO.Unsafe (unsafePerformIO)
180import GHC.Generics (C1, Constructor, (:+:)(..), D1, Rep, Generic, M1(..),
181 from, conName)
182
183import Numeric.LinearAlgebra.Devel (createVector)
184
185import Numeric.LinearAlgebra.HMatrix (Vector, Matrix, toList, rows,
186 cols, toLists, size, reshape,
187 subVector, subMatrix, (><))
188
189import Numeric.Sundials.ODEOpts (ODEOpts(..), Jacobian, SundialsDiagnostics(..))
190import qualified Numeric.Sundials.Arkode as T
191import Numeric.Sundials.Arkode (getDataFromContents, putDataInContents, arkSMax,
192 sDIRK_2_1_2,
193 bILLINGTON_3_3_2,
194 tRBDF2_3_3_2,
195 kVAERNO_4_2_3,
196 aRK324L2SA_DIRK_4_2_3,
197 cASH_5_2_4,
198 cASH_5_3_4,
199 sDIRK_5_3_4,
200 kVAERNO_5_3_4,
201 aRK436L2SA_DIRK_6_3_4,
202 kVAERNO_7_4_5,
203 aRK548L2SA_DIRK_8_4_5,
204 hEUN_EULER_2_1_2,
205 bOGACKI_SHAMPINE_4_2_3,
206 aRK324L2SA_ERK_4_2_3,
207 zONNEVELD_5_3_4,
208 aRK436L2SA_ERK_6_3_4,
209 sAYFY_ABURUB_6_3_4,
210 cASH_KARP_6_4_5,
211 fEHLBERG_6_4_5,
212 dORMAND_PRINCE_7_4_5,
213 aRK548L2SA_ERK_8_4_5,
214 vERNER_8_5_6,
215 fEHLBERG_13_7_8)
216
217
218C.context (C.baseCtx <> C.vecCtx <> C.funCtx <> T.sunCtx)
219
220C.include "<stdlib.h>"
221C.include "<stdio.h>"
222C.include "<math.h>"
223C.include "<arkode/arkode.h>" -- prototypes for ARKODE fcts., consts.
224C.include "<nvector/nvector_serial.h>" -- serial N_Vector types, fcts., macros
225C.include "<sunmatrix/sunmatrix_dense.h>" -- access to dense SUNMatrix
226C.include "<sunlinsol/sunlinsol_dense.h>" -- access to dense SUNLinearSolver
227C.include "<arkode/arkode_direct.h>" -- access to ARKDls interface
228C.include "<sundials/sundials_types.h>" -- definition of type realtype
229C.include "<sundials/sundials_math.h>"
230C.include "../../../helpers.h"
231C.include "Numeric/Sundials/Arkode_hsc.h"
232
233
234-- | Stepping functions
235data ODEMethod = SDIRK_2_1_2 Jacobian
236 | SDIRK_2_1_2'
237 | BILLINGTON_3_3_2 Jacobian
238 | BILLINGTON_3_3_2'
239 | TRBDF2_3_3_2 Jacobian
240 | TRBDF2_3_3_2'
241 | KVAERNO_4_2_3 Jacobian
242 | KVAERNO_4_2_3'
243 | ARK324L2SA_DIRK_4_2_3 Jacobian
244 | ARK324L2SA_DIRK_4_2_3'
245 | CASH_5_2_4 Jacobian
246 | CASH_5_2_4'
247 | CASH_5_3_4 Jacobian
248 | CASH_5_3_4'
249 | SDIRK_5_3_4 Jacobian
250 | SDIRK_5_3_4'
251 | KVAERNO_5_3_4 Jacobian
252 | KVAERNO_5_3_4'
253 | ARK436L2SA_DIRK_6_3_4 Jacobian
254 | ARK436L2SA_DIRK_6_3_4'
255 | KVAERNO_7_4_5 Jacobian
256 | KVAERNO_7_4_5'
257 | ARK548L2SA_DIRK_8_4_5 Jacobian
258 | ARK548L2SA_DIRK_8_4_5'
259 | HEUN_EULER_2_1_2 Jacobian
260 | HEUN_EULER_2_1_2'
261 | BOGACKI_SHAMPINE_4_2_3 Jacobian
262 | BOGACKI_SHAMPINE_4_2_3'
263 | ARK324L2SA_ERK_4_2_3 Jacobian
264 | ARK324L2SA_ERK_4_2_3'
265 | ZONNEVELD_5_3_4 Jacobian
266 | ZONNEVELD_5_3_4'
267 | ARK436L2SA_ERK_6_3_4 Jacobian
268 | ARK436L2SA_ERK_6_3_4'
269 | SAYFY_ABURUB_6_3_4 Jacobian
270 | SAYFY_ABURUB_6_3_4'
271 | CASH_KARP_6_4_5 Jacobian
272 | CASH_KARP_6_4_5'
273 | FEHLBERG_6_4_5 Jacobian
274 | FEHLBERG_6_4_5'
275 | DORMAND_PRINCE_7_4_5 Jacobian
276 | DORMAND_PRINCE_7_4_5'
277 | ARK548L2SA_ERK_8_4_5 Jacobian
278 | ARK548L2SA_ERK_8_4_5'
279 | VERNER_8_5_6 Jacobian
280 | VERNER_8_5_6'
281 | FEHLBERG_13_7_8 Jacobian
282 | FEHLBERG_13_7_8'
283 deriving Generic
284
285constrName :: (HasConstructor (Rep a), Generic a)=> a -> String
286constrName = genericConstrName . from
287
288class HasConstructor (f :: * -> *) where
289 genericConstrName :: f x -> String
290
291instance HasConstructor f => HasConstructor (D1 c f) where
292 genericConstrName (M1 x) = genericConstrName x
293
294instance (HasConstructor x, HasConstructor y) => HasConstructor (x :+: y) where
295 genericConstrName (L1 l) = genericConstrName l
296 genericConstrName (R1 r) = genericConstrName r
297
298instance Constructor c => HasConstructor (C1 c f) where
299 genericConstrName x = conName x
300
301instance Show ODEMethod where
302 show x = constrName x
303
304-- FIXME: We can probably do better here with generics
305getMethod :: ODEMethod -> Int
306getMethod (SDIRK_2_1_2 _) = sDIRK_2_1_2
307getMethod (SDIRK_2_1_2') = sDIRK_2_1_2
308getMethod (BILLINGTON_3_3_2 _) = bILLINGTON_3_3_2
309getMethod (BILLINGTON_3_3_2') = bILLINGTON_3_3_2
310getMethod (TRBDF2_3_3_2 _) = tRBDF2_3_3_2
311getMethod (TRBDF2_3_3_2') = tRBDF2_3_3_2
312getMethod (KVAERNO_4_2_3 _) = kVAERNO_4_2_3
313getMethod (KVAERNO_4_2_3') = kVAERNO_4_2_3
314getMethod (ARK324L2SA_DIRK_4_2_3 _) = aRK324L2SA_DIRK_4_2_3
315getMethod (ARK324L2SA_DIRK_4_2_3') = aRK324L2SA_DIRK_4_2_3
316getMethod (CASH_5_2_4 _) = cASH_5_2_4
317getMethod (CASH_5_2_4') = cASH_5_2_4
318getMethod (CASH_5_3_4 _) = cASH_5_3_4
319getMethod (CASH_5_3_4') = cASH_5_3_4
320getMethod (SDIRK_5_3_4 _) = sDIRK_5_3_4
321getMethod (SDIRK_5_3_4') = sDIRK_5_3_4
322getMethod (KVAERNO_5_3_4 _) = kVAERNO_5_3_4
323getMethod (KVAERNO_5_3_4') = kVAERNO_5_3_4
324getMethod (ARK436L2SA_DIRK_6_3_4 _) = aRK436L2SA_DIRK_6_3_4
325getMethod (ARK436L2SA_DIRK_6_3_4') = aRK436L2SA_DIRK_6_3_4
326getMethod (KVAERNO_7_4_5 _) = kVAERNO_7_4_5
327getMethod (KVAERNO_7_4_5') = kVAERNO_7_4_5
328getMethod (ARK548L2SA_DIRK_8_4_5 _) = aRK548L2SA_DIRK_8_4_5
329getMethod (ARK548L2SA_DIRK_8_4_5') = aRK548L2SA_DIRK_8_4_5
330getMethod (HEUN_EULER_2_1_2 _) = hEUN_EULER_2_1_2
331getMethod (HEUN_EULER_2_1_2') = hEUN_EULER_2_1_2
332getMethod (BOGACKI_SHAMPINE_4_2_3 _) = bOGACKI_SHAMPINE_4_2_3
333getMethod (BOGACKI_SHAMPINE_4_2_3') = bOGACKI_SHAMPINE_4_2_3
334getMethod (ARK324L2SA_ERK_4_2_3 _) = aRK324L2SA_ERK_4_2_3
335getMethod (ARK324L2SA_ERK_4_2_3') = aRK324L2SA_ERK_4_2_3
336getMethod (ZONNEVELD_5_3_4 _) = zONNEVELD_5_3_4
337getMethod (ZONNEVELD_5_3_4') = zONNEVELD_5_3_4
338getMethod (ARK436L2SA_ERK_6_3_4 _) = aRK436L2SA_ERK_6_3_4
339getMethod (ARK436L2SA_ERK_6_3_4') = aRK436L2SA_ERK_6_3_4
340getMethod (SAYFY_ABURUB_6_3_4 _) = sAYFY_ABURUB_6_3_4
341getMethod (SAYFY_ABURUB_6_3_4') = sAYFY_ABURUB_6_3_4
342getMethod (CASH_KARP_6_4_5 _) = cASH_KARP_6_4_5
343getMethod (CASH_KARP_6_4_5') = cASH_KARP_6_4_5
344getMethod (FEHLBERG_6_4_5 _) = fEHLBERG_6_4_5
345getMethod (FEHLBERG_6_4_5' ) = fEHLBERG_6_4_5
346getMethod (DORMAND_PRINCE_7_4_5 _) = dORMAND_PRINCE_7_4_5
347getMethod (DORMAND_PRINCE_7_4_5') = dORMAND_PRINCE_7_4_5
348getMethod (ARK548L2SA_ERK_8_4_5 _) = aRK548L2SA_ERK_8_4_5
349getMethod (ARK548L2SA_ERK_8_4_5') = aRK548L2SA_ERK_8_4_5
350getMethod (VERNER_8_5_6 _) = vERNER_8_5_6
351getMethod (VERNER_8_5_6') = vERNER_8_5_6
352getMethod (FEHLBERG_13_7_8 _) = fEHLBERG_13_7_8
353getMethod (FEHLBERG_13_7_8') = fEHLBERG_13_7_8
354
355getJacobian :: ODEMethod -> Maybe Jacobian
356getJacobian (SDIRK_2_1_2 j) = Just j
357getJacobian (BILLINGTON_3_3_2 j) = Just j
358getJacobian (TRBDF2_3_3_2 j) = Just j
359getJacobian (KVAERNO_4_2_3 j) = Just j
360getJacobian (ARK324L2SA_DIRK_4_2_3 j) = Just j
361getJacobian (CASH_5_2_4 j) = Just j
362getJacobian (CASH_5_3_4 j) = Just j
363getJacobian (SDIRK_5_3_4 j) = Just j
364getJacobian (KVAERNO_5_3_4 j) = Just j
365getJacobian (ARK436L2SA_DIRK_6_3_4 j) = Just j
366getJacobian (KVAERNO_7_4_5 j) = Just j
367getJacobian (ARK548L2SA_DIRK_8_4_5 j) = Just j
368getJacobian (HEUN_EULER_2_1_2 j) = Just j
369getJacobian (BOGACKI_SHAMPINE_4_2_3 j) = Just j
370getJacobian (ARK324L2SA_ERK_4_2_3 j) = Just j
371getJacobian (ZONNEVELD_5_3_4 j) = Just j
372getJacobian (ARK436L2SA_ERK_6_3_4 j) = Just j
373getJacobian (SAYFY_ABURUB_6_3_4 j) = Just j
374getJacobian (CASH_KARP_6_4_5 j) = Just j
375getJacobian (FEHLBERG_6_4_5 j) = Just j
376getJacobian (DORMAND_PRINCE_7_4_5 j) = Just j
377getJacobian (ARK548L2SA_ERK_8_4_5 j) = Just j
378getJacobian (VERNER_8_5_6 j) = Just j
379getJacobian (FEHLBERG_13_7_8 j) = Just j
380getJacobian _ = Nothing
381
382-- | A version of 'odeSolveVWith' with reasonable default step control.
383odeSolveV
384 :: ODEMethod
385 -> Maybe Double -- ^ initial step size - by default, ARKode
386 -- estimates the initial step size to be the
387 -- solution \(h\) of the equation
388 -- \(\|\frac{h^2\ddot{y}}{2}\| = 1\), where
389 -- \(\ddot{y}\) is an estimated value of the
390 -- second derivative of the solution at \(t_0\)
391 -> Double -- ^ absolute tolerance for the state vector
392 -> Double -- ^ relative tolerance for the state vector
393 -> (Double -> Vector Double -> Vector Double) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
394 -> Vector Double -- ^ initial conditions
395 -> Vector Double -- ^ desired solution times
396 -> Matrix Double -- ^ solution
397odeSolveV meth hi epsAbs epsRel f y0 ts =
398 odeSolveVWith meth (X epsAbs epsRel) hi g y0 ts
399 where
400 g t x0 = coerce $ f t x0
401
402-- | A version of 'odeSolveV' with reasonable default parameters and
403-- system of equations defined using lists. FIXME: we should say
404-- something about the fact we could use the Jacobian but don't for
405-- compatibility with hmatrix-gsl.
406odeSolve :: (Double -> [Double] -> [Double]) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
407 -> [Double] -- ^ initial conditions
408 -> Vector Double -- ^ desired solution times
409 -> Matrix Double -- ^ solution
410odeSolve f y0 ts =
411 -- FIXME: These tolerances are different from the ones in GSL
412 odeSolveVWith SDIRK_5_3_4' (XX' 1.0e-6 1.0e-10 1 1) Nothing g (V.fromList y0) (V.fromList $ toList ts)
413 where
414 g t x0 = V.fromList $ f t (V.toList x0)
415
416odeSolveVWith ::
417 ODEMethod
418 -> StepControl
419 -> Maybe Double -- ^ initial step size - by default, ARKode
420 -- estimates the initial step size to be the
421 -- solution \(h\) of the equation
422 -- \(\|\frac{h^2\ddot{y}}{2}\| = 1\), where
423 -- \(\ddot{y}\) is an estimated value of the second
424 -- derivative of the solution at \(t_0\)
425 -> (Double -> V.Vector Double -> V.Vector Double) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
426 -> V.Vector Double -- ^ Initial conditions
427 -> V.Vector Double -- ^ Desired solution times
428 -> Matrix Double -- ^ Error code or solution
429odeSolveVWith method control initStepSize f y0 tt =
430 case odeSolveVWith' opts method control initStepSize f y0 tt of
431 Left (c, _v) -> error $ show c -- FIXME
432 Right (v, _d) -> v
433 where
434 opts = ODEOpts { maxNumSteps = 10000
435 , minStep = 1.0e-12
436 , relTol = error "relTol"
437 , absTols = error "absTol"
438 , initStep = error "initStep"
439 , maxFail = 10
440 }
441
442odeSolveVWith' ::
443 ODEOpts
444 -> ODEMethod
445 -> StepControl
446 -> Maybe Double -- ^ initial step size - by default, ARKode
447 -- estimates the initial step size to be the
448 -- solution \(h\) of the equation
449 -- \(\|\frac{h^2\ddot{y}}{2}\| = 1\), where
450 -- \(\ddot{y}\) is an estimated value of the second
451 -- derivative of the solution at \(t_0\)
452 -> (Double -> V.Vector Double -> V.Vector Double) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
453 -> V.Vector Double -- ^ Initial conditions
454 -> V.Vector Double -- ^ Desired solution times
455 -> Either (Matrix Double, Int) (Matrix Double, SundialsDiagnostics) -- ^ Error code or solution
456odeSolveVWith' opts method control initStepSize f y0 tt =
457 case solveOdeC (fromIntegral $ maxFail opts)
458 (fromIntegral $ maxNumSteps opts) (coerce $ minStep opts)
459 (fromIntegral $ getMethod method) (coerce initStepSize) jacH (scise control)
460 (coerce f) (coerce y0) (coerce tt) of
461 Left (v, c) -> Left (reshape l (coerce v), fromIntegral c)
462 Right (v, d) -> Right (reshape l (coerce v), d)
463 where
464 l = size y0
465 scise (X aTol rTol) = coerce (V.replicate l aTol, rTol)
466 scise (X' aTol rTol) = coerce (V.replicate l aTol, rTol)
467 scise (XX' aTol rTol yScale _yDotScale) = coerce (V.replicate l aTol, yScale * rTol)
468 -- FIXME; Should we check that the length of ss is correct?
469 scise (ScXX' aTol rTol yScale _yDotScale ss) = coerce (V.map (* aTol) ss, yScale * rTol)
470 jacH = fmap (\g t v -> matrixToSunMatrix $ g (coerce t) (coerce v)) $
471 getJacobian method
472 matrixToSunMatrix m = T.SunMatrix { T.rows = nr, T.cols = nc, T.vals = vs }
473 where
474 nr = fromIntegral $ rows m
475 nc = fromIntegral $ cols m
476 -- FIXME: efficiency
477 vs = V.fromList $ map coerce $ concat $ toLists m
478
479solveOdeC ::
480 CInt ->
481 CLong ->
482 CDouble ->
483 CInt ->
484 Maybe CDouble ->
485 (Maybe (CDouble -> V.Vector CDouble -> T.SunMatrix)) ->
486 (V.Vector CDouble, CDouble) ->
487 (CDouble -> V.Vector CDouble -> V.Vector CDouble) -- ^ The RHS of the system \(\dot{y} = f(t,y)\)
488 -> V.Vector CDouble -- ^ Initial conditions
489 -> V.Vector CDouble -- ^ Desired solution times
490 -> Either (V.Vector CDouble, CInt) (V.Vector CDouble, SundialsDiagnostics) -- ^ Partial solution and error code or
491 -- solution and diagnostics
492solveOdeC maxErrTestFails maxNumSteps_ minStep_ method initStepSize
493 jacH (aTols, rTol) fun f0 ts = unsafePerformIO $ do
494
495 let isInitStepSize :: CInt
496 isInitStepSize = fromIntegral $ fromEnum $ isJust initStepSize
497 ss :: CDouble
498 ss = case initStepSize of
499 -- It would be better to put an error message here but
500 -- inline-c seems to evaluate this even if it is never
501 -- used :(
502 Nothing -> 0.0
503 Just x -> x
504
505 let dim = V.length f0
506 nEq :: CLong
507 nEq = fromIntegral dim
508 nTs :: CInt
509 nTs = fromIntegral $ V.length ts
510 quasiMatrixRes <- createVector ((fromIntegral dim) * (fromIntegral nTs))
511 qMatMut <- V.thaw quasiMatrixRes
512 diagnostics :: V.Vector CLong <- createVector 10 -- FIXME
513 diagMut <- V.thaw diagnostics
514 -- We need the types that sundials expects. These are tied together
515 -- in 'CLangToHaskellTypes'. FIXME: The Haskell type is currently empty!
516 let funIO :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt
517 funIO x y f _ptr = do
518 -- Convert the pointer we get from C (y) to a vector, and then
519 -- apply the user-supplied function.
520 fImm <- fun x <$> getDataFromContents dim y
521 -- Fill in the provided pointer with the resulting vector.
522 putDataInContents fImm dim f
523 -- FIXME: I don't understand what this comment means
524 -- Unsafe since the function will be called many times.
525 [CU.exp| int{ 0 } |]
526 let isJac :: CInt
527 isJac = fromIntegral $ fromEnum $ isJust jacH
528 jacIO :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr T.SunMatrix ->
529 Ptr () -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr T.SunVector ->
530 IO CInt
531 jacIO t y _fy jacS _ptr _tmp1 _tmp2 _tmp3 = do
532 case jacH of
533 Nothing -> error "Numeric.Sundials.ARKode.ODE: Jacobian not defined"
534 Just jacI -> do j <- jacI t <$> getDataFromContents dim y
535 poke jacS j
536 -- FIXME: I don't understand what this comment means
537 -- Unsafe since the function will be called many times.
538 [CU.exp| int{ 0 } |]
539
540 res <- [C.block| int {
541 /* general problem variables */
542
543 int flag; /* reusable error-checking flag */
544 int i, j; /* reusable loop indices */
545 N_Vector y = NULL; /* empty vector for storing solution */
546 N_Vector tv = NULL; /* empty vector for storing absolute tolerances */
547 SUNMatrix A = NULL; /* empty matrix for linear solver */
548 SUNLinearSolver LS = NULL; /* empty linear solver object */
549 void *arkode_mem = NULL; /* empty ARKode memory structure */
550 realtype t;
551 long int nst, nst_a, nfe, nfi, nsetups, nje, nfeLS, nni, ncfn, netf;
552
553 /* general problem parameters */
554
555 realtype T0 = RCONST(($vec-ptr:(double *ts))[0]); /* initial time */
556 sunindextype NEQ = $(sunindextype nEq); /* number of dependent vars. */
557
558 /* Initialize data structures */
559
560 y = N_VNew_Serial(NEQ); /* Create serial vector for solution */
561 if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
562 /* Specify initial condition */
563 for (i = 0; i < NEQ; i++) {
564 NV_Ith_S(y,i) = ($vec-ptr:(double *f0))[i];
565 };
566
567 tv = N_VNew_Serial(NEQ); /* Create serial vector for absolute tolerances */
568 if (check_flag((void *)tv, "N_VNew_Serial", 0)) return 1;
569 /* Specify tolerances */
570 for (i = 0; i < NEQ; i++) {
571 NV_Ith_S(tv,i) = ($vec-ptr:(double *aTols))[i];
572 };
573
574 arkode_mem = ARKodeCreate(); /* Create the solver memory */
575 if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1;
576
577 /* Call ARKodeInit to initialize the integrator memory and specify the */
578 /* right-hand side function in y'=f(t,y), the inital time T0, and */
579 /* the initial dependent variable vector y. Note: we treat the */
580 /* problem as fully implicit and set f_E to NULL and f_I to f. */
581
582 /* Here we use the C types defined in helpers.h which tie up with */
583 /* the Haskell types defined in CLangToHaskellTypes */
584 if ($(int method) < MIN_DIRK_NUM) {
585 flag = ARKodeInit(arkode_mem, $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), NULL, T0, y);
586 if (check_flag(&flag, "ARKodeInit", 1)) return 1;
587 } else {
588 flag = ARKodeInit(arkode_mem, NULL, $fun:(int (* funIO) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y);
589 if (check_flag(&flag, "ARKodeInit", 1)) return 1;
590 }
591
592 flag = ARKodeSetMinStep(arkode_mem, $(double minStep_));
593 if (check_flag(&flag, "ARKodeSetMinStep", 1)) return 1;
594 flag = ARKodeSetMaxNumSteps(arkode_mem, $(long int maxNumSteps_));
595 if (check_flag(&flag, "ARKodeSetMaxNumSteps", 1)) return 1;
596 flag = ARKodeSetMaxErrTestFails(arkode_mem, $(int maxErrTestFails));
597 if (check_flag(&flag, "ARKodeSetMaxErrTestFails", 1)) return 1;
598
599 /* Set routines */
600 flag = ARKodeSVtolerances(arkode_mem, $(double rTol), tv);
601 if (check_flag(&flag, "ARKodeSVtolerances", 1)) return 1;
602
603 /* Initialize dense matrix data structure and solver */
604 A = SUNDenseMatrix(NEQ, NEQ);
605 if (check_flag((void *)A, "SUNDenseMatrix", 0)) return 1;
606 LS = SUNDenseLinearSolver(y, A);
607 if (check_flag((void *)LS, "SUNDenseLinearSolver", 0)) return 1;
608
609 /* Attach matrix and linear solver */
610 flag = ARKDlsSetLinearSolver(arkode_mem, LS, A);
611 if (check_flag(&flag, "ARKDlsSetLinearSolver", 1)) return 1;
612
613 /* Set the initial step size if there is one */
614 if ($(int isInitStepSize)) {
615 /* FIXME: We could check if the initial step size is 0 */
616 /* or even NaN and then throw an error */
617 flag = ARKodeSetInitStep(arkode_mem, $(double ss));
618 if (check_flag(&flag, "ARKodeSetInitStep", 1)) return 1;
619 }
620
621 /* Set the Jacobian if there is one */
622 if ($(int isJac)) {
623 flag = ARKDlsSetJacFn(arkode_mem, $fun:(int (* jacIO) (double t, SunVector y[], SunVector fy[], SunMatrix Jac[], void * params, SunVector tmp1[], SunVector tmp2[], SunVector tmp3[])));
624 if (check_flag(&flag, "ARKDlsSetJacFn", 1)) return 1;
625 }
626
627 /* Store initial conditions */
628 for (j = 0; j < NEQ; j++) {
629 ($vec-ptr:(double *qMatMut))[0 * $(int nTs) + j] = NV_Ith_S(y,j);
630 }
631
632 /* Explicitly set the method */
633 if ($(int method) >= MIN_DIRK_NUM) {
634 flag = ARKodeSetIRKTableNum(arkode_mem, $(int method));
635 if (check_flag(&flag, "ARKodeSetIRKTableNum", 1)) return 1;
636 } else {
637 flag = ARKodeSetERKTableNum(arkode_mem, $(int method));
638 if (check_flag(&flag, "ARKodeSetERKTableNum", 1)) return 1;
639 }
640
641 /* Main time-stepping loop: calls ARKode to perform the integration */
642 /* Stops when the final time has been reached */
643 for (i = 1; i < $(int nTs); i++) {
644
645 flag = ARKode(arkode_mem, ($vec-ptr:(double *ts))[i], y, &t, ARK_NORMAL); /* call integrator */
646 if (check_flag(&flag, "ARKode solver failure, stopping integration", 1)) return 1;
647
648 /* Store the results for Haskell */
649 for (j = 0; j < NEQ; j++) {
650 ($vec-ptr:(double *qMatMut))[i * NEQ + j] = NV_Ith_S(y,j);
651 }
652 }
653
654 /* Get some final statistics on how the solve progressed */
655
656 flag = ARKodeGetNumSteps(arkode_mem, &nst);
657 check_flag(&flag, "ARKodeGetNumSteps", 1);
658 ($vec-ptr:(long int *diagMut))[0] = nst;
659
660 flag = ARKodeGetNumStepAttempts(arkode_mem, &nst_a);
661 check_flag(&flag, "ARKodeGetNumStepAttempts", 1);
662 ($vec-ptr:(long int *diagMut))[1] = nst_a;
663
664 flag = ARKodeGetNumRhsEvals(arkode_mem, &nfe, &nfi);
665 check_flag(&flag, "ARKodeGetNumRhsEvals", 1);
666 ($vec-ptr:(long int *diagMut))[2] = nfe;
667 ($vec-ptr:(long int *diagMut))[3] = nfi;
668
669 flag = ARKodeGetNumLinSolvSetups(arkode_mem, &nsetups);
670 check_flag(&flag, "ARKodeGetNumLinSolvSetups", 1);
671 ($vec-ptr:(long int *diagMut))[4] = nsetups;
672
673 flag = ARKodeGetNumErrTestFails(arkode_mem, &netf);
674 check_flag(&flag, "ARKodeGetNumErrTestFails", 1);
675 ($vec-ptr:(long int *diagMut))[5] = netf;
676
677 flag = ARKodeGetNumNonlinSolvIters(arkode_mem, &nni);
678 check_flag(&flag, "ARKodeGetNumNonlinSolvIters", 1);
679 ($vec-ptr:(long int *diagMut))[6] = nni;
680
681 flag = ARKodeGetNumNonlinSolvConvFails(arkode_mem, &ncfn);
682 check_flag(&flag, "ARKodeGetNumNonlinSolvConvFails", 1);
683 ($vec-ptr:(long int *diagMut))[7] = ncfn;
684
685 flag = ARKDlsGetNumJacEvals(arkode_mem, &nje);
686 check_flag(&flag, "ARKDlsGetNumJacEvals", 1);
687 ($vec-ptr:(long int *diagMut))[8] = ncfn;
688
689 flag = ARKDlsGetNumRhsEvals(arkode_mem, &nfeLS);
690 check_flag(&flag, "ARKDlsGetNumRhsEvals", 1);
691 ($vec-ptr:(long int *diagMut))[9] = ncfn;
692
693 /* Clean up and return */
694 N_VDestroy(y); /* Free y vector */
695 N_VDestroy(tv); /* Free tv vector */
696 ARKodeFree(&arkode_mem); /* Free integrator memory */
697 SUNLinSolFree(LS); /* Free linear solver */
698 SUNMatDestroy(A); /* Free A matrix */
699
700 return flag;
701 } |]
702 preD <- V.freeze diagMut
703 let d = SundialsDiagnostics (fromIntegral $ preD V.!0)
704 (fromIntegral $ preD V.!1)
705 (fromIntegral $ preD V.!2)
706 (fromIntegral $ preD V.!3)
707 (fromIntegral $ preD V.!4)
708 (fromIntegral $ preD V.!5)
709 (fromIntegral $ preD V.!6)
710 (fromIntegral $ preD V.!7)
711 (fromIntegral $ preD V.!8)
712 (fromIntegral $ preD V.!9)
713 m <- V.freeze qMatMut
714 if res == 0
715 then do
716 return $ Right (m, d)
717 else do
718 return $ Left (m, res)
719
720data ButcherTable = ButcherTable { am :: Matrix Double
721 , cv :: Vector Double
722 , bv :: Vector Double
723 , b2v :: Vector Double
724 }
725 deriving Show
726
727data ButcherTable' a = ButcherTable' { am' :: V.Vector a
728 , cv' :: V.Vector a
729 , bv' :: V.Vector a
730 , b2v' :: V.Vector a
731 }
732 deriving Show
733
734butcherTable :: ODEMethod -> ButcherTable
735butcherTable method =
736 case getBT method of
737 Left c -> error $ show c -- FIXME
738 Right (ButcherTable' v w x y, sqp) ->
739 ButcherTable { am = subMatrix (0, 0) (s, s) $ (arkSMax >< arkSMax) (V.toList v)
740 , cv = subVector 0 s w
741 , bv = subVector 0 s x
742 , b2v = subVector 0 s y
743 }
744 where
745 s = fromIntegral $ sqp V.! 0
746
747getBT :: ODEMethod -> Either Int (ButcherTable' Double, V.Vector Int)
748getBT method = case getButcherTable method of
749 Left c ->
750 Left $ fromIntegral c
751 Right (ButcherTable' a b c d, sqp) ->
752 Right $ ( ButcherTable' (coerce a) (coerce b) (coerce c) (coerce d)
753 , V.map fromIntegral sqp )
754
755getButcherTable :: ODEMethod
756 -> Either CInt (ButcherTable' CDouble, V.Vector CInt)
757getButcherTable method = unsafePerformIO $ do
758 -- ARKode seems to want an ODE in order to set and then get the
759 -- Butcher tableau so here's one to keep it happy
760 let funI :: CDouble -> V.Vector CDouble -> V.Vector CDouble
761 funI _t ys = V.fromList [ ys V.! 0 ]
762 let funE :: CDouble -> V.Vector CDouble -> V.Vector CDouble
763 funE _t ys = V.fromList [ ys V.! 0 ]
764 f0 = V.fromList [ 1.0 ]
765 ts = V.fromList [ 0.0 ]
766 dim = V.length f0
767 nEq :: CLong
768 nEq = fromIntegral dim
769 mN :: CInt
770 mN = fromIntegral $ getMethod method
771
772 btSQP :: V.Vector CInt <- createVector 3
773 btSQPMut <- V.thaw btSQP
774 btAs :: V.Vector CDouble <- createVector (arkSMax * arkSMax)
775 btAsMut <- V.thaw btAs
776 btCs :: V.Vector CDouble <- createVector arkSMax
777 btBs :: V.Vector CDouble <- createVector arkSMax
778 btB2s :: V.Vector CDouble <- createVector arkSMax
779 btCsMut <- V.thaw btCs
780 btBsMut <- V.thaw btBs
781 btB2sMut <- V.thaw btB2s
782 let funIOI :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt
783 funIOI x y f _ptr = do
784 fImm <- funI x <$> getDataFromContents dim y
785 putDataInContents fImm dim f
786 -- FIXME: I don't understand what this comment means
787 -- Unsafe since the function will be called many times.
788 [CU.exp| int{ 0 } |]
789 let funIOE :: CDouble -> Ptr T.SunVector -> Ptr T.SunVector -> Ptr () -> IO CInt
790 funIOE x y f _ptr = do
791 fImm <- funE x <$> getDataFromContents dim y
792 putDataInContents fImm dim f
793 -- FIXME: I don't understand what this comment means
794 -- Unsafe since the function will be called many times.
795 [CU.exp| int{ 0 } |]
796 res <- [C.block| int {
797 /* general problem variables */
798
799 int flag; /* reusable error-checking flag */
800 N_Vector y = NULL; /* empty vector for storing solution */
801 void *arkode_mem = NULL; /* empty ARKode memory structure */
802 int i, j; /* reusable loop indices */
803
804 /* general problem parameters */
805
806 realtype T0 = RCONST(($vec-ptr:(double *ts))[0]); /* initial time */
807 sunindextype NEQ = $(sunindextype nEq); /* number of dependent vars */
808
809 /* Initialize data structures */
810
811 y = N_VNew_Serial(NEQ); /* Create serial vector for solution */
812 if (check_flag((void *)y, "N_VNew_Serial", 0)) return 1;
813 /* Specify initial condition */
814 for (i = 0; i < NEQ; i++) {
815 NV_Ith_S(y,i) = ($vec-ptr:(double *f0))[i];
816 };
817 arkode_mem = ARKodeCreate(); /* Create the solver memory */
818 if (check_flag((void *)arkode_mem, "ARKodeCreate", 0)) return 1;
819
820 flag = ARKodeInit(arkode_mem, $fun:(int (* funIOE) (double t, SunVector y[], SunVector dydt[], void * params)), $fun:(int (* funIOI) (double t, SunVector y[], SunVector dydt[], void * params)), T0, y);
821 if (check_flag(&flag, "ARKodeInit", 1)) return 1;
822
823 if ($(int mN) >= MIN_DIRK_NUM) {
824 flag = ARKodeSetIRKTableNum(arkode_mem, $(int mN));
825 if (check_flag(&flag, "ARKodeSetIRKTableNum", 1)) return 1;
826 } else {
827 flag = ARKodeSetERKTableNum(arkode_mem, $(int mN));
828 if (check_flag(&flag, "ARKodeSetERKTableNum", 1)) return 1;
829 }
830
831 int s, q, p;
832 realtype *ai = (realtype *)malloc(ARK_S_MAX * ARK_S_MAX * sizeof(realtype));
833 realtype *ae = (realtype *)malloc(ARK_S_MAX * ARK_S_MAX * sizeof(realtype));
834 realtype *ci = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
835 realtype *ce = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
836 realtype *bi = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
837 realtype *be = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
838 realtype *b2i = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
839 realtype *b2e = (realtype *)malloc(ARK_S_MAX * sizeof(realtype));
840 flag = ARKodeGetCurrentButcherTables(arkode_mem, &s, &q, &p, ai, ae, ci, ce, bi, be, b2i, b2e);
841 if (check_flag(&flag, "ARKode", 1)) return 1;
842 $vec-ptr:(int *btSQPMut)[0] = s;
843 $vec-ptr:(int *btSQPMut)[1] = q;
844 $vec-ptr:(int *btSQPMut)[2] = p;
845 for (i = 0; i < s; i++) {
846 for (j = 0; j < s; j++) {
847 /* FIXME: double should be realtype */
848 ($vec-ptr:(double *btAsMut))[i * ARK_S_MAX + j] = ai[i * ARK_S_MAX + j];
849 }
850 }
851
852 for (i = 0; i < s; i++) {
853 ($vec-ptr:(double *btCsMut))[i] = ci[i];
854 ($vec-ptr:(double *btBsMut))[i] = bi[i];
855 ($vec-ptr:(double *btB2sMut))[i] = b2i[i];
856 }
857
858 /* Clean up and return */
859 N_VDestroy(y); /* Free y vector */
860 ARKodeFree(&arkode_mem); /* Free integrator memory */
861
862 return flag;
863 } |]
864 if res == 0
865 then do
866 x <- V.freeze btAsMut
867 y <- V.freeze btSQPMut
868 z <- V.freeze btCsMut
869 u <- V.freeze btBsMut
870 v <- V.freeze btB2sMut
871 return $ Right (ButcherTable' { am' = x, cv' = z, bv' = u, b2v' = v }, y)
872 else do
873 return $ Left res
874
875-- | Adaptive step-size control
876-- functions.
877--
878-- [GSL](https://www.gnu.org/software/gsl/doc/html/ode-initval.html#adaptive-step-size-control)
879-- allows the user to control the step size adjustment using
880-- \(D_i = \epsilon^{abs}s_i + \epsilon^{rel}(a_{y} |y_i| + a_{dy/dt} h |\dot{y}_i|)\) where
881-- \(\epsilon^{abs}\) is the required absolute error, \(\epsilon^{rel}\)
882-- is the required relative error, \(s_i\) is a vector of scaling
883-- factors, \(a_{y}\) is a scaling factor for the solution \(y\) and
884-- \(a_{dydt}\) is a scaling factor for the derivative of the solution \(dy/dt\).
885--
886-- [ARKode](https://computation.llnl.gov/projects/sundials/arkode)
887-- allows the user to control the step size adjustment using
888-- \(\eta^{rel}|y_i| + \eta^{abs}_i\). For compatibility with
889-- [hmatrix-gsl](https://hackage.haskell.org/package/hmatrix-gsl),
890-- tolerances for \(y\) and \(\dot{y}\) can be specified but the latter have no
891-- effect.
892data 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
893 | 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
894 | XX' Double Double Double Double -- ^ include both via relative tolerance
895 -- scaling factors \(a_y\), \(a_{{dy}/{dt}}\); in ARKode terms, the latter is ignored and \(\eta^{rel} = a_{y}\epsilon^{rel}\)
896 | 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 \(\eta^{rel} = a_{y}\epsilon^{rel}\)
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