hmatrix-sundials-0.19.1.0: src/Numeric/Sundials/CVode/ODE.hs
{-# 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.
--
-- <https://computation.llnl.gov/projects/sundials/sundials-software>
--
-- A simple example:
--
-- <<diagrams/brusselator.png#diagram=brusselator&height=400&width=500>>
--
-- @
-- 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 "<stdlib.h>"
C.include "<stdio.h>"
C.include "<math.h>"
C.include "<cvode/cvode.h>" -- prototypes for CVODE fcts., consts.
C.include "<nvector/nvector_serial.h>" -- serial N_Vector types, fcts., macros
C.include "<sunmatrix/sunmatrix_dense.h>" -- access to dense SUNMatrix
C.include "<sunlinsol/sunlinsol_dense.h>" -- access to dense SUNLinearSolver
C.include "<cvode/cvode_direct.h>" -- access to CVDls interface
C.include "<sundials/sundials_types.h>" -- definition of type realtype
C.include "<sundials/sundials_math.h>"
C.include "../../../helpers.h"
C.include "Numeric/Sundials/Arkode_hsc.h"
-- | Stepping functions
data ODEMethod = 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 \(\eta^{rel} = a_{y}\epsilon^{rel}\)