-- |
-- Module : Simulation.Aivika.Internal.Specs
-- Copyright : Copyright (c) 2009-2017, David Sorokin
-- License : BSD3
-- Maintainer : David Sorokin
-- Stability : experimental
-- Tested with: GHC 8.0.1
--
-- It defines the simulation specs and related stuff.
module Simulation.Aivika.Internal.Specs
(Specs(..),
Method(..),
Run(..),
Point(..),
EventQueue(..),
newEventQueue,
basicTime,
integIterationBnds,
integIterationHiBnd,
integIterationLoBnd,
integPhaseBnds,
integPhaseHiBnd,
integPhaseLoBnd,
integTimes,
integPoints,
integPointsStartingFrom,
integStartPoint,
integStopPoint,
simulationStopPoint,
timeGrid,
pointAt,
delayPoint) where
import Data.IORef
import Simulation.Aivika.Generator
import qualified Simulation.Aivika.PriorityQueue as PQ
-- | It defines the simulation specs.
data Specs = Specs { spcStartTime :: Double, -- ^ the start time
spcStopTime :: Double, -- ^ the stop time
spcDT :: Double, -- ^ the integration time step
spcMethod :: Method, -- ^ the integration method
spcGeneratorType :: GeneratorType
-- ^ the type of the random number generator
}
-- | It defines the integration method.
data Method = Euler -- ^ Euler's method
| RungeKutta2 -- ^ the 2nd order Runge-Kutta method
| RungeKutta4 -- ^ the 4th order Runge-Kutta method
| RungeKutta4b -- ^ the 4th order Runge-Kutta 3/8-method
deriving (Eq, Ord, Show)
-- | It indentifies the simulation run.
data Run = Run { runSpecs :: Specs, -- ^ the simulation specs
runIndex :: Int, -- ^ the current simulation run index
runCount :: Int, -- ^ the total number of runs in this experiment
runEventQueue :: EventQueue, -- ^ the event queue
runGenerator :: Generator -- ^ the random number generator
}
-- | It defines the simulation point appended with the additional information.
data Point = Point { pointSpecs :: Specs, -- ^ the simulation specs
pointRun :: Run, -- ^ the simulation run
pointTime :: Double, -- ^ the current time
pointIteration :: Int, -- ^ the current iteration
pointPhase :: Int -- ^ the current phase
}
-- | It represents the event queue.
data EventQueue = EventQueue { queuePQ :: PQ.PriorityQueue (Point -> IO ()),
-- ^ the underlying priority queue
queueBusy :: IORef Bool,
-- ^ whether the queue is currently processing events
queueTime :: IORef Double
-- ^ the actual time of the event queue
}
-- | Create a new event queue by the specified specs.
newEventQueue :: Specs -> IO EventQueue
newEventQueue specs =
do f <- newIORef False
t <- newIORef $ spcStartTime specs
pq <- PQ.newQueue
return EventQueue { queuePQ = pq,
queueBusy = f,
queueTime = t }
-- | Returns the integration iterations starting from zero.
integIterations :: Specs -> [Int]
integIterations sc = [i1 .. i2] where
i1 = integIterationLoBnd sc
i2 = integIterationHiBnd sc
-- | Returns the first and last integration iterations.
integIterationBnds :: Specs -> (Int, Int)
integIterationBnds sc = (i1, i2) where
i1 = integIterationLoBnd sc
i2 = integIterationHiBnd sc
-- | Returns the first integration iteration, i.e. zero.
integIterationLoBnd :: Specs -> Int
integIterationLoBnd sc = 0
-- | Returns the last integration iteration.
integIterationHiBnd :: Specs -> Int
integIterationHiBnd sc =
let n = round ((spcStopTime sc -
spcStartTime sc) / spcDT sc)
in if n < 0
then
error $
"The iteration number in the stop time has a negative value. " ++
"Either the simulation specs are incorrect, " ++
"or a floating point overflow occurred, " ++
"for example, when using a too small integration time step. " ++
"You have to define this time step regardless of " ++
"whether you actually use it or not, " ++
"for Aivika allows combining the ordinary differential equations " ++
"with the discrete event simulation within one model. " ++
"So, if you are still using the 32-bit architecture and " ++
"you do need a small integration time step " ++
"for integrating the equations " ++
"then you might think of using the 64-bit architecture. " ++
"Although you could probably just forget " ++
"to increase the time step " ++
"after increasing the stop time: integIterationHiBnd"
else n
-- | Returns the phases for the specified simulation specs starting from zero.
integPhases :: Specs -> [Int]
integPhases sc =
case spcMethod sc of
Euler -> [0]
RungeKutta2 -> [0, 1]
RungeKutta4 -> [0, 1, 2, 3]
RungeKutta4b -> [0, 1, 2, 3]
-- | Returns the first and last integration phases.
integPhaseBnds :: Specs -> (Int, Int)
integPhaseBnds sc =
case spcMethod sc of
Euler -> (0, 0)
RungeKutta2 -> (0, 1)
RungeKutta4 -> (0, 3)
RungeKutta4b -> (0, 3)
-- | Returns the first integration phase, i.e. zero.
integPhaseLoBnd :: Specs -> Int
integPhaseLoBnd sc = 0
-- | Returns the last integration phase, 0 for Euler's method, 1 for RK2 and 3 for RK4.
integPhaseHiBnd :: Specs -> Int
integPhaseHiBnd sc =
case spcMethod sc of
Euler -> 0
RungeKutta2 -> 1
RungeKutta4 -> 3
RungeKutta4b -> 3
-- | Returns a simulation time for the integration point specified by
-- the specs, iteration and phase.
basicTime :: Specs -> Int -> Int -> Double
basicTime sc n ph =
if ph < 0 then
error "Incorrect phase: basicTime"
else
spcStartTime sc + n' * spcDT sc + delta (spcMethod sc) ph
where n' = fromIntegral n
delta Euler 0 = 0
delta RungeKutta2 0 = 0
delta RungeKutta2 1 = spcDT sc
delta RungeKutta4 0 = 0
delta RungeKutta4 1 = spcDT sc / 2
delta RungeKutta4 2 = spcDT sc / 2
delta RungeKutta4 3 = spcDT sc
delta RungeKutta4b 0 = 0
delta RungeKutta4b 1 = spcDT sc / 3
delta RungeKutta4b 2 = 2 * spcDT sc / 3
delta RungeKutta4b 3 = spcDT sc
-- | Return the integration time values.
integTimes :: Specs -> [Double]
integTimes sc = map t [nl .. nu]
where (nl, nu) = integIterationBnds sc
t n = basicTime sc n 0
-- | Return the integration time points.
integPoints :: Run -> [Point]
integPoints r = points
where sc = runSpecs r
(nl, nu) = integIterationBnds sc
points = map point [nl .. nu]
point n = Point { pointSpecs = sc,
pointRun = r,
pointTime = basicTime sc n 0,
pointIteration = n,
pointPhase = 0 }
-- | Return the start time point.
integStartPoint :: Run -> Point
integStartPoint r = point nl
where sc = runSpecs r
(nl, nu) = integIterationBnds sc
point n = Point { pointSpecs = sc,
pointRun = r,
pointTime = basicTime sc n 0,
pointIteration = n,
pointPhase = 0 }
-- | Return the integration stop time point.
integStopPoint :: Run -> Point
integStopPoint r = point nu
where sc = runSpecs r
(nl, nu) = integIterationBnds sc
point n = Point { pointSpecs = sc,
pointRun = r,
pointTime = basicTime sc n 0,
pointIteration = n,
pointPhase = 0 }
-- | Return the simulation stop time point.
simulationStopPoint :: Run -> Point
simulationStopPoint r = pointAt r (spcStopTime $ runSpecs r)
-- | Return the point at the specified time.
pointAt :: Run -> Double -> Point
pointAt r t = p
where sc = runSpecs r
t0 = spcStartTime sc
dt = spcDT sc
n = fromIntegral $ floor ((t - t0) / dt)
p = Point { pointSpecs = sc,
pointRun = r,
pointTime = t,
pointIteration = n,
pointPhase = -1 }
-- | Return the integration time points startin from the specified iteration.
integPointsStartingFrom :: Point -> [Point]
integPointsStartingFrom p = points
where r = pointRun p
sc = runSpecs r
(nl, nu) = integIterationBnds sc
n0 = if pointPhase p == 0
then pointIteration p
else pointIteration p + 1
points = map point [n0 .. nu]
point n = Point { pointSpecs = sc,
pointRun = r,
pointTime = basicTime sc n 0,
pointIteration = n,
pointPhase = 0 }
-- | Return the indexed time values in the grid by specified size.
timeGrid :: Specs -> Int -> [(Int, Double)]
timeGrid sc n =
let t0 = spcStartTime sc
t2 = spcStopTime sc
n' = max (n - 1) 1
dt = (t2 - t0) / (fromIntegral n')
f i | i == 0 = (i, t0)
| i == n' = (i, t2)
| otherwise = (i, t0 + (fromIntegral i) * dt)
in map f [0 .. n']
-- | Delay the point by the specified positive number of iterations.
delayPoint :: Point -> Int -> Point
delayPoint p dn
| dn <= 0 = error "Expected the positive number of iterations: delayPoint"
| otherwise =
let sc = pointSpecs p
n = pointIteration p
ph = pointPhase p
in if ph < 0
then let t' = pointTime p - fromIntegral dn * spcDT sc
n' = fromIntegral $ floor $ (t' - spcStartTime sc) / spcDT sc
in p { pointTime = t',
pointIteration = n',
pointPhase = -1 }
else let n' = n - dn
t' = basicTime sc n' ph
in p { pointTime = t',
pointIteration = n',
pointPhase = ph }