{-# LANGUAGE RecursiveDo #-} -- | -- Module : Simulation.Aivika.Trans.Dynamics.Extra -- Copyright : Copyright (c) 2009-2017, David Sorokin -- License : BSD3 -- Maintainer : David Sorokin -- Stability : experimental -- Tested with: GHC 8.0.1 -- -- This module defines auxiliary functions such as interpolation ones -- that complement the memoization, for example. There are scan functions too. -- module Simulation.Aivika.Trans.Dynamics.Extra (-- * Interpolation initDynamics, discreteDynamics, interpolateDynamics, -- * Scans scanDynamics, scan1Dynamics) where import Control.Monad.Fix import Simulation.Aivika.Trans.Comp import Simulation.Aivika.Trans.Internal.Specs import Simulation.Aivika.Trans.Internal.Simulation import Simulation.Aivika.Trans.Internal.Dynamics -- | Return the initial value. initDynamics :: Dynamics m a -> Dynamics m a {-# INLINE initDynamics #-} initDynamics (Dynamics m) = Dynamics \$ \p -> let sc = pointSpecs p in m \$ p { pointTime = basicTime sc 0 0, pointIteration = 0, pointPhase = 0 } -- | Discretize the computation in the integration time points. discreteDynamics :: Dynamics m a -> Dynamics m a {-# INLINE discreteDynamics #-} discreteDynamics (Dynamics m) = Dynamics \$ \p -> if pointPhase p == 0 then m p else let sc = pointSpecs p n = pointIteration p in m \$ p { pointTime = basicTime sc n 0, pointPhase = 0 } -- | Interpolate the computation based on the integration time points only. -- Unlike the 'discreteDynamics' function it knows about the intermediate -- time points that are used in the Runge-Kutta method. interpolateDynamics :: Dynamics m a -> Dynamics m a {-# INLINE interpolateDynamics #-} interpolateDynamics (Dynamics m) = Dynamics \$ \p -> if pointPhase p >= 0 then m p else let sc = pointSpecs p n = pointIteration p in m \$ p { pointTime = basicTime sc n 0, pointPhase = 0 } -- | Like the standard 'scanl1' function but applied to values in -- the integration time points. The accumulator values are transformed -- according to the second argument, which should be either function -- 'memo0Dynamics' or its unboxed version. scan1Dynamics :: MonadFix m => (a -> a -> a) -> (Dynamics m a -> Simulation m (Dynamics m a)) -> (Dynamics m a -> Simulation m (Dynamics m a)) {-# INLINABLE scan1Dynamics #-} scan1Dynamics f tr m = mdo y <- tr \$ Dynamics \$ \p -> case pointIteration p of 0 -> invokeDynamics p m n -> do let sc = pointSpecs p ty = basicTime sc (n - 1) 0 py = p { pointTime = ty, pointIteration = n - 1, pointPhase = 0 } s <- invokeDynamics py y x <- invokeDynamics p m return \$! f s x return y -- | Like the standard 'scanl' function but applied to values in -- the integration time points. The accumulator values are transformed -- according to the third argument, which should be either function -- 'memo0Dynamics' or its unboxed version. scanDynamics :: MonadFix m => (a -> b -> a) -> a -> (Dynamics m a -> Simulation m (Dynamics m a)) -> (Dynamics m b -> Simulation m (Dynamics m a)) {-# INLINABLE scanDynamics #-} scanDynamics f acc tr m = mdo y <- tr \$ Dynamics \$ \p -> case pointIteration p of 0 -> do x <- invokeDynamics p m return \$! f acc x n -> do let sc = pointSpecs p ty = basicTime sc (n - 1) 0 py = p { pointTime = ty, pointIteration = n - 1, pointPhase = 0 } s <- invokeDynamics py y x <- invokeDynamics p m return \$! f s x return y