Integrate.hs

{-# OPTIONS_GHC -Wall #-}
{-# Language ScopedTypeVariables #-}
{-# Language TypeOperators #-}
{-# Language DeriveGeneric #-}
{-# Language FlexibleContexts #-}

module Dyno.DirectCollocation.Integrate
       ( withIntegrator
       ) where

import GHC.Generics ( Generic )

import qualified Control.Concurrent as CC
import Control.Monad ( void, forever )
import Data.Proxy ( Proxy(..) )
import Data.Vector ( Vector )
import qualified Data.Foldable as F
import Linear.V

import Casadi.MX ( MX )

import Dyno.SXElement ( SXElement, sxSplitJV, sxCatJV )
import Dyno.View.JV ( JV, splitJV, catJV )
import Dyno.View.Viewable ( Viewable )
import Dyno.View.View ( View(..), J, JNone, JTuple(..), jfill )
import Dyno.View.Fun ( SXFun, call, toSXFun, toMXFun, expandMXFun )
import Dyno.View.JVec ( JVec(..), jreplicate )
import Dyno.View.HList ( (:*:)(..) )
import qualified Dyno.View.M as M
import Dyno.Vectorize ( Vectorize(..), Id(..), vzipWith )
import Dyno.TypeVecs ( Vec )
import qualified Dyno.TypeVecs as TV
import Dyno.LagrangePolynomials ( lagrangeDerivCoeffs )
import Dyno.Solvers ( Solver )
import Dyno.NlpSolver ( runNlpSolver, liftIO, solve
                      , setX0, setLbg, setUbg, setP, setLbx, setUbx, getX )
import Dyno.DirectCollocation.Types ( CollStage(..), CollPoint(..) )
import Dyno.DirectCollocation.Quadratures ( QuadratureRoots, mkTaus, interpolate, timesFromTaus )



data IntegratorX x z n deg a =
  IntegratorX
  { ixStages :: J (JVec n (CollStage (JV x) (JV z) JNone deg)) a
  , ixXf :: J (JV x) a
  } deriving (Generic)
data IntegratorP u p n deg a =
  IntegratorP
  { ipTf :: J (JV Id) a
  , ipParm :: J (JV p) a
  , ipU :: J (JVec n (JVec deg (JV u))) a
  } deriving (Generic)
data IntegratorG x r n deg a =
 IntegratorG
 { igCollPoints :: J (JVec n (JVec deg (JV r))) a
 , igContinuity :: J (JVec n (JV x)) a
 } deriving (Generic)


instance (Vectorize x, Vectorize z, Dim n, Dim deg)
         => View (IntegratorX x z n deg)
instance (Vectorize u, Vectorize p, Dim n, Dim deg)
         => View (IntegratorP u p n deg)
instance (Vectorize x, Vectorize r, Dim n, Dim deg)
         => View (IntegratorG x r n deg)


-- todo: code duplication
dot :: forall x deg a b. (Fractional (J x a), Real b, Dim deg) => Vec deg b -> Vec deg (J x a) -> J x a
dot cks xs = F.sum $ TV.unVec elemwise
  where
    elemwise :: Vec deg (J x a)
    elemwise = TV.tvzipWith smul cks xs

    smul :: b -> J x a -> J x a
    smul x y = realToFrac x * y


-- todo: code duplication
interpolateXDots' :: (Real b, Fractional (J x a), Dim deg) => Vec deg (Vec deg b) -> Vec deg (J x a) -> Vec deg (J x a)
interpolateXDots' cjks xs = fmap (`dot` xs) cjks

interpolateXDots ::
  (Real b, Dim deg, Fractional (J x a)) =>
  Vec (TV.Succ deg) (Vec (TV.Succ deg) b)
  -> Vec (TV.Succ deg) (J x a)
  -> Vec deg (J x a)
interpolateXDots cjks xs = TV.tvtail $ interpolateXDots' cjks xs


-- return dynamics constraints, outputs, and interpolated state
dynStageConstraints' ::
  forall x z u p r deg . (Dim deg, View x, View z, View u, View p, View r)
  => Vec (TV.Succ deg) (Vec (TV.Succ deg) Double) -> Vec deg Double
  -> SXFun (J (JV Id) :*: J p :*: J x :*: J (CollPoint x z u)) (J r)
  -> (J x :*: J (JVec deg (JTuple x z)) :*: J (JVec deg u) :*: J (JV Id) :*: J p :*: J (JVec deg (JV Id))) MX
  -> (J (JVec deg r) :*: J x) MX
dynStageConstraints' cijs taus dynFun (x0 :*: xzs' :*: us' :*: h :*: p :*: stageTimes') =
  cat (JVec dynConstrs) :*: xnext
  where
    xzs = fmap split (unJVec (split xzs')) :: Vec deg (JTuple x z MX)
    us = unJVec (split us') :: Vec deg (J u MX)

    -- interpolated final state
    xnext :: J x MX
    xnext = interpolate taus x0 xs

    stageTimes = unJVec $ split stageTimes'

    -- dae constraints (dynamics)
    dynConstrs :: Vec deg (J r MX)
    dynConstrs = TV.tvzipWith4 applyDae xdots xzs us stageTimes

    applyDae :: J x MX -> JTuple x z MX -> J u MX -> J (JV Id) MX -> J r MX
    applyDae x' (JTuple x z) u t = r
      where
        r = call dynFun (t :*: p :*: x' :*: collPoint)
        collPoint = cat (CollPoint x z u)

    -- state derivatives, maybe these could be useful as outputs
    xdots :: Vec deg (J x MX)
    xdots = fmap (`M.vs` (1/h)) $ interpolateXDots cijs (x0 TV.<| xs)

    xs :: Vec deg (J x MX)
    xs = fmap (\(JTuple x _) -> x) xzs


-- dynamics residual and outputs
dynamicsFunction' ::
  forall x z u p r a . (View x, View z, View u, View r, Viewable a)
  => (J x a -> J x a -> J z a -> J u a -> J p a -> J (JV Id) a -> J r a)
  -> (J (JV Id) :*: J p :*: J x :*: J (CollPoint x z u)) a
  -> J r a
dynamicsFunction' dae (t :*: parm :*: x' :*: collPoint) = dae x' x z u parm t
  where
    CollPoint x z u = split collPoint

type Sxe = SXElement


withIntegrator ::
  forall x z u p r deg n b .
  (Dim n, Dim deg, Vectorize x, Vectorize p, Vectorize u, Vectorize z, Vectorize r)
  => Proxy (n, deg)
  -> QuadratureRoots
  -> x Double
  -> (x Sxe -> x Sxe -> z Sxe -> u Sxe -> p Sxe -> Sxe -> r Sxe)
  -> Solver
  -> ((x Double -> Either (u Double) (Vec n (Vec deg (u Double))) -> p Double -> Double -> IO (x Double)) -> IO b)
  -> IO b
withIntegrator _ roots initialX dae solver userFun = do
  let -- the collocation points
      taus :: Vec deg Double
      taus = mkTaus roots

      n = reflectDim (Proxy :: Proxy n)

      -- coefficients for getting xdot by lagrange interpolating polynomials
      cijs :: Vec (TV.Succ deg) (Vec (TV.Succ deg) Double)
      cijs = lagrangeDerivCoeffs (0 TV.<| taus)

  dynFun <- toSXFun "dynamics" $ dynamicsFunction' $
            \x0 x1 x2 x3 x4 x5 ->
            let r = dae (sxSplitJV x0) (sxSplitJV x1) (sxSplitJV x2) (sxSplitJV x3)
                    (sxSplitJV x4) (unId (sxSplitJV x5))
            in sxCatJV r

  dynStageConFun <- toMXFun "dynamicsStageCon" (dynStageConstraints' cijs taus dynFun)
--  let callDynStageConFun = call dynStageConFun
  callDynStageConFun <- fmap call (expandMXFun dynStageConFun)

  let fg :: J (IntegratorX x z n deg) MX
            -> J (IntegratorP u p n deg) MX
            -> (J (JV Id) MX, J (IntegratorG x r n deg) MX)
      fg = getFgIntegrator taus callDynStageConFun

      scaleX = Nothing
      scaleG = Nothing
--        , nlpScaleX' = Just $ cat $ fillCollTraj
--                       (fromMaybe (fill 1) (ocpXScale ocp))
--                       (fromMaybe (fill 1) (ocpZScale ocp))
--                       (fromMaybe (fill 1) (ocpUScale ocp))
--                       (fromMaybe (fill 1) (ocpPScale ocp))
--                       (fromMaybe       1  (ocpTScale ocp))
--
--        , nlpScaleG' = Just $ cat $ fillCollConstraints
--                       (fromMaybe (fill 1) (ocpXScale ocp))
--                       (fromMaybe (fill 1) (ocpResidualScale ocp))

  inputMVar <- CC.newEmptyMVar
  outputMVar <- CC.newEmptyMVar

  let toParams :: Either (u Double) (Vec n (Vec deg (u Double)))
                  -> p Double
                  -> Double
                  -> J (IntegratorP u p n deg) (Vector Double)
      toParams us p tf =
        cat $
        IntegratorP
        { ipTf = catJV (Id tf)
        , ipParm = catJV p
        , ipU = case us of
          Left u -> jreplicate (jreplicate (catJV u))
          Right us' -> cat $ JVec $ fmap (cat . JVec . fmap catJV) us'
        }

  let toBounds :: x Double -> J (IntegratorX x z n deg) (Vector (Maybe Double))
      toBounds x0 =
        cat $
        IntegratorX
        { ixStages = cat $ JVec $ TV.mkVec' $ take n $ xs0 : repeat (jfill Nothing)
        , ixXf = jfill Nothing
        }
        where
          xs0 :: J (CollStage (JV x) (JV z) JNone deg) (Vector (Maybe Double))
          xs0 = cat $ CollStage (catJV (fmap Just x0)) (jfill Nothing)

  let solverThread = do
        let initialX' :: J (JV x) (Vector Double)
            initialX' = catJV initialX

        setX0 $ cat $
          IntegratorX
          { ixStages = jreplicate $ cat $
                       CollStage initialX' $ jreplicate $ cat $ CollPoint initialX' (jfill 0) (jfill 0)
          , ixXf = initialX'
          }
        setLbg (jfill (Just 0))
        setUbg (jfill (Just 0))

        void $ forever $ do
          (x0, us, p, tf) <- liftIO $ CC.takeMVar inputMVar
          let bx = toBounds x0
--          liftIO $ putStrLn "\n\nsolving optimization problem"
--          liftIO $ printf "lnba, uba: %.3f, %.3f\n" lba uba
--          liftIO $ print (snd woo)

          setP (toParams us p tf)
          setLbx bx
          setUbx bx

          ret <- solve
          xtopt <- case ret of
            Left msg -> error $ "failed solving with error: \"" ++ msg ++ "\""
            Right _ -> getX
          setX0 xtopt

          liftIO $ CC.putMVar outputMVar (splitJV (ixXf (split xtopt)))

  _ <- CC.forkIO $ runNlpSolver solver fg scaleX scaleG Nothing Nothing solverThread

  let getNextValue :: x Double -> Either (u Double) (Vec n (Vec deg (u Double))) -> p Double -> Double -> IO (x Double)
      getNextValue x us p tf = do
        CC.putMVar inputMVar (x, us, p, tf)
        CC.takeMVar outputMVar
  userFun getNextValue


getFgIntegrator ::
  forall x z u p r n deg .
  (Dim deg, Dim n, Vectorize x, Vectorize z, Vectorize u, Vectorize p, Vectorize r)
  => Vec deg Double
  -> ((J (JV x) :*: J (JVec deg (JTuple (JV x) (JV z))) :*: J (JVec deg (JV u)) :*: J (JV Id) :*: J (JV p) :*: J (JVec deg (JV Id))) MX -> (J (JVec deg (JV r)) :*: J (JV x)) MX)
  -> J (IntegratorX x z n deg) MX
  -> J (IntegratorP u p n deg) MX
  -> (J (JV Id) MX, J (IntegratorG x r n deg) MX)
getFgIntegrator taus stageFun ix' ip' = (0, cat g)
  where
    ix = split ix'
    ip = split ip'

    xf = ixXf ix 
    tf = ipTf ip
    parm = ipParm ip
    stages = unJVec (split (ixStages ix)) :: Vec n (J (CollStage (JV x) (JV z) JNone deg) MX)

    spstages :: Vec n (CollStage (JV x) (JV z) JNone deg MX)
    spstages = fmap split stages

    us :: Vec n (J (JVec deg (JV u)) MX)
    us = unJVec $ split $ ipU ip

    -- timestep
    dt = tf / fromIntegral n
    n = reflectDim (Proxy :: Proxy n)

    -- times at each collocation point
    times :: Vec n (Vec deg (J (JV Id) MX))
    times = fmap snd $ timesFromTaus 0 (fmap realToFrac taus) dt

    times' :: Vec n (J (JVec deg (JV Id)) MX)
    times' = fmap (cat . JVec) times

    -- initial point at each stage
    x0s :: Vec n (J (JV x) MX)
    x0s = fmap (\(CollStage x0' _) -> x0') spstages

    -- final point at each stage (for matching constraint)
    xfs :: Vec n (J (JV x) MX)
    xfs = TV.tvshiftl x0s xf

    g = IntegratorG
        { igCollPoints = cat $ JVec dcs
        , igContinuity = cat $ JVec integratorMatchingConstraints
        }
    integratorMatchingConstraints :: Vec n (J (JV x) MX) -- todo: THIS SHOULD BE A NONLINEAR FUNCTION
    integratorMatchingConstraints = vzipWith (-) interpolatedXs xfs

    dcs :: Vec n (J (JVec deg (JV r)) MX)
    interpolatedXs :: Vec n (J (JV x) MX)
    (dcs, interpolatedXs) = TV.tvunzip $ TV.tvzipWith3 fff spstages us times'
    fff :: CollStage (JV x) (JV z) JNone deg MX
           -> J (JVec deg (JV u)) MX
           -> J (JVec deg (JV Id)) MX
           -> (J (JVec deg (JV r)) MX, J (JV x) MX)
    fff (CollStage x0' xzs') us' stageTimes = (dc, interpolatedX')
      where
        dc :*: interpolatedX' = stageFun (x0' :*: xzs :*: us' :*: dt :*: parm :*: stageTimes)

        xzs :: J (JVec deg (JTuple (JV x) (JV z))) MX
        xzs = cat $ JVec $ fmap toTuple $ unJVec $ split xzs'
        toTuple xzu = cat (JTuple x z)
          where
            CollPoint x z _ = split xzu