{-# OPTIONS_GHC -fno-warn-missing-methods #-}
{-# LANGUAGE MultiParamTypeClasses  #-}
{-# LANGUAGE UndecidableInstances   #-}
{-# LANGUAGE FlexibleInstances   #-}
{-# LANGUAGE DeriveDataTypeable   #-}
{-|
    Module      :  Data.Number.ER.RnToRm.Approx.Tuples
    Description :  a list of approximations over the same domain
    Copyright   :  (c) Michal Konecny
    License     :  BSD3

    Maintainer  :  mik@konecny.aow.cz
    Stability   :  experimental
    Portability :  portable

    Lists of function approximations over the same domain. 
-}
module Data.Number.ER.RnToRm.Approx.Tuple 
(
    ERFnTuple(..)
)
where

import qualified Data.Number.ER.RnToRm.Approx as FA 
import qualified Data.Number.ER.Real.Approx as RA
import qualified Data.Number.ER.Real.Approx.Elementary as RAEL
import qualified Data.Number.ER.Real.DomainBox as DBox
import Data.Number.ER.BasicTypes

import Data.Typeable
import Data.Generics.Basics
import Data.Binary


{-|
    A tuple of function approximations allowing one to get from 
    functions @R^n->R@ to a function @R^n -> R^m@.
-}
data ERFnTuple fa = 
    ERFnTuple { erfnTuple :: [fa] }
    deriving (Typeable, Data)
    
instance (Binary a) => Binary (ERFnTuple a) where
  put (ERFnTuple a) = put a
  get = get >>= \a -> return (ERFnTuple a)

tuplesLift1 ::
    (fa -> fa) ->
    (ERFnTuple fa) -> (ERFnTuple fa)
tuplesLift1 op (ERFnTuple fas) =    
    ERFnTuple (map op fas)
        
tuplesLift2 ::
    (Show fa) =>
    String ->
    (fa -> fa -> fa) ->
    (ERFnTuple fa) -> (ERFnTuple fa) -> (ERFnTuple fa)
tuplesLift2 callerLocation op f1@(ERFnTuple fas1) f2@(ERFnTuple fas2) 
        | length fas1 == length fas2 =
            ERFnTuple $ zipWith op fas1 fas2
        | otherwise =
            error $ 
                callerLocation ++ "incompatible lengths: " 
                ++ show (length fas1) ++ " != " ++ show (length fas2)
                ++ "\n first argument = \n" ++ show fas1
                ++ "\n second argument = \n" ++ show fas2

tuplesSplit ::
    (fa -> (fa, fa)) ->
    (ERFnTuple fa) -> (ERFnTuple fa, ERFnTuple fa)
tuplesSplit op f@(ERFnTuple fas) = 
    (ERFnTuple fas1, ERFnTuple fas2)
    where
    (fas1, fas2) = unzip $ map op fas

-- version with Map.Map:
--data ERFnTuple fa = 
--    ERFnTuple (Map.Map varid fa)
--    deriving (Typeable, Data)
--    
--tuplesLift1 ::
--    (fa -> fa) ->
--    (ERFnTuple fa) -> (ERFnTuple fa)
--tuplesLift1 op (ERFnTuple fas) =    
--    ERFnTuple (Map.map op fas)
--        
--tuplesLift2 ::
--    (fa -> fa -> fa) ->
--    (ERFnTuple fa) -> (ERFnTuple fa) -> (ERFnTuple fa)
--tuplesLift2 op f1@(ERFnTuple fas1) f2@(ERFnTuple fas2) 
--        | Map.keys fas1 == Map.keys fas2 =
--            ERFnTuple $ Map.intersectionWith op fas1 fas2
--        | otherwise =
--            error $ 
--                "ERFnTuple: incompatible keys: " 
--                ++ show (Map.keys fas1) ++ "\n*****\n" ++ show (Map.keys fas2)
--
--tuplesSplit ::
--    (fa -> (fa, fa)) ->
--    (ERFnTuple fa) -> (ERFnTuple fa, ERFnTuple fa)
--tuplesSplit op f@(ERFnTuple fas) = 
--    (ERFnTuple fas1, ERFnTuple fas2)
--    where
--    fas1 = Map.map fst fas12 
--    fas2 = Map.map snd fas12
--    fas12 = Map.map op fas
    
    
instance 
    (FA.ERFnDomApprox box varid domra ranra fa) =>
    Show (ERFnTuple fa)
    where
    show f@(ERFnTuple fas) =
        concat $ map showFA $ zip [0,1..] fas
        where
        showFA (fnname, fa) =
            "\n>>> Function " ++ show fnname ++ ":" ++ show fa

instance
    (FA.ERFnApprox box varid domra ranra fa) =>
    Eq (ERFnTuple fa)
    where
    (ERFnTuple fas1) == (ERFnTuple fas2) =
        fas1 == fas2

instance
    (FA.ERFnApprox box varid domra ranra fa, Ord fa) =>
    Ord (ERFnTuple fa)
    where
    compare (ERFnTuple fas1) (ERFnTuple fas2) =
        compare fas1 fas2

instance
    (FA.ERFnDomApprox box varid domra ranra fa) =>
    Num (ERFnTuple fa)
    where
    fromInteger n = ERFnTuple [fromInteger n]
    negate = tuplesLift1 negate
    (+) = tuplesLift2 "ERFnTuple: +: " (+)
    (*) = tuplesLift2 "ERFnTuple: *: " (*)

instance 
    (FA.ERFnDomApprox box varid domra ranra fa) =>
    Fractional (ERFnTuple fa)
    where
    fromRational r = ERFnTuple [fromRational r]
    recip = tuplesLift1 recip 


instance 
    (FA.ERFnDomApprox box varid domra ranra fa) =>
    RA.ERApprox (ERFnTuple fa)
    where
    getGranularity (ERFnTuple fas) =
        foldl max 10 $ map RA.getGranularity fas
    setGranularity gran = tuplesLift1 (RA.setGranularity gran) 
    setMinGranularity gran = tuplesLift1 (RA.setMinGranularity gran)
    f1 /\ f2 = tuplesLift2 "ERFnTuple: /\\: " (RA./\) f1 f2
    intersectMeasureImprovement ix f1@(ERFnTuple fas1) f2@(ERFnTuple fas2)
        | length fas1 == length fas2 =
            (ERFnTuple fasIsect, ERFnTuple fasImpr)
        | otherwise =
            error $ show $ f1 RA./\ f2 
        where
        (fasIsect, fasImpr) = unzip $ zipWith (RA.intersectMeasureImprovement ix) fas1 fas2 
    leqReals f1@(ERFnTuple fas1) f2@(ERFnTuple fas2)
        | length fas1 == length fas2 =
            leqTuple $ zipWith RA.leqReals fas1 fas2
        | otherwise =
            error $ show $ f1 RA./\ f2
        where
        leqTuple [] = Just True
        leqTuple _ = 
            error $ "ERFnTuple: leqReals not implemented" 

instance 
    (FA.ERFnDomApprox box varid domra ranra fa, RA.ERIntApprox fa) =>
    RA.ERIntApprox (ERFnTuple fa)
    where
--    doubleBounds = :: ira -> (Double, Double) 
--    floatBounds :: ira -> (Float, Float)
--    integerBounds :: ira -> (ExtendedInteger, ExtendedInteger)
    bisectDomain maybePt f@(ERFnTuple fas) =
        case maybePt of
            Nothing ->
                tuplesSplit (RA.bisectDomain Nothing) f
            Just (ERFnTuple fasPt) -> 
                (ERFnTuple fas1, ERFnTuple fas2)
                where
                (fas1, fas2) = 
                    unzip $ 
                        map (\(fa, pt) -> RA.bisectDomain (Just pt) fa) $ 
                            zip fas fasPt
    bounds = tuplesSplit RA.bounds
    f1 \/ f2 = tuplesLift2 "ERFnTuple: \\/: " (RA.\/) f1 f2

instance 
    (FA.ERFnDomApprox box varid domra ranra fa, RAEL.ERApproxElementary fa) =>
    RAEL.ERApproxElementary (ERFnTuple fa)
    where
    abs ix = tuplesLift1 $ RAEL.abs ix
    exp ix = tuplesLift1 $ RAEL.exp ix
    log ix = tuplesLift1 $ RAEL.log ix
    sin ix = tuplesLift1 $ RAEL.sin ix
    cos ix = tuplesLift1 $ RAEL.cos ix
    atan ix = tuplesLift1 $ RAEL.atan ix
        
instance 
    (FA.ERFnDomApprox box varid domra ranra fa) =>
    FA.ERFnApprox box varid domra ranra (ERFnTuple fa)
    where
    check prgLocation (ERFnTuple fs) =
        ERFnTuple $ map checkComp $ zip [0..] fs
        where
        checkComp (n, f) =
            FA.check (prgLocation ++ "fn" ++ show n ++ ": ") f
    domra2ranra (ERFnTuple (fa:_)) d =
        FA.domra2ranra fa d
    ranra2domra (ERFnTuple (fa:_)) r =
        FA.ranra2domra fa r
    setMaxDegree maxDegree = tuplesLift1 (FA.setMaxDegree maxDegree)
    getTupleSize (ERFnTuple fas) = length fas
    tuple fs 
        | sameDomains doms = 
            ERFnTuple $ concat $ map erfnTuple fs
        | otherwise = 
            error $ 
                "ERFnTuple: FA.tuple: incompatible domains:\n " 
                ++ (unlines $ map show fs)
        where
        sameDomains [_] = True
        sameDomains (a : rest@(b : _)) =
            sameab && (sameDomains rest)
            where
            sameab =
                and $ map snd $ DBox.zipWithDefault RA.bottomApprox RA.equalApprox a b
        doms = map FA.dom fs
    applyTupleFn tupleFn (ERFnTuple fs) =
        FA.tuple $ tupleFn $ map (\fa -> ERFnTuple [fa]) fs
    volume (ERFnTuple fas) = sum $ map (FA.volume) fas
    scale ratio = tuplesLift1 (FA.scale ratio)
    partialIntersect ix substitutions =
        tuplesLift2 "ERFnTuple: partialIntersect: " $ FA.partialIntersect ix substitutions
    eval ptBox (ERFnTuple fas) =
        concat $ map (FA.eval ptBox) fas
    partialEval substitutions = tuplesLift1 $ FA.partialEval substitutions
            
instance 
    (FA.ERFnDomApprox box varid domra ranra fa) =>
    FA.ERFnDomApprox box varid domra ranra (ERFnTuple fa)
    where
    dom (ERFnTuple (fa:_)) = FA.dom fa
    bottomApprox domB tupleSize =
        ERFnTuple $ replicate tupleSize $ FA.bottomApprox domB 1
    const domB vals =
        ERFnTuple $ map (\v -> FA.const domB [v]) vals
    proj domB i =
        ERFnTuple [FA.proj domB i] 

    bisect var maybePt =
        tuplesSplit $ FA.bisect var maybePt
    integrate ix (ERFnTuple fasD) x integdomBox origin (ERFnTuple fasInit) =
        ERFnTuple $ map integ $ zip fasD fasInit
        where
        integ (faD, faInit) =
            FA.integrate ix faD x integdomBox origin faInit
    integrateMeasureImprovement ix (ERFnTuple fasD) x integdomBox origin (ERFnTuple fasP) =
        (ERFnTuple fasIsect, ERFnTuple fasImpr) 
        where
        (fasIsect, fasImpr) =
            unzip $ map integ $ zip fasD fasP
        integ (faD, faP) =
            FA.integrateMeasureImprovement ix faD x integdomBox origin faP