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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Data/LinearMap/HerMetric.hs b/Data/LinearMap/HerMetric.hs new file mode 100644 --- /dev/null +++ b/Data/LinearMap/HerMetric.hs @@ -0,0 +1,86 @@ +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE StandaloneDeriving #-} +{-# LANGUAGE ConstraintKinds #-} + + + + +module Data.LinearMap.HerMetric ( + HasMetric(..) + , (^<.>) + , HerMetric + , projector + , metricSq, metric, metrics + , metriScale + ) where + + + + +import Data.VectorSpace +import Data.LinearMap +import Data.Basis +import Data.MemoTrie + + +import Diagrams.Prelude + + +infixr 7 <.>^, ^<.> + +class ( HasBasis v, RealFloat (Scalar v), HasTrie (Basis v) + , VectorSpace (DualSpace v), HasBasis (DualSpace v) + , Scalar v ~ Scalar (DualSpace v), Basis v ~ Basis (DualSpace v) ) + => HasMetric v where + type DualSpace v :: * + type DualSpace v = v + (<.>^) :: DualSpace v -> v -> Scalar v + + +(^<.>) :: HasMetric v => v -> DualSpace v -> Scalar v +ket ^<.> bra = bra <.>^ ket + +instance HasMetric Double where + (<.>^) = (<.>) +instance (HasMetric v, HasMetric w, Scalar v ~ Scalar w) => HasMetric (v,w) where + type DualSpace (v,w) = (DualSpace v, DualSpace w) + (v,w)<.>^(v',w') = v<.>^v' + w<.>^w' +instance HasMetric R2 where + (<.>^) = (<.>) + + +-- | 'HerMetric' is a portmanteau of /Hermitian/ and /metric/ (in the sense as used +-- in e.g. general relativity). +newtype HerMetric v = HerMetric { getHerMetric :: DualSpace v :-* v } + +instance HasMetric v => AdditiveGroup (HerMetric v) where + zeroV = HerMetric zeroV + negateV (HerMetric m) = HerMetric $ negateV m + HerMetric m ^+^ HerMetric n = HerMetric $ m ^+^ n +instance HasMetric v => VectorSpace (HerMetric v) where + type Scalar (HerMetric v) = Scalar v + s *^ (HerMetric m) = HerMetric $ s *^ m + +projector :: HasMetric v => v -> HerMetric v +projector v = HerMetric (linear $ \u -> v ^* (v^<.>u)) + + +metricSq, metric :: HasMetric v => HerMetric v -> DualSpace v -> Scalar v +metricSq (HerMetric m) v = v <.>^ lapply m v +metric (HerMetric m) v = sqrt $ v <.>^ lapply m v + + +metriScale :: HasMetric v => HerMetric v -> DualSpace v -> DualSpace v +metriScale m v = metric m v *^ v + + +metrics :: HasMetric v => HerMetric v -> [DualSpace v] -> Scalar v +metrics m vs = sqrt . sum $ metricSq m <$> vs + + + + diff --git a/Graphics/Dynamic/Plot/Colour.hs b/Graphics/Dynamic/Plot/Colour.hs new file mode 100644 --- /dev/null +++ b/Graphics/Dynamic/Plot/Colour.hs @@ -0,0 +1,84 @@ +-- | +-- Module : Graphics.Dynamic.Plot.Colour +-- Copyright : (c) Justus Sagemüller 2013 +-- License : GPL v3 +-- +-- Maintainer : (@) sagemuej $ smail.uni-koeln.de +-- Stability : experimental +-- Portability : requires GHC>6 extensions + +module Graphics.Dynamic.Plot.Colour where + + +import qualified Data.Colour as DCol +import Data.Colour (opaque) +import qualified Data.Colour.Names as N +import Data.Colour.CIE hiding (Colour) +import qualified Data.Colour.CIE.Illuminant as Illum + + +type FColour = DCol.Colour Double +type AColour = DCol.AlphaColour Double + +-- | Unlike the typical types such as 'Draw.Color', this one has /semantic/ +-- more than physical meaning. +data Colour = BaseColour BaseColour + | Contrast BaseColour + | Paler Colour + | CustomColour FColour + deriving (Eq) +data BaseColour = Neutral -- ^ Either black or white, depending on the context. + | Red -- ^ Contrast cyan. + | Yellow -- ^ Contrast violet. + | Green -- ^ Contrast magenta. + | Blue -- ^ Contrast orange. + deriving (Eq, Show, Enum) + + +neutral, contrast, grey + , magenta, red, orange, yellow, green, cyan, blue, violet :: Colour +neutral = BaseColour Neutral +contrast= Contrast Neutral +grey = paler contrast +magenta = Contrast Green +red = BaseColour Red +orange = Contrast Blue +yellow = BaseColour Yellow +green = BaseColour Green +cyan = Contrast Red +blue = BaseColour Blue +violet = Contrast Yellow + +paler, opposite :: Colour -> Colour +paler = Paler +opposite (BaseColour c) = Contrast c +opposite (Contrast c) = BaseColour c +opposite (Paler c) = Paler $ opposite c +opposite (CustomColour c) = CustomColour $ hueInvert c + +type ColourScheme = Colour -> AColour + +defaultColourScheme :: ColourScheme +defaultColourScheme (BaseColour Neutral) = opaque N.black +defaultColourScheme (BaseColour Red ) = opaque N.red +defaultColourScheme (BaseColour Yellow ) = opaque N.yellow +defaultColourScheme (BaseColour Green ) = opaque N.green +defaultColourScheme (BaseColour Blue ) = opaque N.blue +defaultColourScheme (Contrast Neutral) = opaque N.white +defaultColourScheme (Contrast Red ) = opaque N.cyan +defaultColourScheme (Contrast Yellow ) = opaque N.violet +defaultColourScheme (Contrast Green ) = opaque N.magenta +defaultColourScheme (Contrast Blue ) = opaque N.orange +defaultColourScheme (Paler c) = DCol.dissolve 0.5 $ defaultColourScheme c +defaultColourScheme (CustomColour c) = opaque c + + +defaultColourSeq :: [Colour] +defaultColourSeq = cycle [blue, red, green, orange, cyan, magenta, yellow, violet] + + + +hueInvert :: FColour -> FColour +hueInvert c = let (l,a,b) = cieLABView i c + in cieLAB i l (1-a) (1-b) + where i = Illum.a diff --git a/Graphics/Dynamic/Plot/R2.hs b/Graphics/Dynamic/Plot/R2.hs new file mode 100644 --- /dev/null +++ b/Graphics/Dynamic/Plot/R2.hs @@ -0,0 +1,1297 @@ +-- | +-- Module : Graphics.Dynamic.Plot.R2 +-- Copyright : (c) Justus Sagemüller 2013-2014 +-- License : GPL v3 +-- +-- Maintainer : (@) sagemueller $ geo.uni-koeln.de +-- Stability : experimental +-- Portability : requires GHC>6 extensions + + +{-# LANGUAGE NoMonomorphismRestriction #-} +{-# LANGUAGE GADTs #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# LANGUAGE RecordWildCards #-} +{-# LANGUAGE TupleSections #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE GeneralizedNewtypeDeriving #-} +{-# LANGUAGE DeriveFunctor #-} +{-# LANGUAGE StandaloneDeriving #-} + +module Graphics.Dynamic.Plot.R2 ( + -- * Interactive display + plotWindow + -- * Plottable objects + -- ** Class + , Plottable(..) + -- ** Simple function plots + , fnPlot, paramPlot + , continFnPlot + , tracePlot + -- ** View selection + , xInterval, yInterval + -- ** Plot type + , DynamicPlottable + ) where + +import Graphics.Dynamic.Plot.Colour + + + +import qualified Prelude + +-- import Graphics.DrawingCombinators ((%%), R, R2) +-- import qualified Graphics.DrawingCombinators as Draw +-- import qualified Graphics.UI.GLFW as GLFW +-- import qualified Graphics.Rendering.OpenGL as OpenGL +-- import Graphics.Rendering.OpenGL (($=)) +import Diagrams.Prelude (R2, P2, (^&), (&), _x, _y) +import qualified Diagrams.Prelude as Dia +import qualified Diagrams.TwoD.Size as Dia +import qualified Diagrams.TwoD.Types as DiaTypes +import Diagrams.BoundingBox (BoundingBox) +import qualified Diagrams.BoundingBox as DiaBB +import qualified Diagrams.Backend.Cairo as Cairo +import qualified Diagrams.Backend.Cairo.Text as CairoTxt + +import qualified Data.Colour as DCol + +import qualified Diagrams.Backend.Gtk as BGTK +import qualified Graphics.UI.Gtk as GTK +import Graphics.UI.Gtk ( AttrOp((:=)) ) +import qualified Graphics.UI.Gtk.Gdk.EventM as Event +import qualified System.Glib.Signals (on) + +import Control.Monad.Trans (liftIO) + +import qualified Control.Category.Hask as Hask +import Control.Category.Constrained.Prelude hiding ((^)) +import Control.Arrow.Constrained +import Control.Monad.Constrained + +import Control.Lens hiding ((...)) + + +import Control.Concurrent.Async +import Control.DeepSeq + + +import Data.List (foldl', sort, intercalate, isPrefixOf, isInfixOf, find, zip4) +import qualified Data.Vector as Arr +import Data.Maybe +import Data.Semigroup +import Data.Foldable (fold, foldMap) +import Data.Function (on) + +import Data.VectorSpace +import Data.AffineSpace +import Data.LinearMap.HerMetric +import qualified Data.Map.Lazy as Map + +import Data.Manifold ((:-->)) +import qualified Data.Manifold as 𝓒⁰ + +import Text.Printf + +import Data.IORef + +import System.IO +import System.Exit +import System.Process +import Data.Time + + + +(^) :: Num n => n -> Int -> n +(^) = (Prelude.^) + + +type R = Double + +type Diagram = Dia.Diagram Cairo.B R2 + + + + +class Plottable p where + plot :: p -> DynamicPlottable + +instance (RealFloat r₁, RealFloat r₂) => Plottable (r₁ -> r₂) where + plot f = continFnPlot $ realToFrac . f . realToFrac + +-- {-# RULES "plot/R->R" plot = fnPlot #-} + +instance Plottable (Double :--> Double) where + plot f = DynamicPlottable{ + relevantRange_x = const mempty + , relevantRange_y = fmap yRangef + , isTintableMonochromic = True + , axesNecessity = 1 + , dynamicPlot = plot } + where yRangef (Interval l r) = uncurry Interval . (minimum &&& maximum) + . map snd $ 𝓒⁰.finiteGraphContinℝtoℝ + (𝓒⁰.GraphWindowSpec l r fgb fgt 9 9) f + where (fgb, fgt) = (minimum &&& maximum) [f $ l, f $ m, f $ r] + m = l + (r-l) * 0.352479608143 + + plot (GraphWindowSpec{..}) = curve `deepseq` Plot [] (trace curve) + where curve :: [Dia.P2] + curve = map convℝ² $ 𝓒⁰.finiteGraphContinℝtoℝ mWindow f + mWindow = 𝓒⁰.GraphWindowSpec (c lBound) (c rBound) (c bBound) (c tBound) + xResolution yResolution + trace (p:q:ps) = simpleLine p q <> trace (q:ps) + trace _ = mempty + + convℝ² = Dia.p2 + c = realToFrac + +instance Plottable (Double :--> (Double, Double)) where + plot f = DynamicPlottable{ + relevantRange_x = const mempty + , relevantRange_y = const mempty + , isTintableMonochromic = True + , axesNecessity = 1 + , dynamicPlot = plot } + where plot (GraphWindowSpec{..}) = curves `deepseq` Plot [] (foldMap trace curves) + where curves :: [[Dia.P2]] + curves = map (map convℝ²) $ 𝓒⁰.finiteGraphContinℝtoℝ² mWindow f + mWindow = 𝓒⁰.GraphWindowSpec (c lBound) (c rBound) (c bBound) (c tBound) + xResolution yResolution + trace (p:q:ps) = simpleLine p q <> trace (q:ps) + trace _ = mempty + + convℝ² = Dia.p2 + c = realToFrac + + +instance (Plottable p) => Plottable [p] where + plot l0 = DynamicPlottable{ + relevantRange_x = \ry -> foldMap (($ry) . relevantRange_x) l + , relevantRange_y = \rx -> foldMap (($rx) . relevantRange_y) l + , isTintableMonochromic = or $ isTintableMonochromic <$> l + , axesNecessity = sum $ axesNecessity <$> l + , dynamicPlot = foldMap dynamicPlot l + } + where l = map plot l0 + +instance Plottable Diagram where + plot d = DynamicPlottable{ + relevantRange_x = const $ Option rlx + , relevantRange_y = const $ Option rly + , isTintableMonochromic = False + , axesNecessity = -1 + , dynamicPlot = plot + } + where bb = DiaBB.boundingBox d + (rlx,rly) = case DiaBB.getCorners bb of + Just (c1, c2) + -> ( Just $ c1^._x ... c2^._x + , Just $ c1^._y ... c2^._y ) + plot _ = Plot [] d + + + + + +data Pair p = Pair !p !p + deriving (Hask.Functor, Show, Eq, Ord) +data Triple p = Triple !p !p !p + deriving (Hask.Functor, Show, Eq, Ord) + +data DiffList a = DiffList { getDiffList :: [a]->[a], diffListLen :: Int } +diffList :: Arr.Vector a -> DiffList a +diffList l = DiffList (Arr.toList l++) (Arr.length l) + +instance Semigroup (DiffList a) where + DiffList dl n <> DiffList dl' n' = DiffList (dl . dl') (n+n') +instance Monoid (DiffList a) where + mappend = (<>); mempty = DiffList id 0 + + +newtype SplitList a = SplitList { getSplList :: Arr.Vector a } + deriving (Hask.Functor, Monoid) +presplitList :: [a] -> SplitList a +presplitList = SplitList . Arr.fromList + +splitEvenly :: Int -> SplitList a -> Either (Arr.Vector a) [SplitList a] +splitEvenly k _ | k < 1 = error "Can't split a list to less than one part." +splitEvenly k (SplitList v) + | k >= n = Left v + | otherwise = Right $ splits splitIs 0 + where splitIs = take k . map round . tail + $ iterate (+ (fromIntegral n/fromIntegral k :: Double)) 0 + splits [_] i₀ = [SplitList $ Arr.drop i₀ v] + splits (i:is) i₀ = SplitList (Arr.slice i₀ (i-i₀) v) : splits is i + n = Arr.length v + +instance Semigroup (SplitList a) where + SplitList l <> SplitList l' = SplitList (l Arr.++ l') + +fromDiffList :: DiffList a -> SplitList a +fromDiffList (DiffList f _) = SplitList . Arr.fromList $ f[] + + + + +data LinFitParams y = LinFitParams { constCoeff :: y + , linCoeff :: Diff y } +deriving instance (AffineSpace y, Show y, Show (Diff y)) => Show (LinFitParams y) + + +linFitMeanInCtrdUnitIntv :: + (AffineSpace y, v~Diff y, VectorSpace v, Fractional (Scalar v)) + => LinFitParams y -> y +linFitMeanInCtrdUnitIntv (LinFitParams{..}) = constCoeff + + + +data DevBoxes y = DevBoxes { deviations :: HerMetric (Diff y) + , maxDeviation :: Scalar (Diff y) } + + + + + +data PCMRange x = PCMRange { pcmStart, pcmSampleDuration :: x } deriving (Show) + +data RecursiveSamples' n x y t + = RecursivePCM { rPCMlinFit :: LinFitParams y + , details :: Either (Pair (RecursiveSamples' n x y t)) + (Arr.Vector (y,t)) + , pFitDeviations :: DevBoxes y + , samplingSpec :: PCMRange x + , splIdLen :: Int + , rPCMNodeInfo :: n + } +instance Hask.Functor (RecursiveSamples' n x y) where + fmap f (RecursivePCM l d v s n i) = RecursivePCM l d' v s n i + where d' = case d of Left rs' -> Left (fmap (fmap f) rs') + Right ps -> Right $ fmap (second f) ps + +fmapRPCMNodeInfo :: (n->n') -> RecursivePCM n x y -> RecursivePCM n' x y +fmapRPCMNodeInfo f (RecursivePCM l d v s n i) = RecursivePCM l d' v s n $ f i + where d' = case d of Left rs' -> Left (fmap (fmapRPCMNodeInfo f) rs') + Right ps -> Right ps + +type RecursiveSamples = RecursiveSamples' () +type RecursivePCM n x y = RecursiveSamples' n x y () +type (x-.^>y) = RecursivePCM () x y + +recursiveSamples' :: forall x y v t . + ( VectorSpace x, Real (Scalar x) + , AffineSpace y, v~Diff y, InnerSpace v, HasMetric v, RealFloat (Scalar v) ) + => PCMRange x -> [(y,t)] -> RecursiveSamples x y t +recursiveSamples' xrng_g ys = calcDeviations . go xrng_g $ presplitList ys + where go :: PCMRange x -> SplitList (y,t) -> RecursiveSamples' (Arr.Vector y) x y t + go xrng@(PCMRange xl wsp) l@(SplitList arr) = case splitEvenly 2 l of + Right sps + | [sp1, sp2] <- lIndThru xl sps + -> let pFit = solveToLinFit + $ (linFitMeanInCtrdUnitIntv.rPCMlinFit) <$> [sp1,sp2] + in RecursivePCM pFit + (Left $ Pair sp1 sp2) + (undefined) + xrng (Arr.length arr) + (fmap fst arr) + Right _ -> evenSplitErr + Left pSpls -> RecursivePCM (solveToLinFit $ Arr.toList (fmap fst pSpls)) + (Right $ pSpls) + (undefined) + xrng (Arr.length arr) + (fmap fst arr) + where lIndThru _ [] = [] + lIndThru x₀₁ (sp₁@(SplitList arr₁):sps) + = let x₀₂ = x₀₁ ^+^ fromIntegral (Arr.length arr₁) *^ wsp + in go (PCMRange x₀₁ wsp) sp₁ : lIndThru x₀₂ sps + evenSplitErr = error "'splitEvenly' returned wrong number of slices." + + calcDeviations :: RecursiveSamples' (Arr.Vector y) x y t + -> RecursiveSamples x y t + calcDeviations = cdvs Nothing Nothing + where cdvs lPFits rPFits + rPCM@( RecursivePCM pFit dtls _ sSpc@(PCMRange xl wsp) slLn pts ) + = RecursivePCM pFit dtls' (DevBoxes stdDev maxDev) sSpc slLn () + where stdDev = (^/ fromIntegral slLn) . sumV $ projector <$> msqs + maxDev = sqrt . maximum $ magnitudeSq <$> msqs + msqs = [ (y .-. ff x) + | (x,y) <- normlsdIdd $ SplitList pts ] + ff = l₀splineRep (Pair lPFits rPFits) rPCM + dtls' = case dtls of + Left (Pair r₁ r₂) + -> let r₁' = cdvs (rRoute=< Right pSpls + (LinFitParams b a) = pFit +lRoute, rRoute :: RecursiveSamples' n x y t -> Maybe (RecursiveSamples' n x y t) +lRoute (RecursivePCM {details = Right _}) = Nothing +lRoute (RecursivePCM {details = Left (Pair l _)}) = Just l +rRoute (RecursivePCM {details = Right _}) = Nothing +rRoute (RecursivePCM {details = Left (Pair _ r)}) = Just r + + +recursiveSamples :: + ( AffineSpace y, v~Diff y, InnerSpace v, HasMetric v, RealFloat (Scalar v) ) + => [(y,t)] -> RecursiveSamples Int y t +recursiveSamples = recursiveSamples' (PCMRange 0 1) + +recursivePCM :: ( VectorSpace x, Real (Scalar x) + , AffineSpace y, v~Diff y, InnerSpace v, HasMetric v, RealFloat (Scalar v) ) + => PCMRange x -> [y] -> x-.^>y +recursivePCM xrng_g = recursiveSamples' xrng_g . fmap (,()) + + +splineRep :: ( AffineSpace y, v~Diff y, InnerSpace v, Floating (Scalar v), Ord (Scalar v) ) + => Int -- ^ Number of subdivisions to \"go down\". + -> (R-.^>y) -> R -> y +splineRep n₀ rPCM@(RecursivePCM _ _ _ (PCMRange xl wsp) slLn ()) + = go n₀ Nothing Nothing rPCM . normaliseR + where go n lPFits rPFits (RecursivePCM _ (Left (Pair r₁ r₂)) _ _ slLn ()) + | n>0, f₁ <- go (n-1) (rRoute=< if x<0.5 then f₁ $ x*2 + else f₂ $ x*2 - 1 + go _ lPFits rPFits rPCM = l₀splineRep (Pair lPFits rPFits) rPCM + + normaliseR x = (x - xl)/(wsp * fromIntegral slLn) + +l₀splineRep :: + ( VectorSpace x, Num (Scalar x) + , AffineSpace y, v~Diff y, VectorSpace v, Floating (Scalar v), Ord (Scalar v) ) + => Pair (Maybe (RecursiveSamples' n x y t')) + -> (RecursiveSamples' n x y t) + -> R{-Sample position normalised to [0,1]-} -> y +l₀splineRep (Pair lPFits rPFits) + (RecursivePCM{ rPCMlinFit=LinFitParams b a + , samplingSpec=PCMRange x₀ wsp + , splIdLen = n }) + = f + where f x | x < 0.5, t <- realToFrac $ 0.5 - x + , Just(RecursivePCM{rPCMlinFit=LinFitParams b'l a'l}) <- lPFits + = b .+^ (b'l.-.b) ^* h₀₁ t + .-^ a ^* h₁₀ t + .-^ a'l ^* h₁₁ t + | x > 0.5, t <- realToFrac $ x - 0.5 + , Just(RecursivePCM{rPCMlinFit=LinFitParams b'r a'r}) <- rPFits + = b .+^ (b'r.-.b) ^* h₀₁ t + .+^ a ^* h₁₀ t + .+^ a'r ^* h₁₁ t + | t <- realToFrac $ x-0.5 + = b .+^ t*^a + h₀₀ t = (1 + 2*t) * (1 - t)^2 -- Cubic Hermite splines + h₀₁ t = t^2 * (3 - 2*t) + h₁₀ t = t * (1 - t)^2 + h₁₁ t = t^2 * (t - 1) + + + +rPCMSample :: (AffineSpace y, v~Diff y, InnerSpace v, HasMetric v, RealFloat (Scalar v)) + => Interval R -> R -> (R->y) -> R-.^>y +rPCMSample (Interval l r) δx f = recursivePCM (PCMRange l δx) [f x | x<-[l, l+δx .. r]] + + +instance Plottable (R-.^>R) where + plot rPCM@(RecursivePCM gPFit gDetails gFitDevs (PCMRange x₀ wsp) gSplN ()) + = DynamicPlottable{ + relevantRange_x = const . pure $ Interval x₀ xr + , relevantRange_y = fmap $ rPCMLinFitRange rPCM + , isTintableMonochromic = True + , axesNecessity = 1 + , dynamicPlot = plot + } + where + xr = wsp * fromIntegral gSplN + plot (GraphWindowSpec{..}) = Plot [] . trace $ flattenPCM_resoCut bb δx rPCM + where + trace dPath = fold [ trMBound [ p & _y +~ s*δ + | (p, DevBoxes _ δ) <- dPath ] + | s <- [-1, 1] ] + <> trStRange dPath + trStRange ((p,DevBoxes σp' δp) : qd@(q,DevBoxes σq' δq) : ps) + = (let η = (σp/δp + σq/δq)/2 + in Dia.opacity (1-η) + (Dia.strokeLocLoop (Dia.fromVertices + [_y+~σq $ q, _y+~σp $ p, _y-~σp $ p, _y-~σq $ q + ,_y+~σq $ q ])) + <> Dia.opacity (η^2) + (Dia.strokeLocLoop (Dia.fromVertices + [_y+~δq $ q, _y+~δp $ p, _y-~δp $ p, _y-~δq $ q + ,_y+~δq $ q ])) + ) <> trStRange (qd:ps) + where [σp,σq] = map (`metric`1) [σp', σq'] + trStRange _ = mempty + trMBound l = Dia.fromVertices l & Dia.dashingO [2,2] 0 + + w = rBound - lBound; h = tBound - bBound + δx = w * 3/fromIntegral xResolution + bb = Interval lBound rBound + -*| Interval (bBound - h) (tBound + h) -- Heuristic \"buffering\", + -- to account for the missing ability of 'flattenPCM_resoCut' to + -- take deviations from quadratic-fit into account. + + +instance Plottable (RecursiveSamples Int P2 (DevBoxes P2)) where + plot rPCM@(RecursivePCM gPFit gDetails gFitDevs (PCMRange t₀ τsp) gSplN ()) + = DynamicPlottable{ + relevantRange_x = const $ pure xRange + , relevantRange_y = const $ pure yRange + , isTintableMonochromic = True + , axesNecessity = 1 + , dynamicPlot = plot + } + where plot (GraphWindowSpec{..}) = Plot [] + . foldMap trStRange + $ flattenPCM_P2_resoCut bbView [(1/δxl)^&0, 0^&(1/δyl)] rPCM + where trStRange (Left appr) = trSR $ map calcNormDev appr + where trSR ((pl,pr) : qd@(ql,qr) : ps) + = Dia.opacity 0.3 + (Dia.strokeLocLoop (Dia.fromVertices + [ ql, pl, pr, qr, ql ] + )) <> trSR (qd:ps) + trSR _ = mempty + calcNormDev ((p,v), DevBoxes σ _) = (p .+^ d, p .-^ d) + where d = metriScale σ $ turnLeft v + trStRange (Right pts) = (`foldMap`pts) + $ \(p, DevBoxes dv _) + -> let δxm = metric dv $ 1^&0 + δym = metric dv $ 0^&1 + in if δxm > δx && δym > δy + then simpleLine (_x +~ δxm $ p) (_x -~ δxm $ p) + <> simpleLine (_y +~ δym $ p) (_y -~ δym $ p) + else (Dia.rect (max δx $ δxm*2) (max δy $ δym*2) + & Dia.moveTo p) + + w = rBound - lBound; h = tBound - bBound + δxl = 6 * δx; δyl = 6 * δy + δx = w/fromIntegral xResolution; δy = h/fromIntegral yResolution + bbView = Interval lBound rBound -*| Interval bBound tBound + bb = rPCM_R2_boundingBox rPCM + (xRange,yRange) = xyRanges bb + + + +instance Plottable (Int -.^> P2) where + plot = plot . fmap (\() -> DevBoxes zeroV zeroV :: DevBoxes P2) + + + +-- | Plot a sequence of points @(x,y)@. The appearance of the plot will be automatically +-- chosen to match resolution and point density: at low densities, each point will simply +-- get displayed on its own. When the density goes so high you couldn't distinguish +-- individual points anyway, we switch to a “trace view”, approximating +-- the probability density function around a “local mean path”, which is +-- rather more insightful (and much less obstructive/clunky) than a simple cloud of +-- independent points. +-- +-- In principle, this should be able to handle vast amounts of data +-- (so you can, say, directly plot an audio file); at the moment the implementation +-- isn't efficient enough and will get slow for more than some 100000 data points. +tracePlot :: [(Double, Double)] -> DynamicPlottable +tracePlot = plot . recursiveSamples . map ((,()) . Dia.p2) + + +flattenPCM_resoCut :: BoundingBox R2 -> R -> (R-.^>R) -> [(P2, DevBoxes R)] +flattenPCM_resoCut bb δx = case DiaBB.getCorners bb of + Nothing -> const [] + Just cs -> ($[]) . go' cs + where go' cs@(lCorn,rCorn) = go where + go rPCM@(RecursivePCM pFit details fitDevs (PCMRange x₁ wsp) splN ()) + | DiaBB.isEmptyBox $ DiaBB.intersection bb sqRange + = id + | w > δx, Left (Pair s1 s2) <- details + = go s1 . go s2 + | otherwise + = ((xm ^& constCoeff pFit, fitDevs) :) + where xr = x₁ + w + xm = x₁ + w / 2 + w = wsp * fromIntegral splN + sqRange = xRange -*| rPCMLinFitRange rPCM xRange_norm'd + xRange = x₁ ... xr + xRange_norm'd = max (-1) ((lCorn^._x - xm)/w) + ... min 1 ((rCorn^._x - xm)/w) + +flattenPCM_P2_resoCut :: BoundingBox R2 -> [DualSpace R2] + -> (RecursiveSamples x P2 t) + -> [ Either [((P2, R2), DevBoxes P2)] + [(P2, t)] ] +flattenPCM_P2_resoCut bb δs = case DiaBB.getCorners bb of + Nothing -> const [] + Just cs -> ($[]) . go' cs + where go' cs@(lCorn,rCorn) = go where + go rPCM@(RecursivePCM (LinFitParams pm pa) details fitDevs@(DevBoxes dev _) _ _ ()) + | DiaBB.isEmptyBox $ DiaBB.intersection bb (rPCM_R2_boundingBox rPCM) + = \case l@(Left [] : _) -> l + l -> Left [] : l + | metrics dev δs > 0.5 || (sum $ ((^2).(pa<.>^)) <$> δs) > 3 + , Left (Pair s1 s2) <- details + = go s1 . go s2 + | Right pts <- details = (Right (Arr.toList pts) :) + | otherwise + = \case + (Left h : r) -> Left (((pm, dir), fitDevs) : h) : r + r -> Left [((pm, dir), fitDevs)] : r + where dir = case magnitude pa of 0 -> zeroV; m -> pa ^/ m + +turnLeft :: R2 -> R2 +turnLeft (DiaTypes.R2 x y) = DiaTypes.R2 (-y) x + + +rPCM_R2_boundingBox :: (RecursiveSamples x P2 t) -> BoundingBox R2 +rPCM_R2_boundingBox rPCM@(RecursivePCM pFit _ (DevBoxes dev _) _ _ ()) + = Interval (xl - ux*2) (xr + ux*2) + -*| Interval (yb - uy*2) (yt + uy*2) + where pm = constCoeff pFit + p₀ = pm .-^ linCoeff pFit; pe = pm .+^ linCoeff pFit + ux = metric dev $ 1^&0; uy = metric dev $ 0^&1 + [xl,xr] = sort[p₀^._x, pe^._x]; [yb,yt] = sort[p₀^._y, pe^._y] + + + +solveToLinFit :: (AffineSpace y, v~Diff y, VectorSpace v, Floating (Scalar v)) + => [y] -> LinFitParams y +solveToLinFit [] = error + "LinFit solve under-specified (need at least one reference point)." +solveToLinFit [y] = LinFitParams { constCoeff=y, linCoeff=zeroV } +solveToLinFit [y₁,y₂] -- @[x₁, x₂] ≡ [-½, ½]@, and @f(½) = (y₁+y₂)/2 + ½·(y₂-y₁) = y₂@. + -- (Likewise for @f(-½) = y₁@). + = LinFitParams { constCoeff = alerp y₁ y₂ 0.5 + , linCoeff = y₂ .-. y₁ } +solveToLinFit _ = error "LinFit solve over-specified (can't solve more than two points)." + + +normlsdIdd :: Fractional x => SplitList y -> [(x, y)] +normlsdIdd (SplitList l) = zip [ (k+1/2)/fromIntegral (Arr.length l) + | k<-iterate(+1)0] $ Arr.toList l + + +rPCMLinFitRange :: (R-.^>R) -> Interval R -> Interval R +rPCMLinFitRange rPCM@(RecursivePCM _ _ (DevBoxes _ δ) _ _ ()) ix + = let (Interval b t) = rppm rPCM ix in Interval (b-δ) (t+δ) + where rppm rPCM@(RecursivePCM (LinFitParams b a) _ _ _ _ ()) (Interval l r) + | r < (-1) = spInterval $ b - a + | l > 1 = spInterval $ b + a + | l < (-1) = rppm rPCM $ Interval (-1) r + | r > 1 = rppm rPCM $ Interval l 1 + | otherwise = (b + l*a) ... (b + r*a) + + + +rPCMPlot :: [R] -> DynamicPlottable +rPCMPlot = plot . recursivePCM (PCMRange (0 :: Double) 1) + +-- plotSamples :: [R2] + + + + + +data GraphWindowSpec = GraphWindowSpec { + lBound, rBound, bBound, tBound :: R + , xResolution, yResolution :: Int + , colourScheme :: ColourScheme + } +instance Show GraphWindowSpec where + show (GraphWindowSpec{..}) = "GraphWindowSpec{\ + \lBound="++show lBound++", \ + \rBound="++show rBound++", \ + \bBound="++show bBound++", \ + \tBound="++show tBound++", \ + \xResolution="++show xResolution++", \ + \yResolution="++show yResolution++"}" + +moveStepRel :: (R, R) -- ^ Relative translation @(Δx/w, Δy/h)@. + -> (R, R) -- ^ Relative zoom. + -> GraphWindowSpec -> GraphWindowSpec +moveStepRel (δx,δy) (ζx,ζy) (GraphWindowSpec l r b t xRes yRes clSchm) + = GraphWindowSpec l' r' b' t' xRes yRes clSchm + where qx = (r-l)/2 ; qy = (t-b)/2 + mx'= l + qx*(1+δx) ; my'= b + qy*(1+δy) + qx'= zoomSafeGuard mx' $ qx/ζx; qy'= zoomSafeGuard my' $ qy/ζy + l' = mx' - qx' ; b' = my' - qy' + r' = mx' + qx' ; t' = my' + qy' + zoomSafeGuard m = max (1e-250 + abs m*1e-6) . min 1e+250 + + + +data Interval r = Interval !r !r deriving (Show) +instance (Ord r) => Semigroup (Interval r) where -- WRT closed hull of the union. + Interval l₁ u₁ <> Interval l₂ u₂ = Interval (min l₁ l₂) (max u₁ u₂) + +realInterval :: Real r => Interval r -> Interval R +realInterval (Interval a b) = Interval (realToFrac a) (realToFrac b) + +onInterval :: ((R,R) -> (R,R)) -> Interval R -> Interval R +onInterval f (Interval l r) = uncurry Interval $ f (l, r) + +infixl 6 ... +-- | Build an interval from specified boundary points. No matter which of these +-- points is higher, the result will always be the interval in between (i.e., +-- @3 '...' 1@ will yield the interval [1,3], not an empty set or some \"oriented +-- interval\" [3,1]). +-- The fixity @infixl 6@ was chosen so you can write 2D bounding-boxes as e.g. +-- @-1...4 -*| -1...1@. +(...) :: (Ord r) => r -> r -> Interval r +x1...x2 | x1 < x2 = Interval x1 x2 + | otherwise = Interval x2 x1 + +spInterval :: r -> Interval r +spInterval x = Interval x x + +intersects :: Ord r => Interval r -> Interval r -> Bool +intersects (Interval a b) (Interval c d) = a<=d && b>=c + +includes :: Ord r => Interval r -> r -> Bool +Interval a b `includes` x = x>=a && x<=b + +infix 5 -*| + +-- | Cartesian product of intervals. +(-*|) :: Interval R -> Interval R -> BoundingBox R2 +Interval l r -*| Interval b t = DiaBB.fromCorners (l^&b) (r^&t) + +-- | Inverse of @uncurry ('-*|')@. /This is a partial function/, since +-- 'BoundingBox'es can be empty. +xyRanges :: BoundingBox R2 -> (Interval R, Interval R) +xyRanges bb = let Just (c₁, c₂) = DiaBB.getCorners bb + in (c₁^._x ... c₂^._x, c₁^._y ... c₂^._y) + + + + + + + + +data Plot = Plot { + plotAnnotations :: [Annotation] + , getPlot :: Diagram + } +instance Semigroup Plot where + Plot a1 d1 <> Plot a2 d2 = Plot (a1<>a2) (d1<>d2) +instance Monoid Plot where + mempty = Plot mempty mempty + mappend = (<>) + +data DynamicPlottable = DynamicPlottable { + relevantRange_x, relevantRange_y :: Option (Interval R) -> Option (Interval R) + , isTintableMonochromic :: Bool + , axesNecessity :: Necessity + , dynamicPlot :: GraphWindowSpec -> Plot + } + +data GraphViewState = GraphViewState { + lastStableView :: Maybe (GraphWindowSpec, Plot) + , realtimeView, nextTgtView :: Async Plot + , graphColor :: Maybe AColour + } + + + + + + +-- | Plot some plot objects to a new interactive GTK window. Useful for a quick +-- preview of some unknown data or real-valued functions; things like selection +-- of reasonable view range and colourisation are automatically chosen. +-- +-- Example: +-- +-- @ +-- plotWindow [ fnPlot cos +-- , tracePlot [(x,y) | x<-[-1,-0.96..1] +-- , y<-[0,0.01..1] +-- , abs (x^2 + y^2 - 1) < 0.01 ]] +-- @ +-- +-- This gives such a plot window: +-- +-- <> +-- +-- And that can with the mouse wheel be zoomed/browsed, like +-- +-- <> +-- +-- The individual objects you want to plot can be evaluated in multiple threads, so +-- a single hard calculatation won't freeze the responsitivity of the whole window. +-- Invoke e.g. from @ghci +RTS -N4@ to benefit from this. +plotWindow :: [DynamicPlottable] -> IO GraphWindowSpec +plotWindow [] = plotWindow [dynamicAxes] +plotWindow graphs' = do + + dgStore <- newIORef $ mempty + + + let defColourScheme = defaultColourScheme + + + ([viewTgt, viewState], graphs) <- do + let window₀ = autoDefaultView graphs' + assignGrViews :: [DynamicPlottable] -> [Colour] -> Double + -> IO [(DynamicPlottable, GraphViewState)] + assignGrViews (g@DynamicPlottable{..}:gs) (c:cs) axn = do + v <- async $ return $! dynamicPlot window₀ + fmap ((g, GraphViewState { lastStableView = Nothing + , realtimeView = v, nextTgtView = v + , graphColor = cl } + ) : ) $ assignGrViews gs cs' (axn + axesNecessity) + where (cl, cs') + | isTintableMonochromic = (Just $ defColourScheme c, cs) + | otherwise = (Nothing, c:cs) + assignGrViews [] _ axesNeed + | axesNeed > 0 = assignGrViews [dynamicAxes] [grey] (-1) + | otherwise = return [] + w <- mapM newIORef $ replicate 2 window₀ + gs <- newIORef =<< assignGrViews graphs' defaultColourSeq 0 + return (w,gs) + + + GTK.initGUI + window <- GTK.windowNew + + refreshDraw <- do + drawA <- GTK.drawingAreaNew + GTK.onExpose drawA $ \_ -> do + (canvasX,canvasY) <- GTK.widgetGetSize drawA + modifyIORef viewTgt $ \view -> view{ xResolution = fromIntegral canvasX + , yResolution = fromIntegral canvasY } + dia <- readIORef dgStore + let oldSize = Dia.size2D dia + scaledDia = Dia.bg Dia.black + . Dia.scaleX (fromInt canvasX / 2) + . Dia.scaleY (-fromInt canvasY / 2) + . Dia.translate (1 ^& (-1)) + . Dia.withEnvelope (Dia.rect 2 2 :: Diagram) + $ dia + drawWindow <- GTK.widgetGetDrawWindow drawA + -- putStrLn $ "redrawing"++show(canvasX,canvasY) + -- putStrLn . ("with state now:\n"++) . show =<< readIORef viewState + BGTK.renderToGtk drawWindow $ scaledDia + -- putStrLn $ "redrawn." + return True + + GTK.on drawA GTK.scrollEvent . Event.tryEvent $ do + (canvasX,canvasY) <- liftIO $ GTK.widgetGetSize drawA + (scrollX,scrollY) <- Event.eventCoordinates + let (rcX,rcY) = ( scrollX*2 / fromIntegral canvasX - 1 + , 1 - scrollY*2 / fromIntegral canvasY ) + scrollD <- Event.eventScrollDirection + case defaultScrollBehaviour scrollD of + ScrollZoomIn -> liftIO $ do + modifyIORef viewTgt $ \view@GraphWindowSpec{..} + -> let w = rBound - lBound + h = tBound - bBound + in view{ lBound = lBound + w * (rcX + 1)^2 * scrollZoomStrength + , rBound = rBound - w * (rcX - 1)^2 * scrollZoomStrength + , tBound = tBound - h * (rcY - 1)^2 * scrollZoomStrength + , bBound = bBound + h * (rcY + 1)^2 * scrollZoomStrength + } + ScrollZoomOut -> liftIO $ do + modifyIORef viewTgt $ \view@GraphWindowSpec{..} + -> let w = rBound - lBound + h = tBound - bBound + in view{ lBound = lBound - w * (rcX - 1)^2 * scrollZoomStrength + , rBound = rBound + w * (rcX + 1)^2 * scrollZoomStrength + , tBound = tBound + h * (rcY + 1)^2 * scrollZoomStrength + , bBound = bBound - h * (rcY - 1)^2 * scrollZoomStrength + } + + + + GTK.set window [ GTK.windowTitle := "Plot" + , GTK.windowDefaultWidth := defResX + , GTK.windowDefaultHeight := defResY + , GTK.containerChild := drawA + ] + + GTK.widgetShowAll window + + return $ GTK.widgetQueueDraw drawA + + + let updateRTView, updateTgtView :: (GraphWindowSpec -> GraphWindowSpec) -> IO () + updateRTView updRealView = do + vstOld <- readIORef viewState + let newRealView = updRealView vstOld + grViewsOld <- readIORef graphs + writeIORef graphs <=< forM grViewsOld $ + \(o@DynamicPlottable{..}, gv) -> do + newRt <- async $ return $! dynamicPlot newRealView + poll (realtimeView gv) >>= \case + Just(Right vw) -> return (o + , gv{ realtimeView = newRt, lastStableView = Just (vstOld, vw) }) + _ -> do + cancel $ realtimeView gv + poll (nextTgtView gv) >>= \case + Just(Right vw) -> do + ttvn <- readIORef viewTgt + return (o, gv{ realtimeView = newRt, lastStableView = Just (ttvn, vw) }) + _ -> return (o, gv{ realtimeView = newRt }) + writeIORef viewState newRealView + updateTgtView updTgtView = do + newTgtView <- updTgtView <$> readIORef viewTgt + grViewsOld <- readIORef graphs + writeIORef graphs <=< forM grViewsOld $ + \(o@DynamicPlottable{..}, gv) -> do + newTt <- async $ return $! dynamicPlot newTgtView + cancel $ nextTgtView gv + return (o, gv{ nextTgtView = newTt }) + writeIORef viewTgt newTgtView + + t₀ <- getCurrentTime + lastFrameTime <- newIORef t₀ + + let minKeyImpact = 0.05 + + keyImpactState <- newIORef $ Map.fromList [ (ka, (t₀, minKeyImpact)) | ka<-[MoveLeft .. ZoomOut_y] ] + + + let refreshScreen = do + currentView@(GraphWindowSpec{..}) <- readIORef viewState + let normaliseView :: Diagram -> Diagram + normaliseView = (Dia.scaleX xUnZ :: Diagram->Diagram) . Dia.scaleY yUnZ + . Dia.translate (Dia.r2(-x₀,-y₀)) + where xUnZ = 1/w; yUnZ = 1/h + w = (rBound - lBound)/2; h = (tBound - bBound)/2 + x₀ = lBound + w; y₀ = bBound + h + renderComp (DynamicPlottable{..}, GraphViewState{..}) = do + plt <- poll realtimeView >>= \case + Just (Right pl) -> return $ Just pl + _ -> case lastStableView of + Just (_, vw) -> return $ Just vw + _ -> poll nextTgtView >> return Nothing + return $ case plt of + Nothing -> mempty + Just Plot{..} -> let + antTK = DiagramTK { viewScope = currentView + , textTools = TextTK defaultTxtStyle + txtSize aspect 0.2 0.2 } + txtSize = h * fontPts / fromIntegral yResolution + aspect = w * fromIntegral yResolution + / (h * fromIntegral xResolution) + fontPts = 12 + transform :: Diagram -> Diagram + transform = normaliseView . clr + where clr | Just c <- graphColor = Dia.lcA c . Dia.fcA c + | otherwise = id + in transform $ foldMap (prerenderAnnotation antTK) plotAnnotations + <> getPlot + + gvStates <- readIORef graphs + waitAny $ map (realtimeView . snd) gvStates + + writeIORef dgStore + . mconcat . reverse =<< mapM renderComp (reverse gvStates) + + refreshDraw + + let mainLoop = do + t <- getCurrentTime + δt <- fmap (diffUTCTime t) $ readIORef lastFrameTime + writeIORef lastFrameTime t + + do vt <- readIORef viewTgt + updateRTView $ \vo -> + let a%b = let η = min 1 $ 2 * realToFrac δt in η*a + (1-η)*b + in GraphWindowSpec (lBound vt % lBound vo) (rBound vt % rBound vo) + (bBound vt % bBound vo) (tBound vt % tBound vo) + (xResolution vt) (yResolution vt) + defColourScheme + -- GTK.sleep 0.01 + refreshScreen + -- GTK.pollEvents + return True + + let keyImpact key = do + t <- getCurrentTime + Just (_, impact) <- fmap (Map.lookup key) $ readIORef keyImpactState + modifyIORef keyImpactState $ Map.adjust ( \(t₁, p) + -> (t, min 1 $ ( (p - minKeyImpact) * (exp . (*3) . realToFrac $ diffUTCTime t₁ t) + + minKeyImpact ) * 2 ) + ) key + return impact + +-- GLFW.keyCallback $= \key state -> do +-- let keyStepSize = 0.1 +-- (state==GLFW.Press) `when` do +-- case defaultKeyMap key of +-- Just QuitProgram -> writeIORef done True +-- Just movement -> do +-- impact <- keyImpact movement +-- updateTgtView $ case movement of +-- MoveUp -> moveStepRel (0, impact) (1, 1) +-- MoveDown -> moveStepRel (0, -impact) (1, 1) +-- MoveLeft -> moveStepRel (-impact, 0) (1, 1) +-- MoveRight -> moveStepRel (impact , 0) (1, 1) +-- ZoomIn_x -> moveStepRel (0, 0) (1+impact, 1) +-- ZoomOut_x -> moveStepRel (0, 0) (1-impact/2, 1) +-- ZoomIn_y -> moveStepRel (0, 0) (1, 1+impact/2) +-- ZoomOut_y -> moveStepRel (0, 0) (1, 1-impact/2) +-- _ -> return () +-- + GTK.onDestroy window $ do + (readIORef graphs >>=) . mapM_ -- cancel remaining threads + $ \(_, GraphViewState{..}) -> cancel realtimeView >> cancel nextTgtView + GTK.mainQuit + + + -- putStrLn "Enter Main loop..." + +-- mainLoop + GTK.timeoutAdd mainLoop 100 + + + GTK.mainGUI + + -- putStrLn "Done." + + -- GTK.mainQuit + + readIORef viewState + + +autoDefaultView :: [DynamicPlottable] -> GraphWindowSpec +autoDefaultView graphs = GraphWindowSpec l r b t defResX defResY defaultColourScheme + where (xRange, yRange) = foldMap (relevantRange_x &&& relevantRange_y) graphs + ((l,r), (b,t)) = ( xRange `dependentOn` yRange + , yRange `dependentOn` xRange ) + ξ`dependentOn`υ = addMargin . defRng . ξ . return . defRng $ υ mempty + defRng = Interval (-1) 1 `option` id + addMargin (Interval a b) = (a - q, b + q) + where q = (b - a) / 6 + + + +-- render :: Diagram -> IO() +-- render = Dia.clearRender + +defResX, defResY :: Integral i => i +defResX = 640 +defResY = 480 + + +data ScrollAction = ScrollZoomIn | ScrollZoomOut + +defaultScrollBehaviour :: Event.ScrollDirection -> ScrollAction +defaultScrollBehaviour Event.ScrollUp = ScrollZoomIn +defaultScrollBehaviour Event.ScrollDown = ScrollZoomOut + +scrollZoomStrength :: Double +scrollZoomStrength = 1/20 + + +data KeyAction = MoveLeft + | MoveRight + | MoveUp + | MoveDown + | ZoomIn_x + | ZoomOut_x + | ZoomIn_y + | ZoomOut_y + | QuitProgram + deriving (Eq, Ord, Enum) + +defaultKeyMap :: GTK.KeyVal -> Maybe KeyAction +-- defaultKeyMap (GLFW.SpecialKey GLFW.UP ) = Just MoveUp +-- defaultKeyMap (GLFW.SpecialKey GLFW.DOWN ) = Just MoveDown +-- defaultKeyMap (GLFW.SpecialKey GLFW.LEFT ) = Just MoveLeft +-- defaultKeyMap (GLFW.SpecialKey GLFW.RIGHT) = Just MoveRight +-- defaultKeyMap (GLFW.CharKey 'K') = Just MoveUp +-- defaultKeyMap (GLFW.CharKey 'J') = Just MoveDown +-- defaultKeyMap (GLFW.CharKey 'H') = Just MoveLeft +-- defaultKeyMap (GLFW.CharKey 'L') = Just MoveRight +-- defaultKeyMap (GLFW.CharKey 'B') = Just ZoomIn_x +-- defaultKeyMap (GLFW.CharKey 'N') = Just ZoomOut_x +-- defaultKeyMap (GLFW.CharKey 'I') = Just ZoomIn_y +-- defaultKeyMap (GLFW.CharKey 'O') = Just ZoomOut_y +-- defaultKeyMap (GLFW.SpecialKey GLFW.ESC) = Just QuitProgram +defaultKeyMap _ = Nothing + +-- instance NFData Draw.R + + +-- | Plot an (assumed continuous) function in the usual way. +-- Since this uses functions of actual 'Double' values, you have more liberty +-- of defining functions with range-pattern-matching etc., which is at the moment +-- not possible in the ':-->' category. +-- +-- However, because 'Double' can't really proove properties of a mathematical +-- function, aliasing and similar problems are not taken into account. So it only works +-- accurately when the function is locally linear on pixel scales (what most +-- other plot programs just assume silently). In case of singularities, the +-- naïve thing is done (extend as far as possible; vertical line at sign change), +-- which again is common enough though not really right. +-- +-- We'd like to recommend using 'fnPlot' whenever possible, which automatically adjusts +-- the resolution so the plot is guaranteed accurate (but it's not usable yet for +-- a lot of real applications). +continFnPlot :: (Double -> Double) -> DynamicPlottable +continFnPlot f = DynamicPlottable{ + relevantRange_x = const mempty + , relevantRange_y = yRangef + , isTintableMonochromic = True + , axesNecessity = 1 + , dynamicPlot = plot } + where yRangef = fmap . onInterval $ \(l, r) -> ((!10) &&& (!70)) . sort . pruneOutlyers + $ map f [l, l + (r-l)/80 .. r] + plot (GraphWindowSpec{..}) = curve `deepseq` Plot [] (trace curve) + where δx = (rBound - lBound) * 2 / fromIntegral xResolution + curve = [ (x ^& f x) | x<-[lBound, lBound+δx .. rBound] ] + trace (p:q:ps) = simpleLine p q <> trace (q:ps) + trace _ = mempty + pruneOutlyers = filter (not . isNaN) + l!n | (x:_)<-drop n l = x + | otherwise = error "Function appears to yield NaN most of the time. Cannot be plotted." + + +-- | Plot a continuous function in the usual way, taking arguments from the +-- x-Coordinate and results to the y one. +-- The signature looks more complicated than it is; think about it as requiring +-- a polymorphic 'Floating' function. Any simple expression like +-- @'fnPlot' (\\x -> sin x / exp (x^2))@ will work (but the view must not contain +-- singularities). +-- +-- Under the hood this uses the category of continuous functions, ':-->', to proove +-- that no details are omitted (like small high-frequency bumps). The flip side is that +-- this does not always work very efficiently, in fact it can easily become exponentially +-- slow for some parameters. +-- Make sure to run multithreaded, to prevent hanging your program this way. Also consider +-- limiting the memory: if you try to plot across singularities, the program may well +-- eat up all available resorces before failing. (But it will never “succeed” and +-- plot something wrong!) +-- +-- In the future, we would like to switch to the category of piecewise continuously-differentiable +-- functions. That wouldn't suffer from said problems, and should +-- also generally be more efficient. (That category is not yet implemented in Haskell.) +fnPlot :: (forall m . 𝓒⁰.Manifold m + => ProxyVal (:-->) m Double -> ProxyVal (:-->) m Double) + -> DynamicPlottable +fnPlot f = plot fc + where fc :: Double :--> Double + fc = alg f + +-- | Plot a continuous, “parametric function”, i.e. mapping the real +-- line to a path in ℝ². +paramPlot :: (forall m . 𝓒⁰.Manifold m + => ProxyVal (:-->) m Double + -> (ProxyVal (:-->) m Double, ProxyVal (:-->) m Double)) + -> DynamicPlottable +paramPlot f = plot fc + where fc :: Double :--> (Double, Double) + fc = alg1to2 f + + + + +data AxesStyle = DynamicAxesStyle +data DynamicAxes = DynamicAxes { yAxisClasses, xAxisClasses :: [AxisClass] } +data AxisClass = AxisClass { visibleAxes :: [Axis], axisStrength :: Double, decPrecision :: Int } +data Axis = Axis { axisPosition :: R } + +crtDynamicAxes :: GraphWindowSpec -> DynamicAxes +crtDynamicAxes (GraphWindowSpec {..}) = DynamicAxes yAxCls xAxCls + where [yAxCls, xAxCls] = zipWith3 directional + [lBound, bBound] [rBound, tBound] [xResolution, yResolution] + directional l u res = map lvl lvlSpecs + where span = u - l + upDecaSpan = 10**(ceil $ lg span) + pixelScale = span / (fromIntegral res * upDecaSpan) + baseDecaval = upDecaSpan * (flor $ l / upDecaSpan) + lvl (minSpc, strength) + = AxisClass [ Axis v | i<-[0 .. luDSdiv*2] + , let v=(baseDecaval + i*laSpc), v>l, v pixelScale * minSpc < 1/d ) + . join $ iterate (map(*10)) [1, 2, 5] + ll [] = error $ "pixelScale = "++show pixelScale + ++"; minSpc = "++show minSpc + ll l = last l + lvlSpecs = [ (80, 0.3), (18, 0.1) ] + + + +dynamicAxes :: DynamicPlottable +dynamicAxes = DynamicPlottable { + relevantRange_x = const mempty + , relevantRange_y = const mempty + , isTintableMonochromic = False + , axesNecessity = superfluent + , dynamicPlot = plot } + where plot gwSpec@(GraphWindowSpec{..}) = Plot labels lines + where (DynamicAxes yAxCls xAxCls) = crtDynamicAxes gwSpec + lines = zeroLine (lBound^&0) (rBound^&0) `provided`(bBound<0 && tBound>0) + <> zeroLine (0^&bBound) (0^&tBound) `provided`(lBound<0 && rBound>0) + <> foldMap (renderClass $ \x -> (x^&bBound, x^&tBound)) yAxCls + <> foldMap (renderClass $ \y -> (lBound^&y, rBound^&y)) xAxCls + labels = do (dirq, hAlign, vAlign, acl) <- zip4 [\x -> x^&0, \y -> 0^&y ] + [AlignMid , AlignTop ] + [AlignTop , AlignMid ] + [yAxCls , xAxCls ] + let (AxisClass vaxs _ prc) = head acl + prepAnnotation (Axis{axisPosition=z}) = do + guard(z/=0) + [Annotation (TextAnnotation txt align) place False] + where txt = PlainText . prettyFloatShow prc $ realToFrac z + place = ExactPlace $ dirq z + align = TextAlignment hAlign vAlign + prepAnnotation =<< vaxs + zeroLine p1 p2 = simpleLine p1 p2 & Dia.lc Dia.grey + renderClass crd (AxisClass axes strength _) + = foldMap (uncurry simpleLine . crd . axisPosition) axes + & Dia.lcA (Dia.grey `DCol.withOpacity` strength) + + + +type Necessity = Double +superfluent = -1e+32 :: Necessity + + + +simpleLine :: Dia.P2 -> Dia.P2 -> Diagram +simpleLine p q = Dia.fromVertices [p,q] & Dia.lwO 2 + + + +-- | When you “plot” 'xInterval' / 'yInterval', it is ensured that the (initial) view encompasses +-- (at least) the specified range. +-- Note there is nothing special about these “flag” objects: /any/ 'Plottable' can request a +-- certain view, e.g. for a discrete point cloud it's obvious and a function defines at least +-- a @y@-range for a given @x@-range. Only use explicit range when necessary. +xInterval, yInterval :: (Double, Double) -> DynamicPlottable +xInterval (l,r) = DynamicPlottable { + relevantRange_x = const . return $ Interval l r + , relevantRange_y = const mempty + , isTintableMonochromic = False + , axesNecessity = 0 + , dynamicPlot = plot } + where plot _ = Plot mempty mempty +yInterval (b,t) = DynamicPlottable { + relevantRange_x = const mempty + , relevantRange_y = const . return $ Interval b t + , isTintableMonochromic = False + , axesNecessity = 0 + , dynamicPlot = plot } + where plot _ = Plot mempty mempty + + +prettyFloatShow :: Int -> Double -> String +prettyFloatShow _ 0 = "0" +prettyFloatShow preci x + | preci >= 0, preci < 4 = show $ round x + | preci < 0, preci > -2 = printf "%.1f" x + | otherwise = case ceiling (0.01 + lg (abs x/10^^(preci+1))) + preci of + 0 | preci < 0 -> printf ("%."++show(-preci)++"f") x + expn | expn>preci -> printf ("%."++show(expn-preci)++"f*10^%i") + (x/10^^expn) expn + | otherwise -> printf ("%i*10^%i") + (round $ x/10^^expn :: Int) expn + + + + + +maybeRead :: Read a => String -> Maybe a +maybeRead = fmap fst . listToMaybe . reads + +data Annotation = Annotation { + getAnnotation :: AnnotationObj + , placement :: AnnotationPlace + , isOptional :: Bool + } +data AnnotationObj = TextAnnotation TextObj TextAlignment +data AnnotationPlace = ExactPlace R2 + +data TextObj = PlainText String +data TextAlignment = TextAlignment { hAlign, vAlign :: Alignment } -- , blockSpread :: Bool } +data Alignment = AlignBottom | AlignMid | AlignTop + +data DiagramTK = DiagramTK { textTools :: TextTK, viewScope :: GraphWindowSpec } +data TextTK = TextTK { txtCairoStyle :: Dia.Style R2 -- Draw.Font + , txtSize, xAspect, padding, extraTopPad :: R } + +defaultTxtStyle :: Dia.Style R2 +defaultTxtStyle = mempty & Dia.fontSizeO 9 + & Dia.fc Dia.grey + & Dia.lc Dia.grey + + +prerenderAnnotation :: DiagramTK -> Annotation -> Diagram +prerenderAnnotation (DiagramTK{ textTools = TextTK{..}, viewScope = GraphWindowSpec{..} }) + (Annotation{..}) + | TextAnnotation (PlainText str) (TextAlignment{..}) <- getAnnotation + , ExactPlace p₀ <- placement + = let rnTextLines = map (CairoTxt.textVisualBounded txtCairoStyle) $ lines str + lineWidths = map ((/4 {- Magic number ??? -}) + . Dia.width) rnTextLines + nLines = length lineWidths + lineHeight = 1 + extraTopPad + 2*padding + ζx = ζy * xAspect + ζy = txtSize -- / lineHeight + width = (maximum $ 0 : lineWidths) + 2*padding + height = fromIntegral nLines * lineHeight + y₀ = case vAlign of + AlignBottom -> padding + height - lineHeight + AlignMid -> height/2 - lineHeight + AlignTop -> - (lineHeight + padding) + fullText = mconcat $ zipWith3 ( \n w -> + let y = n*lineHeight + in (Dia.translate $ Dia.r2 (case hAlign of + AlignBottom -> (padding , y₀-y) + AlignMid -> (- w/2 , y₀-y) + AlignTop -> (-(w + padding), y₀-y) + ) ) ) [0..] lineWidths rnTextLines + p = px ^& py + where px = max l' . min r' $ p₀^._x + py = max b' . min t' $ p₀^._y + (l', r') = case hAlign of + AlignBottom -> (lBound , rBound - w ) + AlignMid -> (lBound + w/2, rBound - w/2) + AlignTop -> (lBound + w , rBound ) + (b', t') = case vAlign of + AlignBottom -> (bBound , tBound - h ) + AlignMid -> (bBound + h/2, tBound - h/2) + AlignTop -> (bBound + h , tBound ) + w = ζx * width; h = ζy * height + in Dia.translate p . Dia.scaleX ζx . Dia.scaleY ζy + $ Dia.lc Dia.grey fullText + + + + + + +infixl 7 `provided` +provided :: Monoid m => m -> Bool -> m +provided m True = m +provided m False = mempty + + +lg :: Floating a => a -> a +lg x = log x / log 10 + + +-- instance (Monoid v) => Semigroup (Draw.Image v) where +-- (<>) = mappend +-- instance Semigroup (Draw.Affine) where +-- (<>) = mappend +-- +ceil, flor :: R -> R +ceil = fromInt . ceiling +flor = fromInt . floor + +fromInt :: Num a => Int -> a +fromInt = fromIntegral + + + +instance NFData Dia.P2 + diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,6 @@ +module Main (main) where + +import Distribution.Simple + +main :: IO () +main = defaultMain diff --git a/dynamic-plot.cabal b/dynamic-plot.cabal new file mode 100644 --- /dev/null +++ b/dynamic-plot.cabal @@ -0,0 +1,76 @@ +Name: dynamic-plot +Version: 0.1.0.0 +Category: graphics +Synopsis: Interactive diagram windows +Description: Haskell excels at handling data like continuous functions + in a nice way, i.e. without discretising anything to finite arrays as + is typically done in languages like Matlab. Instead, you can simply pass + around functions or infinite data structures (or /very/ high-resolution data + that would be infeasible to handle in a strict language). + . + However when you want to /view/ the data, it will eventually need to be exported out of Haskell + in some finite form. The purpose of this library is to delay this discretisation + as long as possible: it implements an interactive plotting window that accepts continuous/recursive + data and only “flattens” it according to the specific view configuration. + You can then zoom in to a shown diagram and it will automatically calculate + the features more detailedly, or zoom out and discover previosly unexpected + features. You don't need to worry about specifying the range and/or resolution beforehand: + the program will try to find a suitable default view based on /all/ data your displaying, + and you can always still zoom, resize or move later. + . + are used as the “pre-rendered” type. This + makes the output usable in a very wide range of applications, though at the moment only the GTK + window view is implemented. +License: GPL-3 +License-file: COPYING +Author: Justus Sagemüller +Maintainer: (@) sagemuej $ smail.uni-koeln.de +Homepage: https://github.com/leftaroundabout/dynamic-plot +Build-Type: Simple +Cabal-Version: >=1.10 +Extra-Doc-Files: images/examples/*.png + +Source-Repository head + type: git + location: git://github.com/leftaroundabout/dynamic-plot.git + +Library + Build-Depends: base>=4.5 && <6 + , transformers + , mtl + , vector-space>=0.8 + , MemoTrie + , vector + , containers + , semigroups + , random + , MonadRandom + , time + , async + , deepseq + , process + , constrained-categories + , diagrams-core == 1.2.0.2 + , diagrams-lib >= 1 && < 1.4 + , diagrams-cairo == 1.2.0.2 + , diagrams-gtk + , gtk > 0.10 && < 0.15 + , glib + , colour >= 2 && < 3 + , manifolds < 0.1.1 + , lens + Other-Extensions: FlexibleInstances + , TypeFamilies + , FlexibleContexts + , GADTs + , RankNTypes + , ConstraintKinds + , PatternGuards + , ScopedTypeVariables + , RecordWildCards + , TupleSections + ghc-options: -O2 + default-language: Haskell2010 + Exposed-modules: Graphics.Dynamic.Plot.R2 + Other-modules: Graphics.Dynamic.Plot.Colour + , Data.LinearMap.HerMetric diff --git a/images/examples/cos-encircle-points-far.png b/images/examples/cos-encircle-points-far.png new file mode 100644 Binary files /dev/null and b/images/examples/cos-encircle-points-far.png differ diff --git a/images/examples/cos-encircle-points.png b/images/examples/cos-encircle-points.png new file mode 100644 Binary files /dev/null and b/images/examples/cos-encircle-points.png differ