-- | -- Module : Graphics.Dynamic.Plot.R2 -- Copyright : (c) Justus Sagemüller 2013-2015 -- 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 UnicodeSyntax #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE LiberalTypeSynonyms #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE ConstraintKinds #-} {-# 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 , lineSegPlot , PlainGraphicsR2 , shapePlot , diagramPlot -- ** Legend captions , legendName -- ** View selection , xInterval, yInterval, forceXRange, forceYRange -- ** View dependance , ViewXCenter(..), ViewYCenter(..), ViewWidth(..), ViewHeight(..) , ViewXResolution(..), ViewYResolution(..) -- ** Auxiliary plot objects , dynamicAxes, noDynamicAxes -- ** Plot type , DynamicPlottable -- ** Legacy , PlainGraphics(..) ) where import Graphics.Dynamic.Plot.Colour import Graphics.Dynamic.Plot.Internal.Types import Graphics.Text.Annotation import qualified Prelude import Diagrams.Prelude ((^&), (&), _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, sortBy, intercalate, isPrefixOf, isInfixOf, find, zip4) import qualified Data.Vector as Arr import Data.Maybe import Data.Semigroup import Data.Default import Data.Foldable (fold, foldMap) import Data.Function (on) import Data.Ord (comparing) import Data.VectorSpace import Data.Basis import Data.AffineSpace import Data.LinearMap.HerMetric import Data.Manifold.PseudoAffine import Data.Manifold.Types import Data.Manifold.TreeCover import qualified Data.Map.Lazy as Map import Data.Tagged 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 newtype PlainGraphics = PlainGraphics { getPlainGraphics :: PlainGraphicsR2 } deriving (Semigroup, Monoid) -- | Class for types that can be plotted in some canonical, “obvious” -- way. If you want to display something and don't know about any specific caveats, -- try just using 'plot'! class Plottable p where plot :: p -> DynamicPlottable instance Plottable DynamicPlottable where plot = id instance Plottable (R -> R) where plot f = continFnPlot $ realToFrac . f . realToFrac -- {-# RULES "plot/R->R" plot = fnPlot #-} instance Plottable (Double :--> Double) where plot f = def { relevantRange_y = otherDimDependence 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 (GraphWindowSpecR2{..}) = curve `deepseq` mkPlot (trace curve) where curve :: [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 = def { isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where plot (GraphWindowSpecR2{..}) = curves `deepseq` mkPlot (foldMap trace curves) where curves :: [[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 = foldMap plot instance Plottable PlainGraphics where plot (PlainGraphics d) = def { relevantRange_x = atLeastInterval rlx , relevantRange_y = atLeastInterval rly , axesNecessity = -1 , dynamicPlot = plot } where bb = DiaBB.boundingBox d (rlx,rly) = case DiaBB.getCorners bb of Just (c1, c2) -> ( c1^._x ... c2^._x , c1^._y ... c2^._y ) plot _ = mkPlot d -- | Use a generic diagram within a plot. -- -- Like with the various specialised function plotters, this will get automatically -- tinted to be distinguishable from other plot objects in the same window. -- Use 'diagramPlot' instead, if you want to view the diagram as-is. shapePlot :: PlainGraphicsR2 -> DynamicPlottable shapePlot d = (diagramPlot d) { isTintableMonochromic = True, axesNecessity = 0 } -- | Plot a generic 'Dia.Diagram'. diagramPlot :: PlainGraphicsR2 -> DynamicPlottable diagramPlot d = plot $ PlainGraphics d instance Plottable (R-->R) where plot f = def { relevantRange_y = mempty -- otherDimDependence yRangef , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where yRangef (Interval l r) = undefined plot gs@(GraphWindowSpecR2{..}) = curves `deepseq` mkPlot (foldMap trace curves) where curves :: [[P2]] curves = map (map $ convℝ² . snd) $ discretisePathSegs xResolution (resolutionFunction gs) (id&&&f <<< alg(+point x₀)) x₀ = (lBound + rBound)/2 trace (p:q:ps) = simpleLine p q <> trace (q:ps) trace _ = mempty convℝ² = Dia.p2 c = realToFrac resolutionFunction :: GraphWindowSpecR2 -> RieMetric ℝ² resolutionFunction GraphWindowSpecR2{..} = resoFunc where x₀ = (lBound + rBound)/2 w = rBound - lBound; h = tBound - bBound ε = projector (recip δx, 0) + projector (0, recip δy) δx = w / fromIntegral xResolution δy = h / fromIntegral yResolution resoFunc (x,y) | x > lBound, x < rBound, y > bBound, y < tBound = ε | otherwise = projector (qx,0) + projector (0,qy) where qx | x < lBound = lBound - x | x > rBound = x - rBound | otherwise = δx * qy/δy qy | y < bBound = bBound - y | y > tBound = y - tBound | otherwise = δy * qx/δx instance Plottable (R-.^>R) where plot rPCM@(RecursivePCM gPFit gDetails gFitDevs (PCMRange x₀ wsp) gSplN ()) = def { relevantRange_x = atLeastInterval $ Interval x₀ xr , relevantRange_y = otherDimDependence $ rPCMLinFitRange rPCM , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where xr = wsp * fromIntegral gSplN plot (GraphWindowSpecR2{..}) = mkPlot . 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 ()) = def { relevantRange_x = atLeastInterval xRange , relevantRange_y = atLeastInterval yRange , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where plot (GraphWindowSpecR2{..}) = mkPlot . 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) -- | Simply connect the points by straight line segments, in the given order. -- Beware that this will always slow down the performance when the list is large; -- there is no Éc;statistic optimisationÉd; as in 'tracePlot'. lineSegPlot :: [(Double, Double)] -> DynamicPlottable lineSegPlot ps = def { relevantRange_x = atLeastInterval' $ foldMap (pure . spInterval . fst) ps , relevantRange_y = atLeastInterval' $ foldMap (pure . spInterval . snd) ps , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where plot (GraphWindowSpecR2{..}) = mkPlot (trace ps) where trace (p:q:ps) = simpleLine (Dia.p2 p) (Dia.p2 q) <> trace (q:ps) trace _ = mempty flattenPCM_resoCut :: R2Box -> 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 :: R2Box -> [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.V2 x y) = DiaTypes.V2 (-y) x rPCMPlot :: [R] -> DynamicPlottable rPCMPlot = plot . recursivePCM (PCMRange (0 :: Double) 1) instance Plottable (Shade P2) where plot shade = def { relevantRange_x = atLeastInterval xRange , relevantRange_y = atLeastInterval yRange , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where plot grWS@(GraphWindowSpecR2{..}) = mkPlot $ foldMap axLine eigVs where (pixWdth, pixHght) = pixelDim grWS axLine eigV = simpleLine (ctr .-~^ eigV) (ctr .+~^ eigV) (xRange,yRange) = shadeExtends shade ctr = shade^.shadeCtr eigVs = eigenSpan $ shade^.shadeExpanse instance Plottable (SimpleTree P2) where plot (GenericTree Nothing) = plot ([] :: [SimpleTree P2]) plot (GenericTree (Just (ctr, root))) = def{ relevantRange_x = atLeastInterval xRange , relevantRange_y = atLeastInterval yRange , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where plot _ = mkPlot $ go 4 ctr (treeBranches root) where go w bctr = foldMap (\(c,GenericTree b) -> autoDashLine w bctr c <> go (w*0.6) c b ) (xRange, yRange) = let allPoints = gPts tree (xmin,xmax) = (minimum&&&maximum) $ (^._x) <$> allPoints (ymin,ymax) = (minimum&&&maximum) $ (^._y) <$> allPoints in (xmin ... xmax, ymin ... ymax) where gPts (GenericTree brchs) = foldr (\(c,b) r -> c : gPts b ++ r) [] brchs tree = GenericTree [(ctr,root)] instance Plottable (Trees P2) where plot (GenericTree ts) = plot $ (GenericTree . Just) <$> ts pixelDim :: GraphWindowSpecR2 -> (R, R) pixelDim grWS = ( graphWindowWidth grWS / fromIntegral (xResolution grWS) , graphWindowHeight grWS / fromIntegral (yResolution grWS) ) type GraphWindowSpec = GraphWindowSpecR2 moveStepRel :: (R, R) -- ^ Relative translation @(Δx/w, Δy/h)@. -> (R, R) -- ^ Relative zoom. -> GraphWindowSpec -> GraphWindowSpec moveStepRel (δx,δy) (ζx,ζy) (GraphWindowSpecR2 l r b t xRes yRes clSchm) = GraphWindowSpecR2 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 graphWindowWidth, graphWindowHeight :: GraphWindowSpec -> R graphWindowWidth grWS = rBound grWS - lBound grWS graphWindowHeight grWS = tBound grWS - bBound grWS data Plot = Plot { plotAnnotations :: [Annotation] , getPlot :: PlainGraphicsR2 } instance Semigroup Plot where Plot a1 d1 <> Plot a2 d2 = Plot (a1<>a2) (d1<>d2) instance Monoid Plot where mempty = Plot mempty mempty mappend = (<>) mkPlot :: PlainGraphicsR2 -> Plot mkPlot = Plot mempty mkAnnotatedPlot :: [Annotation] -> PlainGraphicsR2 -> Plot mkAnnotatedPlot ans = Plot ans data DynamicPlottable = DynamicPlottable { relevantRange_x, relevantRange_y :: RangeRequest R , isTintableMonochromic :: Bool , occlusiveness :: Double -- ^ How surface-occupying the plot is. -- Use positive values for opaque 2D plots that would tend to obscure -- other objects, negative values for sparse/small point plots. -- The z-order will be chosen accordingly. , axesNecessity :: Necessity , legendEntries :: [LegendEntry] , dynamicPlot :: GraphWindowSpec -> Plot } instance Semigroup DynamicPlottable where DynamicPlottable rx₁ ry₁ tm₁ oc₁ ax₁ le₁ dp₁ <> DynamicPlottable rx₂ ry₂ tm₂ oc₂ ax₂ le₂ dp₂ = DynamicPlottable (rx₁<>rx₂) (ry₁<>ry₂) (tm₁||tm₂) (oc₁+oc₂) (ax₁+ax₂) (le₁++le₂) (dp₁<>dp₂) instance Monoid DynamicPlottable where mempty = DynamicPlottable mempty mempty False 0 0 [] mempty mappend = (<>) instance Default DynamicPlottable where def = mempty data GraphViewState = GraphViewState { lastStableView :: Maybe (GraphWindowSpec, Plot) , realtimeView, nextTgtView :: Async Plot , graphColor :: Maybe AColour } legendName :: String -> DynamicPlottable -> DynamicPlottable legendName n d = d { legendEntries = LegendEntry (PlainText n) mempty : legendEntries d } data RangeRequest r = OtherDimDependantRange (Option (Interval r) -> Option (Interval r)) | MustBeThisRange (Interval r) instance (Ord r) => Semigroup (RangeRequest r) where MustBeThisRange r <> _ = MustBeThisRange r _ <> MustBeThisRange r = MustBeThisRange r OtherDimDependantRange r1 <> OtherDimDependantRange r2 = OtherDimDependantRange $ r1<>r2 instance (Ord r) => Monoid (RangeRequest r) where mempty = OtherDimDependantRange $ const mempty mappend = (<>) otherDimDependence :: (Interval r->Interval r) -> RangeRequest r otherDimDependence = OtherDimDependantRange . fmap atLeastInterval :: Interval r -> RangeRequest r atLeastInterval = atLeastInterval' . pure atLeastInterval' :: Option (Interval r) -> RangeRequest r atLeastInterval' = OtherDimDependantRange . const -- | 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 [] graphs'' = sortBy (comparing occlusiveness) graphs' 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.size 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 :: PlainGraphicsR2) $ dia drawWindow <- GTK.widgetGetDrawWindow drawA BGTK.renderToGtk drawWindow $ scaledDia 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@GraphWindowSpecR2{..} -> 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@GraphWindowSpecR2{..} -> 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@(GraphWindowSpecR2{..}) <- readIORef viewState let normaliseView :: PlainGraphicsR2 -> PlainGraphicsR2 normaliseView = (Dia.scaleX xUnZ :: PlainGraphicsR2->PlainGraphicsR2) . 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 textTK txSiz asp = TextTK defaultTxtStyle txSiz asp 0.2 0.2 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 case plt of Nothing -> return mempty Just Plot{..} -> let antTK = DiagramTK { viewScope = currentView , textTools = textTK txtSize aspect } txtSize = h * fontPts / fromIntegral yResolution aspect = w * fromIntegral yResolution / (h * fromIntegral xResolution) fontPts = 12 transform :: PlainGraphicsR2 -> PlainGraphicsR2 transform = normaliseView . clr where clr | Just c <- graphColor = Dia.lcA c . Dia.fcA c | otherwise = id in do renderedAnnot <- mapM (prerenderAnnotation antTK) plotAnnotations return . transform $ fold renderedAnnot <> getPlot gvStates <- readIORef graphs waitAny $ map (realtimeView . snd) gvStates thePlot <- (mconcat . reverse) <$> mapM renderComp (reverse gvStates) theLegend <- prerenderLegend (textTK 10 1) colourScheme $ (\(p,g) -> (,) <$> legendEntries p <*> [graphColor g]) =<< gvStates writeIORef dgStore $ ( theLegend & Dia.scaleX (0.1 / sqrt (fromIntegral xResolution)) & Dia.scaleY (0.1 / sqrt (fromIntegral yResolution)) & (`Dia.place`(0.75^&0.75)) ) <> thePlot 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 GraphWindowSpecR2 (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 GTK.onDestroy window $ do (readIORef graphs >>=) . mapM_ -- cancel remaining threads $ \(_, GraphViewState{..}) -> cancel realtimeView >> cancel nextTgtView GTK.mainQuit GTK.timeoutAdd mainLoop 100 GTK.mainGUI readIORef viewState autoDefaultView :: [DynamicPlottable] -> GraphWindowSpec autoDefaultView graphs = GraphWindowSpecR2 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 ) MustBeThisRange (Interval a b) `dependentOn` _ = (a,b) OtherDimDependantRange ξ `dependentOn` MustBeThisRange i = addMargin . defRng . ξ $ pure i OtherDimDependantRange ξ `dependentOn` OtherDimDependantRange υ = addMargin . defRng . ξ . pure . defRng $ υ mempty defRng = Interval (-1) 1 `option` id addMargin (Interval a b) = (a - q, b + q) where q = (b - a) / 6 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 -- | 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 = def{ relevantRange_y = otherDimDependence yRangef , isTintableMonochromic = True , axesNecessity = 1 , dynamicPlot = plot } where yRangef = onInterval $ \(l, r) -> ((!10) &&& (!70)) . sort . pruneOutlyers $ map f [l, l + (r-l)/80 .. r] plot (GraphWindowSpecR2{..}) = curve `deepseq` mkPlot (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." type (-->) = RWDiffable ℝ diffableFnPlot :: (∀ m . ( WithField ℝ PseudoAffine m , HasMetric (Needle (Interior m)) ) => AgentVal (-->) m ℝ -> AgentVal (-->) m ℝ ) -> DynamicPlottable diffableFnPlot f = plot fd where fd :: ℝ --> ℝ fd = alg f scrutiniseDiffability :: (∀ m . ( WithField ℝ PseudoAffine m , HasMetric (Needle (Interior m)) ) => AgentVal (-->) m ℝ -> AgentVal (-->) m ℝ ) -> DynamicPlottable scrutiniseDiffability f = plot [{-plot fd, -}dframe 0.2, dframe 0.02] where fd :: ℝ --> ℝ fd = alg f fscrut = analyseLocalBehaviour fd dframe rfh = def{ isTintableMonochromic = True , dynamicPlot = mkFrame } where mkFrame (GraphWindowSpecR2{..}) = case fscrut xm of Option (Just ((ym,y'm), δOδx²)) | Option (Just δx) <- δOδx² δy -> δx `seq` let frame = mconcat [ simpleLine ((xm-δx)^&(ym+yo-δx*y'm)) ((xm+δx)^&(ym+yo+δx*y'm)) | yo <- [-δy, δy] ] in mkPlot frame | otherwise -> y'm `seq` mkPlot ( simpleLine ((xm-δxdef)^&(ym-δxdef*y'm)) ((xm+δxdef)^&(ym+δxdef*y'm)) ) where xm = (rBound + lBound) / 2 δxdef = (rBound - lBound) / 10 δy = rfh * (tBound - bBound) -- | 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 prove -- 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 => AgentVal (:-->) m Double -> AgentVal (:-->) 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 => AgentVal (:-->) m Double -> (AgentVal (:-->) m Double, AgentVal (:-->) m Double)) -> DynamicPlottable paramPlot f = plot fc where fc :: Double :--> (Double, Double) fc = alg1to2 f continColourSurfaceFnPlot :: ((Double,Double) -> DCol.Colour Double) -> DynamicPlottable continColourSurfaceFnPlot f = def { axesNecessity = 1 , occlusiveness = 4 , dynamicPlot = plot } where plot (GraphWindowSpecR2{..}) = mkPlot $ Dia.place ( Dia.rasterDia cf (xResolution`div`4) (yResolution`div`4) & Dia.scaleX wPix & Dia.scaleY hPix ) ( ((lBound+rBound-wPix)/2) ^& ((tBound+bBound+hPix)/2) ) where cf i j = f ( lBound + wPix * fromIntegral i, tBound - hPix * fromIntegral j ) `Dia.withOpacity` 0.2 w = rBound - lBound; h = tBound - bBound wPix = w*4 / fromIntegral xResolution hPix = h*4 / fromIntegral yResolution 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 (GraphWindowSpecR2 {..}) = 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) ] -- | Coordinate axes with labels. For many plottable objects, these will be added -- automatically, by default (unless inhibited with 'noDynamicAxes'). dynamicAxes :: DynamicPlottable dynamicAxes = def { axesNecessity = superfluent , occlusiveness = 1 , dynamicPlot = plot } where plot gwSpec@(GraphWindowSpecR2{..}) = 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) noDynamicAxes :: DynamicPlottable noDynamicAxes = def { axesNecessity = superfluent } simpleLine :: P2 -> P2 -> PlainGraphicsR2 simpleLine = simpleLine' 2 simpleLine' :: Double -> P2 -> P2 -> PlainGraphicsR2 simpleLine' w p q = Dia.fromVertices [p,q] & Dia.lwO w autoDashLine :: Double -> P2 -> P2 -> PlainGraphicsR2 autoDashLine w p q = simpleLine' (max 1 w) p q & if w < 1 then Dia.dashingO [w*6, 3] 0 else id -- | 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 :: (Double, Double) -> DynamicPlottable -- | Like 'xInterval', this only affects what range is plotted. However, it doesn't merely -- request that a certain interval /should be visible/, but actually enforces particular -- values for the left and right boundary. Nothing outside the range will be plotted -- (unless there is another, contradicting 'forceXRange'). forceXRange :: (Double, Double) -> DynamicPlottable yInterval, forceYRange :: (Double, Double) -> DynamicPlottable xInterval (l,r) = mempty { relevantRange_x = atLeastInterval $ Interval l r } forceXRange (l,r) = mempty { relevantRange_x = MustBeThisRange $ Interval l r } yInterval (b,t) = mempty { relevantRange_y = atLeastInterval $ Interval b t } forceYRange (b,t) = mempty { relevantRange_y = MustBeThisRange $ Interval b t } -- | 'ViewXCenter', 'ViewYResolution' etc. can be used as arguments to some object -- you 'plot', if its rendering is to depend explicitly on the screen's visible range. -- You should not need to do that manually except for special applications (the -- standard plot objects like 'fnPlot' already take the range into account anyway) -- – e.g. comparing with the linear regression /of all visible points/ -- from some sample with some function's tangent /at the screen center/. -- -- @ -- plotWindow [fnPlot sin, plot $ \\(ViewXCenter xc) x -> sin xc + (x-xc) * cos xc] -- @ -- -- <> newtype ViewXCenter = ViewXCenter { getViewXCenter :: Double } instance (Plottable p) => Plottable (ViewXCenter -> p) where plot f = def { relevantRange_y = OtherDimDependantRange $ \g -> deescalate relevantRange_y g . plot . f . cxI =<< g , isTintableMonochromic = isTintableMonochromic fcxVoid , axesNecessity = axesNecessity fcxVoid , dynamicPlot = \g -> dynamicPlot (plot . f $ cx g) g } where cx (GraphWindowSpecR2{..}) = ViewXCenter $ (lBound+rBound)/2 cxI (Interval l r) = ViewXCenter $ (l+r)/2 fcxVoid = plot . f $ ViewXCenter 0.23421 -- Yup, it's magic. deescalate rfind otherdim p = case rfind p of MustBeThisRange i -> pure i OtherDimDependantRange ifr -> ifr otherdim newtype ViewYCenter = ViewYCenter { getViewYCenter :: Double } instance (Plottable p) => Plottable (ViewYCenter -> p) where plot f = def { relevantRange_x = OtherDimDependantRange $ \g -> deescalate relevantRange_x g . plot . f . cyI =<< g , isTintableMonochromic = isTintableMonochromic fcyVoid , axesNecessity = axesNecessity fcyVoid , dynamicPlot = \g -> dynamicPlot (plot . f $ cy g) g } where cy (GraphWindowSpecR2{..}) = ViewYCenter $ (bBound+tBound)/2 cyI (Interval b t) = ViewYCenter $ (b+t)/2 fcyVoid = plot . f $ ViewYCenter 0.319421 -- Alright, alright... the idea is to avoid exact equality with zero or any other number that might come up in some plot object, since such an equality can lead to div-by-zero problems. deescalate rfind otherdim p = case rfind p of MustBeThisRange i -> pure i OtherDimDependantRange ifr -> ifr otherdim newtype ViewWidth = ViewWidth { getViewWidth :: Double } instance (Plottable p) => Plottable (ViewWidth -> p) where plot f = def { relevantRange_y = OtherDimDependantRange $ \g -> deescalate relevantRange_y g . plot . f . wI =<< g , isTintableMonochromic = isTintableMonochromic fwVoid , axesNecessity = axesNecessity fwVoid , dynamicPlot = \g -> dynamicPlot (plot . f $ w g) g } where w (GraphWindowSpecR2{..}) = ViewWidth $ rBound - lBound wI (Interval l r) = ViewWidth $ r - l fwVoid = plot . f $ ViewWidth 2.142349 deescalate rfind otherdim p = case rfind p of MustBeThisRange i -> pure i OtherDimDependantRange ifr -> ifr otherdim newtype ViewHeight = ViewHeight { getViewHeight :: Double } instance (Plottable p) => Plottable (ViewHeight -> p) where plot f = def { relevantRange_x = OtherDimDependantRange $ \g -> deescalate relevantRange_x g . plot . f . hI =<< g , isTintableMonochromic = isTintableMonochromic fhVoid , axesNecessity = axesNecessity fhVoid , dynamicPlot = \g -> dynamicPlot (plot . f $ h g) g } where h (GraphWindowSpecR2{..}) = ViewHeight $ tBound - bBound hI (Interval b t) = ViewHeight $ t - b fhVoid = plot . f $ ViewHeight 1.494213 deescalate rfind otherdim p = case rfind p of MustBeThisRange i -> pure i OtherDimDependantRange ifr -> ifr otherdim newtype ViewXResolution = ViewXResolution { getViewXResolution :: Int } newtype ViewYResolution = ViewYResolution { getViewYResolution :: Int } atExtendOf :: PlainGraphicsR2 -> PlainGraphicsR2 -> PlainGraphicsR2 atExtendOf d₁ = atExtendOf' d₁ 1 atExtendOf' :: PlainGraphicsR2 -> Double -> PlainGraphicsR2 -> PlainGraphicsR2 atExtendOf' d₁ q d₂ = d₂ & Dia.translate ((pux+plx-lux-llx)/2 ^& (puy+ply-luy-lly)/2) & Dia.scaleX (q*(pux-plx)/(lux-llx)) & Dia.scaleY (q*(puy-ply)/(luy-lly)) where (Just (plx,pux)) = Dia.extentX d₁; (Just (ply,puy)) = Dia.extentY d₁ (Just (llx,lux)) = Dia.extentX d₂; (Just (lly,luy)) = Dia.extentY d₂