-- | -- 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 #-} {-# LANGUAGE TemplateHaskell #-} module Graphics.Dynamic.Plot.R2 ( -- * Interactive display plotWindow -- * Plottable objects -- ** Class , Plottable(..) -- ** Simple function plots , fnPlot, paramPlot , continFnPlot , tracePlot , lineSegPlot , linregressionPlot , PlainGraphicsR2 , shapePlot , diagramPlot -- ** Computation in progress , plotLatest -- * Plot-object attributes -- ** Colour , tint, autoTint -- ** Legend captions , legendName -- ** Animation , plotDelay -- * Viewport -- ** View selection , xInterval, yInterval, forceXRange, forceYRange -- ** View dependence , ViewXCenter(..), ViewYCenter(..), ViewWidth(..), ViewHeight(..) , ViewXResolution(..), ViewYResolution(..) -- * Auxiliary plot objects , dynamicAxes, noDynamicAxes -- * The plot type , DynamicPlottable , tweakPrerendered ) 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 Data.Colour.Names as DCol import qualified Codec.Picture as JPix import qualified Codec.Picture.Types as JPix 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, lift) import Control.Monad.ST import Data.STRef 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.Lens.TH(makeLenses) import Control.Concurrent (runInBoundThread, threadDelay, ThreadId, forkIO, killThread) import Control.Concurrent.MVar import Control.DeepSeq import Control.Exception (evaluate) import Data.List (foldl', sort, sortBy, partition, zip4) import qualified Data.List.NonEmpty as NE import Data.List.NonEmpty (NonEmpty (..)) import qualified Data.Vector as Arr import Data.Maybe import Data.Semigroup import Data.Default import Data.Foldable (fold, foldMap) import qualified Data.Foldable as Hask import Data.Function (on) import Data.Ord (comparing) import Data.VectorSpace import Math.LinearMap.Category import Data.Basis import Data.AffineSpace import Data.Manifold.PseudoAffine import Data.Function.Differentiable import Data.Manifold.Types import Data.Manifold.Shade import Data.Manifold.TreeCover import Data.Manifold.Web import Data.Manifold.Riemannian (Geodesic, pointsBarycenter) import qualified Data.Map.Lazy as Map import qualified Data.Colour.Manifold as CSp import qualified Data.Random as Random import qualified System.Random as Random import qualified Data.Random.Manifold import Data.IORef import System.IO import System.Exit import System.Process import Data.Time data Plot = Plot { _plotAnnotations :: [Annotation] , _getPlot :: PlainGraphicsR2 } makeLenses ''Plot data RangeRequest r = OtherDimDependantRange (Maybe (Interval r) -> Maybe (Interval r)) | MustBeThisRange (Interval r) type GraphWindowSpec = GraphWindowSpecR2 data DynamicPlottable' m = DynamicPlottable { _relevantRange_x, _relevantRange_y :: RangeRequest R , _inherentColours :: [DCol.Colour ℝ] , _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 , _frameDelay :: NominalDiffTime , _legendEntries :: [LegendEntry] , _futurePlots :: Maybe (DynamicPlottable' m) , _dynamicPlot :: GraphWindowSpec -> m Plot } makeLenses ''DynamicPlottable' type DynamicPlottable = DynamicPlottable' Random.RVar type AnnotPlot = (Plot, [LegendEntry]) data ObjInPlot = ObjInPlot { _lastStableView :: IORef (Maybe (GraphWindowSpec, AnnotPlot)) , _newPlotView :: MVar (GraphWindowSpec, AnnotPlot) , _plotObjColour :: Maybe AColour , _originalPlotObject :: DynamicPlottable } makeLenses ''ObjInPlot 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 p) => Plottable [p] where plot = foldMap plot instance (Plottable p) => Plottable (Option p) where plot = foldMap plot instance (Plottable p) => Plottable (Maybe p) where plot = foldMap plot instance Plottable PlainGraphics where plot (PlainGraphics d) = def & relevantRange_x .~ atLeastInterval rlx & relevantRange_y .~ atLeastInterval rly & inherentColours .~ [DCol.grey] & axesNecessity .~ -1 & dynamicPlot .~ pure.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 & inherentColours .~ [] & axesNecessity .~ 0 -- | Plot a generic 'Dia.Diagram'. diagramPlot :: PlainGraphicsR2 -> DynamicPlottable diagramPlot d = plot $ PlainGraphics d metricFromLength :: ∀ s . RealFrac' s => s -> Norm s metricFromLength l | l>0 = case closedScalarWitness :: ClosedScalarWitness s of ClosedScalarWitness -> spanNorm [1 / l] instance Plottable (R-->R) where plot f = def & relevantRange_y .~ OtherDimDependantRange yRangef & autoTint & axesNecessity .~ 1 & dynamicPlot .~ pure.plot where yRangef Nothing = Nothing yRangef (Just (Interval l r)) = case intervalImages 100 ( const . metricFromLength $ (r-l)/16 , const $ metricFromLength 0.0001 ) ( alg (\x -> ( point l? (f$~x) ))) of ([],[]) -> Nothing (liv,riv) -> pure . foldr1 (<>) . map (uncurry Interval . snd) $ take 4 liv ++ take 4 riv plot gs@(GraphWindowSpecR2{..}) = curves `deepseq` mkPlot (foldMap trace curves) where curves :: [[P2]] curves = map (map $ convℝ² . snd) . gatherSides $ discretisePathSegs 10000 ( const . metricFromLength $ (rBound-lBound)/fromIntegral xResolution , coerceMetric $ resolutionFunction gs ) ((id&&&f) . alg (\x -> ( point lBound? x ))) trace (p:q:ps) = simpleLine p q <> trace (q:ps) trace _ = mempty gatherSides = uncurry (++) . (take 50 *** take 50) convℝ² = Dia.p2 c = realToFrac instance Plottable (R-->(R,R)) where plot f = def & relevantRange_y .~ mempty & autoTint & axesNecessity .~ 1 & dynamicPlot .~ pure.plot where plot gs@(GraphWindowSpecR2{..}) = curves `deepseq` mkPlot (foldMap trace curves) where curves :: [[P2]] curves = map (map $ convℝ² . snd) . gatherSides $ discretisePathSegs 1000 ( const . metricFromLength $ 1/100 , coerceMetric $ resolutionFunction gs ) f trace (p:q:ps) = simpleLine p q <> trace (q:ps) trace _ = mempty gatherSides = uncurry (++) . (take 50 *** take 50) convℝ² = Dia.p2 c = realToFrac resolutionFunction :: GraphWindowSpecR2 -> RieMetric ℝ² resolutionFunction GraphWindowSpecR2{..} = resoFunc where w = rBound - lBound; h = tBound - bBound ε = spanNorm [(recip δx^&0), (0^&recip δy)] δx = w / fromIntegral xResolution δy = h / fromIntegral yResolution resoFunc (DiaTypes.V2 x y) | x >= lBound, x <= rBound, y >= bBound, y <= tBound = ε | otherwise = spanNorm [(recip qx^&0), (0^&recip 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) & autoTint & axesNecessity .~ 1 & dynamicPlot .~ plot where xr = wsp * fromIntegral gSplN plot (GraphWindowSpecR2{..}) = pure . 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 (|$|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 & autoTint & axesNecessity .~ 1 & dynamicPlot .~ plot where plot (GraphWindowSpecR2{..}) = pure . 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 = let v' = turnLeft v in v' ^* (σ|$|v') trStRange (Right pts) = (`foldMap`pts) $ \(p, DevBoxes dv _) -> let δxm = dv |$| 1^&0 δym = dv |$| 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 mempty 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' | null ps = mempty & autoTint | otherwise = def & relevantRange_x .~ atLeastInterval' ( getOption $ foldMap (pure . spInterval . fst) (concat ps) ) & relevantRange_y .~ atLeastInterval' ( getOption $ foldMap (pure . spInterval . snd) (concat ps) ) & autoTint & axesNecessity .~ 1 & dynamicPlot .~ pure . plot where plot (GraphWindowSpecR2{..}) = mkPlot (foldMap trace ps) where trace (p:q:ps) = simpleLine (Dia.p2 p) (Dia.p2 q) <> trace (q:ps) trace _ = mempty ps = filter ((>1) . length) $ safeSeg ps' safeSeg [] = [[]] safeSeg ((x,y):l) | x==x && not (isInfinite x) && y==y && not (isInfinite y) = case safeSeg l of { h:r -> ((x,y):h):r } | otherwise = [] : safeSeg l 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 -> [DualVector 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 | sum (normSq dev<$>δs) > 1/4 || (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 & autoTint & axesNecessity .~ 1 & dynamicPlot .~ plot where plot _ = pure . mkPlot $ foldMap axLine eigVs where axLine eigV = simpleLine (ctr .-~^ eigV) (ctr .+~^ eigV) (xRange,yRange) = shadeExtends shade ctr = shade^.shadeCtr eigVs = normSpanningSystem $ shade^.shadeExpanse instance Plottable (Shade ℝ²) where plot (Shade v e) = plot (Shade (Dia.P v) e :: Shade P2) instance Plottable (Shade (R,R)) where plot sh = plot (coerceShade sh :: Shade R2) instance Plottable (Shade' (R,R)) where plot shade = def & autoTint & axesNecessity .~ 1 & dynamicPlot .~ plot where plot wSpec = pure . mkPlot $ Dia.circle 1 & Dia.scaleX w₁ & Dia.scaleY w₂ & Dia.rotate ϑ & Dia.opacity 0.2 & Dia.moveTo ctr where [w₁,w₂] = recip . sqrt . max (recip $ 100 * max ((wSpec^.windowDiameter)^2) ctrDistance) . fst <$> [ev₁, ev₂] ctrDistance = distanceSq (shade^.shadeCtr) (wSpec^.windowCenter) ctr = Dia.p2 $ shade^.shadeCtr Norm expanr = shade^.shadeNarrowness [ev₁@(_,(e₁x,e₁y)),ev₂] = case eigen $ arr expanr of (e₁:e₂:_) -> [e₁,e₂] [e@(_,(vx,vy))] -> [e, (0,(-vx,vy))] [] -> [(0,(1,0)), (0,(0,1))] ϑ = atan2 e₁y e₁x Dia.@@ Dia.rad instance Plottable (ConvexSet ℝ²) where plot EmptyConvex = mempty plot (ConvexSet hull intersects) = plot (ConvexSet (coerceShade hull) (coerceShade<$>intersects) :: ConvexSet (ℝ,ℝ)) instance Plottable (ConvexSet (R,R)) where plot EmptyConvex = mempty plot (ConvexSet hull intersects) = plot [ plot intersects & tweakPrerendered (Dia.opacity (1 / fromIntegral (length intersects)) ) , plot hull & tweakPrerendered ( Dia.lwO 3 >>> Dia.opacity 1 >>> Dia.fcA (Dia.withOpacity Dia.grey 0.01) ) ] instance Plottable (Shade' ℝ²) where plot sh = plot (coerceShade sh :: Shade' (ℝ,ℝ)) instance Plottable (Shade' P2) where plot (Shade' (Dia.P v) e) = plot (Shade' v e :: Shade' ℝ²) instance Plottable (Shaded ℝ ℝ) where plot tr | length trivs' >= 2 = def & relevantRange_x .~ atLeastInterval (Interval xmin xmax) & relevantRange_y .~ atLeastInterval (Interval ymin ymax) & autoTint & axesNecessity .~ 1 & dynamicPlot .~ plot where plot grWS@(GraphWindowSpecR2{..}) = pure . mkPlot $ foldMap parallelogram trivs <> (foldMap (singlePointFor grWS) leafPoints -- & Dia.dashingO [2,3] 0 & Dia.opacity 0.4 ) where parallelogram ((x,δx), ((y,δy), j)) = lLoop [ (x+δx)^&(y+δy+jδx), (x-δx)^&(y+δy-jδx) , (x-δx)^&(y-δy-jδx), (x+δx)^&(y-δy+jδx) ] & Dia.strokeLocLoop & Dia.opacity 0.3 where jδx = j $ δx trivs' = sortBy (comparing fst) $ stiAsIntervalMapping tr trivs = NE.fromList $ ccδs trivs' where ccδs [(x, yq), (x', yq')] = [((x,δx),yq), ((x',δx),yq')] where δx = (x' - x)/2 ccδs [(x, yq), (x', yq'), (x'', yq'')] = [((x,δx),yq), ((x',δx),yq'), ((x'',δx),yq'')] where δx = (x'' - x)/4 ccδs ((x, yq) : xyqs@((x', yq') : (x'', _) : _)) = ((x,δx),yq) : ((x',δx),yq') : tail (ccδs xyqs) where δx = (x'' - x)/4 [xmin, ymin, xmax, ymax] = [minimum, maximum]<*>[_topological<$>allLeaves, _untopological<$>allLeaves] lLoop ps@(p:_) = Dia.fromVertices $ ps++[p] leafPoints = sortBy (comparing (^._x)) $ (\(x`WithAny`y) -> y^&x) <$> allLeaves allLeaves = onlyLeaves tr plot _ = def instance Plottable (PointsWeb ℝ (Shade' ℝ)) where plot web | length locals >= 2 = def & relevantRange_x .~ atLeastInterval (Interval xmin xmax) & relevantRange_y .~ atLeastInterval (Interval ymin ymax) & autoTint & axesNecessity .~ 1 & dynamicPlot .~ pure . plot where plot grWS@(GraphWindowSpecR2{..}) = mkPlot $ foldMap parallelogram trivs <> foldMap vbar divis where parallelogram ((x,(δxl,δxr)), ((y,δy), j)) = lLoop [ (x+δxr)^&(y+δy+jδxr), (x-δxl)^&(y+δy-jδxl) , (x-δxl)^&(y-δy-jδxl), (x+δxr)^&(y-δy+jδxr) ] & Dia.strokeLocLoop & Dia.opacity 0.3 where jδxl = j $ δxl jδxr = j $ δxr vbar (x,(δxl,δxr)) = Dia.fromVertices [ (x-δxl)^&tBound, (x-δxl)^&bBound , (x+δxr)^&bBound, (x+δxr)^&tBound ] trivs :: [((ℝ, (Diff ℝ,Diff ℝ)), ((ℝ, Diff ℝ), LocalLinear ℝ ℝ))] divis :: [(ℝ, (Diff ℝ,Diff ℝ))] (trivs,divis) = concat***concat $ unzip (map mkTriv locals) where mkTriv :: ((ℝ, Shade' ℝ), [(ℝ, Shade' ℝ)]) -> ( [((ℝ, (Diff ℝ,Diff ℝ)), ((ℝ, Diff ℝ), LocalLinear ℝ ℝ))] , [(ℝ, (Diff ℝ,Diff ℝ))] ) mkTriv ((xc,Shade' yc yce), [(δxo, Shade' yo _)]) = case findNormalLength yce of Just ry -> ( [ ( (xc, dirSort 0 δxo) , ( (yc, ry) , id ^* ((yo-yc)/δxo) ) ) ], [] ) Nothing -> ( [], [(xc, dirSort 0 δxo)] ) mkTriv ((xc,Shade' yc yce), [(δxl, Shade' yl _), (δxr, Shade' yr _)]) = case findNormalLength yce of Just ry -> ( [ ( (xc, dirSort δxl δxr) , ( (yc, ry) , id ^* η ) ) ], [] ) Nothing -> ( [], [(xc, dirSort δxl δxr)] ) where δxg = (δxr - δxl)/2 η = (yr - yl)/(2*δxg) mkTriv (p,lrs) = concat***concat $ unzip [mkTriv (p,[l,r]) | l<-ls, r<-rs] where (ls,rs) = partition ((<0) . fst) lrs dirSort δ₁ δ₂ | δ₁ < δ₂ = (-δ₁, δ₂) | otherwise = (-δ₂, δ₁) lLoop ps@(p:_) = Dia.fromVertices $ ps++[p] [xmin, ymin, xmax, ymax] = [minimum, maximum]<*>[fst.fst<$>locals, (^.shadeCtr).snd.fst<$>locals] locals :: [((ℝ, Shade' ℝ), [(ℝ, Shade' ℝ)])] locals = Hask.toList $ localFocusWeb web plot _ = def instance Plottable (PointsWeb ℝ² (CSp.Colour ℝ)) where plot web = plot (coerceWebDomain web :: PointsWeb (ℝ,ℝ) (CSp.Colour ℝ)) instance Plottable (PointsWeb (ℝ,ℝ) (CSp.Colour ℝ)) where plot = webbedSurfPlot $ pure . toRGBA where toRGBA (Just c) = JPix.promotePixel (CSp.quantiseColour c :: JPix.PixelRGB8) toRGBA _ = JPix.PixelRGBA8 0 0 0 0 instance Plottable (PointsWeb ℝ² (Shade (CSp.Colour ℝ))) where plot web = plot (coerceWebDomain web :: PointsWeb (ℝ,ℝ) (Shade (CSp.Colour ℝ))) instance Plottable (PointsWeb (ℝ,ℝ) (Shade (CSp.Colour ℝ))) where plot = webbedSurfPlot $ toRGBA where toRGBA (Just c) = JPix.promotePixel . (CSp.quantiseColour :: CSp.Colour ℝ -> JPix.PixelRGB8) <$> Random.rvar c toRGBA _ = return $ JPix.PixelRGBA8 0 0 0 0 webbedSurfPlot :: Geodesic a => (Maybe a -> Random.RVar JPix.PixelRGBA8) -> PointsWeb (ℝ,ℝ) a -> DynamicPlottable webbedSurfPlot toRGBA web = def & dynamicPlot .~ plotWeb & relevantRange_x .~ atLeastInterval (x₀...x₁) & relevantRange_y .~ atLeastInterval (y₀...y₁) & occlusiveness .~ 4 where plotWeb graSpec = do pixRendered <- pixRender pure . mkPlot $ (Dia.image $ Dia.DImage (Dia.ImageRaster $ JPix.ImageRGBA8 pixRendered) renderWidth renderHeight placement) cartesianed = sampleEntireWeb_2Dcartesian_lin web renderWidth renderHeight renderWidth = 120 -- xResolution graSpec renderHeight = 90 -- yResolution graSpec x₀ = minimum (fst<$>pts) x₁ = maximum (fst<$>pts) y₀ = minimum (snd<$>pts) y₁ = maximum (snd<$>pts) pts = fst . fst <$> Hask.toList (localFocusWeb web) xc = (x₀+x₁)/2 yc = (y₀+y₁)/2 wPix = (x₁ - x₀)/renderWidth hPix = (y₁ - y₀)/renderHeight placement = Dia.translation (xc^&yc) <> Dia.scalingX wPix <> Dia.scalingY hPix pixRender = do seed <- Random.mkStdGen <$> Random.stdUniform return $ runST (do randomGen <- newSTRef seed cursorState <- newSTRef (0, reverse cartesianed) JPix.withImage renderWidth renderHeight $ \_ix iy -> do (iyPrev, (y, xvs) : yvs) <- readSTRef cursorState vc <- if iy > iyPrev then case yvs of ((y',(_x,vc):xvs') : yvs') -> do writeSTRef cursorState (iy, (y', xvs') : yvs') return vc else case xvs of ((_x,vc) : xvs') -> do writeSTRef cursorState (iy, (y, xvs') : yvs) return vc rg <- readSTRef randomGen let (c, rg') = Random.sampleState (toRGBA vc) rg writeSTRef randomGen rg' return c ) instance (Plottable x) => Plottable (Latest x) where plot (Latest (ev₀ :| [])) = plot ev₀ plot (Latest (ev₀ :| ev₁:evs)) = plot ev₀ & futurePlots .~ (Just . plot . Latest $ ev₁:|evs) plotLatest :: Plottable x => [x] -> DynamicPlottable plotLatest (x:xs) = plot $ Latest (x:|xs) plotLatest l = plot l 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 & autoTint & axesNecessity .~ 1 & dynamicPlot .~ plot where plot _ = pure . 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 instance Plottable (Trees R2) where plot = plot . fmap Dia.P instance Plottable (SimpleTree (R,R)) where plot = plot . fmap (\(x,y) -> DiaTypes.p2 (x,y)) instance Plottable (Trees (R,R)) where plot (GenericTree ts) = plot $ (GenericTree . Just) <$> ts instance Plottable (SimpleTree (R`WithAny`R)) where plot = plot . fmap (\(WithAny y x) -> DiaTypes.p2 (x,y)) instance Plottable (Trees (R`WithAny`R)) where plot (GenericTree ts) = plot $ (GenericTree . Just) <$> ts pixelDim :: GraphWindowSpecR2 -> (R, R) pixelDim grWS = ( graphWindowWidth grWS / fromIntegral (xResolution grWS) , graphWindowHeight grWS / fromIntegral (yResolution grWS) ) singlePointFor :: GraphWindowSpecR2 -> P2 -> PlainGraphicsR2 singlePointFor spec = Dia.place circ where (pxw,pxh) = pixelDim spec circ = Dia.circle 1 & Dia.scaleX pxw & Dia.scaleY pxh 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 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 instance Semigroup DynamicPlottable where DynamicPlottable rx₁ ry₁ tm₁ oc₁ ax₁ dl₁ le₁ fu₁ dp₁ <> DynamicPlottable rx₂ ry₂ tm₂ oc₂ ax₂ dl₂ le₂ fu₂ dp₂ = DynamicPlottable (rx₁<>rx₂) (ry₁<>ry₂) (tm₁++tm₂) (oc₁+oc₂) (ax₁+ax₂) (max dl₁ dl₂) (le₁++le₂) ((<>)<$>fu₁<*>fu₂) (liftA2(<>)<$>dp₁<*>dp₂) instance Monoid DynamicPlottable where mempty = DynamicPlottable mempty -- don't request any range mempty [] -- no colours 0 -- neither obscures anything nor has details that could be obscured 0 -- don't need axis (but don't mind them either) (1/20) -- 20 fps is at the moment the fastest enabled refresh rate anyway [] -- no legend entries mempty -- no time-evolution (const $ pure mempty) mappend = (<>) instance Default DynamicPlottable where def = mempty -- | Set the caption for this plot object that should appear in the -- plot legend. legendName :: String -> DynamicPlottable -> DynamicPlottable legendName n = legendEntries %~ (LegendEntry (PlainText n) mempty :) >>> futurePlots %~ fmap (legendName n) -- | Colour this plot object in a fixed shade. tint :: DCol.Colour ℝ -> DynamicPlottable -> DynamicPlottable tint col = inherentColours .~ [col] >>> dynamicPlot %~ fmap (fmap $ getPlot %~ Dia.lc col . Dia.fc col) -- | Allow the object to be automatically assigned a colour that's otherwise -- unused in the plot. (This is the default for most plot objects.) autoTint :: DynamicPlottable -> DynamicPlottable autoTint = inherentColours .~ [] 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 Nothing mappend = (<>) otherDimDependence :: (Interval r->Interval r) -> RangeRequest r otherDimDependence = OtherDimDependantRange . fmap atLeastInterval :: Interval r -> RangeRequest r atLeastInterval = atLeastInterval' . pure atLeastInterval' :: Maybe (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. -- -- ATTENTION: the window may sometimes freeze, especially when displaying -- complicated functions with 'fnPlot` from ghci. This is apparently -- a kind of deadlock problem with one of the C libraries that are invoked, -- At the moment, we can recommend no better solution than to abort and restart ghci -- (or what else you use – iHaskell kernel, process, ...) if this occurs. plotWindow :: [DynamicPlottable] -> IO GraphWindowSpec plotWindow [] = plotWindow [dynamicAxes] plotWindow givenPlotObjs = runInBoundThread $ do let defColourScheme = defaultColourScheme viewState <- newIORef $ autoDefaultView givenPlotObjs viewTgt <- newIORef =<< readIORef viewState viewTgtGlobal <- newMVar =<< readIORef viewState screenResolution <- newIORef (640, 480) dgStore <- newIORef mempty (plotObjs, cancelWorkers) :: ([ObjInPlot], IO ()) <- do let assignPlObjPropties :: [DynamicPlottable] -> [Colour] -> Necessity -> IO [(ObjInPlot, ThreadId)] assignPlObjPropties [] _ axesNeed | axesNeed > 0 = assignPlObjPropties [dynamicAxes] [grey] (-1) | otherwise = return [] assignPlObjPropties (o:os) (c:cs) axn = do newDia <- newEmptyMVar workerId <- forkIO $ objectPlotterThread o viewTgtGlobal newDia stableView <- newIORef Nothing ((ObjInPlot stableView newDia cl o, workerId) :) <$> assignPlObjPropties os cs' (axn + o^.axesNecessity) where (cl, cs') | null (o^.inherentColours) = (Just $ defColourScheme c, cs) | otherwise = (Nothing, c:cs) (pObs, workerId) <- unzip <$> assignPlObjPropties givenPlotObjs defaultColourSeq 0 return ( sortBy (comparing $ _occlusiveness . _originalPlotObject) pObs , forM_ workerId killThread ) GTK.initGUI window <- GTK.windowNew mouseAnchor <- newIORef Nothing 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 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.buttonPressEvent . Event.tryEvent $ do Event.eventButton >>= guard.(==defaultDragButton) anchXY <- Event.eventCoordinates liftIO . writeIORef mouseAnchor $ Just anchXY GTK.on drawA GTK.buttonReleaseEvent . Event.tryEvent $ do Event.eventButton >>= guard.(==defaultDragButton) liftIO . writeIORef mouseAnchor $ Nothing GTK.on drawA GTK.motionNotifyEvent . Event.tryEvent $ do liftIO (readIORef mouseAnchor) >>= \case Just (oldX,oldY) -> do (mvX,mvY) <- Event.eventCoordinates (canvasX,canvasY) <- liftIO $ GTK.widgetGetSize drawA let ηX = (oldX-mvX) / fromIntegral canvasX ηY = (mvY-oldY) / fromIntegral canvasY liftIO . modifyIORef viewTgt $ \view@GraphWindowSpecR2{..} -> let w = rBound - lBound h = tBound - bBound in view{ lBound = lBound + w * ηX , rBound = rBound + w * ηX , tBound = tBound + h * ηY , bBound = bBound + h * ηY } liftIO . modifyIORef mouseAnchor . fmap $ const (mvX,mvY) Nothing -> mzero GTK.widgetAddEvents drawA [GTK.ButtonMotionMask] 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 liftIO . modifyIORef viewTgt $ \view@GraphWindowSpecR2{..} -> let w = rBound - lBound h = tBound - bBound ηl = (rcX + 1)^2/4; ηr = (rcX - 1)^2/4 ηb = (rcY + 1)^2/4; ηt = (rcY - 1)^2/4 ηh = (1-ηt) * (1-ηb) + ηl + ηr ηv = (1-ηl) * (1-ηr) + ηt + ηb in case defaultScrollBehaviour scrollD of ScrollZoomIn -> view{ lBound = lBound + w * ηl * ηh * scrollZoomStrength , rBound = rBound - w * ηr * ηh * scrollZoomStrength , tBound = tBound - h * ηt * ηv * scrollZoomStrength , bBound = bBound + h * ηb * ηv * scrollZoomStrength } ScrollZoomOut -> view{ lBound = lBound - w * ηr * ηh * scrollZoomStrength , rBound = rBound + w * ηl * ηh * scrollZoomStrength , tBound = tBound + h * ηb * ηv * scrollZoomStrength , bBound = bBound - h * ηt * ηv * scrollZoomStrength } GTK.set window [ GTK.windowTitle := "Plot" , GTK.windowDefaultWidth := defResX , GTK.windowDefaultHeight := defResY , GTK.containerChild := drawA ] GTK.widgetShowAll window return $ GTK.widgetQueueDraw drawA t₀ <- getCurrentTime lastFrameTime <- newIORef t₀ 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 plotObj = do plt <- tryTakeMVar (plotObj^.newPlotView) >>= \case Nothing -> fmap snd <$> readIORef (plotObj^.lastStableView) newDia -> do writeIORef (plotObj^.lastStableView) newDia return $ snd <$> newDia case plt of Nothing -> return mempty Just (Plot{..}, objLegend) -> 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 <- plotObj^.plotObjColour = Dia.lcA c . Dia.fcA c | otherwise = id in do renderedAnnot <- mapM (prerenderAnnotation antTK) _plotAnnotations return (transform $ fold renderedAnnot <> _getPlot, objLegend) (thisPlots, thisLegends) <- unzip . reverse <$> mapM renderComp (reverse plotObjs) let thePlot = mconcat thisPlots theLegend <- prerenderLegend (textTK 10 1) colourScheme $ (\(g,l) -> (,) <$> l <*> [g^.plotObjColour] ) =<< zip plotObjs thisLegends 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 modifyMVar_ viewTgtGlobal . const $ return vt modifyIORef viewState $ \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 GTK.onDestroy window $ do cancelWorkers GTK.mainQuit GTK.timeoutAdd mainLoop 50 GTK.mainGUI readIORef viewState objectPlotterThread :: DynamicPlottable -> MVar GraphWindowSpec -> MVar (GraphWindowSpec, (Plot, [LegendEntry])) -> IO () objectPlotterThread pl₀ viewVar diaVar = loop pl₀ where loop pl = do tPrev <- getCurrentTime view <- readMVar viewVar diagram <- evaluate =<< Random.runRVar (pl^.dynamicPlot $ view) Random.StdRandom putMVar diaVar (view, (diagram, pl^.legendEntries)) waitTill $ addUTCTime (pl^.frameDelay) tPrev case pl^.futurePlots of Just pl' -> loop pl' Nothing -> loop pl 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 ) dependentOn :: RangeRequest R -> RangeRequest R -> (R,R) 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 Nothing defRng (Just (Interval a b)) | b>a = Interval a b defRng _ = Interval (-1) 1 -- ad-hoc hack to catch NaNs etc.. 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 defaultDragButton :: Event.MouseButton defaultDragButton = Event.MiddleButton scrollZoomStrength :: Double scrollZoomStrength = 1/20 -- | 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 prove 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 & autoTint & axesNecessity .~ 1 & dynamicPlot .~ pure . plot where yRangef = onInterval $ \(l, r) -> ((!%0.1) &&& (!%0.9)) . 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!%η = case length l of ll | ll<2 -> error "Function appears to yield NaN most of the time. Cannot be plotted." | otherwise -> l !! floor (fromIntegral ll * η) type (-->) = RWDiffable ℝ -- | 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 / cos (sqrt x))@ will work. -- -- Under the hood this uses the category of region-wise differentiable functions, -- 'RWDiffable', to prove that no details are omitted (like small high-frequency -- bumps). Note that this can become difficult for contrived cases like @cos(1/sin x)@ -- – while such functions will never come out with aliasing artifacts, they also -- may not come out quickly at all. (But for well-behaved functions, using the -- differentiable category actually tends to be more effective, because the algorithm -- immediately sees when it can describe an almost-linear region with only a few line -- segments.) -- -- This function is equivalent to using 'plot' on an 'RWDiffable' arrow. fnPlot :: (∀ m . Object (RWDiffable ℝ) m => AgentVal (-->) m ℝ -> AgentVal (-->) m ℝ ) -> DynamicPlottable fnPlot f = plot fd where fd :: ℝ --> ℝ fd = alg f uncertainFnPlot :: ∀ m . (SimpleSpace m, Scalar m ~ ℝ) => (ℝ -> (m +> ℝ)) -> Shade' m -> DynamicPlottable uncertainFnPlot = case linearManifoldWitness :: LinearManifoldWitness m of LinearManifoldWitness BoundarylessWitness -> \mfun (Shade' mBest me) -> plot $ continFnPlot (($ mBest) . mfun) : [ tweakPrerendered (Dia.opacity 0.2) $ continFnPlot (($ mBest^+^σ*^δm) . mfun) | δm <- normSpanningSystem' me , σ <- [-1,1] ] linregressionPlot :: ∀ x m y . ( SimpleSpace m, Scalar m ~ ℝ, y ~ ℝ, x ~ ℝ ) => (x -> (m +> y)) -> [(x, Shade' y)] -> (Shade' m -> DynamicPlottable -> DynamicPlottable -> DynamicPlottable) -> DynamicPlottable linregressionPlot = lrp (linearManifoldWitness, dualSpaceWitness) where lrp :: (LinearManifoldWitness m, DualSpaceWitness m) -> (x -> (m +> y)) -> [(x, Shade' y)] -> (Shade' m -> DynamicPlottable -> DynamicPlottable -> DynamicPlottable) -> DynamicPlottable lrp _ _ [] _ = mempty lrp (LinearManifoldWitness BoundarylessWitness, DualSpaceWitness) mfun dataPts resultHook = resultHook shm (plot [ plot (Shade (x,y) (sumSubspaceNorms mempty $ dualNorm ey) :: Shade (ℝ,ℝ)) | (x, Shade' y ey) <- dataPts ]) (uncertainFnPlot mfun shm) where (mBest, mDevs) = linearRegressionWVar (mfun . (bcx.+~^)) [ (δx,(fromInterior y,ey)) | (x,Shade' y ey)<-dataPts , let Just δx = x.-~.bcx ] Just bcx = (pointsBarycenter . NE.fromList $ fst<$>dataPts) shm :: Shade' m shm@(Shade' _ em) = dualShade . coverAllAround mBest $ convexPolytopeRepresentatives mDevs -- | Plot a continuous, “parametric function”, i.e. mapping the real line to a path in ℝ². paramPlot :: (∀ m . ( WithField ℝ PseudoAffine m, SimpleSpace (Needle m) ) => AgentVal (-->) m ℝ -> (AgentVal (-->) m ℝ, AgentVal (-->) m ℝ) ) -> DynamicPlottable paramPlot f = plot fd where fd :: ℝ --> (ℝ,ℝ) fd = alg1to2 f scrutiniseDiffability :: (∀ m . ( WithField ℝ PseudoAffine m , SimpleSpace (Needle 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 & autoTint & dynamicPlot .~ pure . mkFrame where mkFrame (GraphWindowSpecR2{..}) = case fscrut xm of Just ((ym,y'm), δOδx²) | 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 ( autoDashLine 0.5 ((xm-δxdef)^&(ym-δxdef*y'm)) ((xm+δxdef)^&(ym+δxdef*y'm)) ) _ -> mempty where xm = (rBound + lBound) / 2 δxdef = (rBound - lBound) / 10 δy = rfh * (tBound - bBound) continColourSurfaceFnPlot :: ((Double,Double) -> DCol.Colour Double) -> DynamicPlottable continColourSurfaceFnPlot f = def & axesNecessity .~ 1 & occlusiveness .~ 4 & dynamicPlot .~ plot where plot (GraphWindowSpecR2{..}) = pure . 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 .~ pure . 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 tweakPrerendered :: (PlainGraphicsR2->PlainGraphicsR2) -> DynamicPlottable->DynamicPlottable tweakPrerendered f = dynamicPlot %~ (fmap tweak .) where tweak = getPlot %~ f opacityFactor :: Double -> DynamicPlottable -> DynamicPlottable opacityFactor = tweakPrerendered . Dia.opacity -- | 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) & inherentColours .~ fcxVoid^.inherentColours & axesNecessity .~ fcxVoid^.axesNecessity & 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 p^.rfind 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) & inherentColours .~ fcyVoid^.inherentColours & axesNecessity .~ fcyVoid^.axesNecessity & 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 p^.rfind 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) & inherentColours .~ fwVoid^.inherentColours & axesNecessity .~ fwVoid^.axesNecessity & 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 p^.rfind 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) & inherentColours .~ fhVoid^.inherentColours & axesNecessity .~ fhVoid^.axesNecessity & 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 p^.rfind 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 waitTill :: UTCTime -> IO () waitTill t = do tnow <- getCurrentTime threadDelay . max 1000 . round $ diffUTCTime t tnow * 1e+6 -- threadDelay ticks in microseconds -- | Limit the refresh / frame rate for this plot object. Useful to slowly -- study some sequence of plots with 'plotLatest', or to just reduce processor load. -- -- Note: the argument will probably change to -- from the -- library soon. plotDelay :: NominalDiffTime -> DynamicPlottable -> DynamicPlottable plotDelay dly = frameDelay .~ dly >>> futurePlots %~ fmap (plotDelay dly)