packages feed

dynamic-plot (empty) → 0.1.0.0

raw patch · 8 files changed

+2223/−0 lines, 8 filesdep +MemoTriedep +MonadRandomdep +asyncsetup-changedbinary-added

Dependencies added: MemoTrie, MonadRandom, async, base, colour, constrained-categories, containers, deepseq, diagrams-cairo, diagrams-core, diagrams-gtk, diagrams-lib, glib, gtk, lens, manifolds, mtl, process, random, semigroups, time, transformers, vector, vector-space

Files

+ COPYING view
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Of course, your program's commands+might be different; for a GUI interface, you would use an "about box".++  You should also get your employer (if you work as a programmer) or school,+if any, to sign a "copyright disclaimer" for the program, if necessary.+For more information on this, and how to apply and follow the GNU GPL, see+<http://www.gnu.org/licenses/>.++  The GNU General Public License does not permit incorporating your program+into proprietary programs.  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+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+ Data/LinearMap/HerMetric.hs view
@@ -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++++
+ Graphics/Dynamic/Plot/Colour.hs view
@@ -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
+ Graphics/Dynamic/Plot/R2.hs view
@@ -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=<<lPFits) (Just r₂) r₁+                                      r₂' = cdvs (Just r₁) (lRoute=<<rPFits) r₂+                                  in Left $ Pair r₁' r₂'+                             Right pSpls -> 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=<<lPFits) (Just r₂) r₁+              , f₂ <- go (n-1) (Just r₁) (lRoute=<<rPFits) r₂+                =  \x -> 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 &#x201c;trace view&#x201d;, approximating+--   the probability density function around a &#x201c;local mean path&#x201d;, 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:+-- +--   <<images/examples/cos-encircle-points.png>>+-- +--   And that can with the mouse wheel be zoomed/browsed, like+-- +--   <<images/examples/cos-encircle-points-far.png>>+--  +--   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 &#x201c;succeed&#x201d; 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, &#x201c;parametric function&#x201d;, i.e. mapping the real+--   line to a path in &#x211d;&#xb2;.+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<u ] +                            strength+                            (floor $ lg laSpc)+               where laSpc = upDecaSpan / luDSdiv+                     luDSdiv = ll -- maybe 1 id . listToMaybe +                                . takeWhile (\d -> 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 &#x201c;plot&#x201d; 'xInterval' / 'yInterval', it is ensured that the (initial) view encompasses +-- (at least) the specified range.+-- Note there is nothing special about these &#x201c;flag&#x201d; 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+
+ Setup.hs view
@@ -0,0 +1,6 @@+module Main (main) where++import Distribution.Simple++main :: IO ()+main = defaultMain
+ dynamic-plot.cabal view
@@ -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 &#x201c;flattens&#x201d; 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.+                     .+                     <http://projects.haskell.org/diagrams> are used as the &#x201c;pre-rendered&#x201d; 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
+ images/examples/cos-encircle-points-far.png view

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+ images/examples/cos-encircle-points.png view

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