Graphics.Dynamic.Plot.R2

Interactive display

plotWindow :: [DynamicPlottable] -> IO GraphWindowSpec

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.

Plottable objects

Class

class Plottable p where

Methods

plot :: p -> DynamicPlottable

Instances

Plottable p => Plottable [p]

(RealFloat r₁, RealFloat r₂) => Plottable (r₁ -> r₂)

Plottable ((:-->) Double Double)

Plottable ((:-->) Double (Double, Double))

Simple function plots

fnPlot :: (forall m. Manifold m => ProxyVal (:-->) m Double -> ProxyVal (:-->) m Double) -> DynamicPlottable

Plot a continuous function in the usual way, taking arguments from the x-Coordinate and results to the y one. The signature looks more complicated than it is; think about it as requiring a polymorphic Floating function. Any simple expression like fnPlot (\x -> sin x / exp (x^2)) will work (but the view must not contain singularities).

Under the hood this uses the category of continuous functions, :-->, to proove that no details are omitted (like small high-frequency bumps). The flip side is that this does not always work very efficiently, in fact it can easily become exponentially slow for some parameters. Make sure to run multithreaded, to prevent hanging your program this way. Also consider limiting the memory: if you try to plot across singularities, the program may well eat up all available resorces before failing. (But it will never “succeed” and plot something wrong!)

In the future, we would like to switch to the category of piecewise continuously-differentiable functions. That wouldn't suffer from said problems, and should also generally be more efficient. (That category is not yet implemented in Haskell.)

paramPlot :: (forall m. Manifold m => ProxyVal (:-->) m Double -> (ProxyVal (:-->) m Double, ProxyVal (:-->) m Double)) -> DynamicPlottable

Plot a continuous, “parametric function”, i.e. mapping the real line to a path in ℝ².

continFnPlot :: (Double -> Double) -> DynamicPlottable

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).

tracePlot :: [(Double, Double)] -> DynamicPlottable

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.

View selection

xInterval :: (Double, Double) -> DynamicPlottable

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.

yInterval :: (Double, Double) -> DynamicPlottable

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.

Plot type

data DynamicPlottable