LChart: displaying charts in F# – Part III

The last post is here. In this post we’ll look at how things work under the cover and to why I came to believe that they shouldn’t work this way.

First of all each one of the functions to create charts looks something like this:

static member bar (?y,?x, ?isValueShownAsLabel, ?markerSize, ?markerStyle, ?color, ?xname, ?yname, ?seriesName, ?title, ?drawingStyle) = 
    let c = Create (SeriesChartType.Bar, x, y, isValueShownAsLabel, markerSize, markerStyle, color, xname, yname, seriesName, title)
    c.Series.[0].["DrawingStyle"] <- defaultArg drawingStyle (c.Series.[0].["DrawingStyle"])
    c

This returns an object of type lc (this is the type of ‘c’). But lc inherits from Chart which is the main class in the Microsoft Chart Controls.

type lc() =
    inherit Chart()

I should have said at the start that you need to reference such controls.

#r "System.Windows.Forms.DataVisualization.dll"
open System.Collections
open System.Drawing
open System.IO
open System.Windows.Forms
open System.Windows.Forms.DataVisualization.Charting
open System.Windows.Forms.DataVisualization.Charting.Utilities
open System

It is convenient that the return value of each function is a subtype of Chart. You can then go and customize this object as you like (i.e. changing graphical appearance) before calling display. Given the Chart inherits from Control you can code the display method as follows:

let display (c:lc) =
    let copy () =
        let stream = new MemoryStream()
        c.SaveImage(stream, Imaging.ImageFormat.Bmp)
        let bmp = new Bitmap(stream)
        Clipboard.SetDataObject(bmp)
    
    c.KeyDown.Add(fun e -> if e.Control = true && e.KeyCode = Keys.C then copy ())
    let pressToCopy = "(press CTRL+C to copy)"     
    let name = if c.Titles.Count = 0 then sprintf "%s %s " "lc" pressToCopy else sprintf "%s %s " c.Titles.[0].Text  pressToCopy
    let f = new Form(Text = name, Size = new Size(800,600), TopMost = true)
    c.Dock <- DockStyle.Fill
    f.Controls.Add(c)
    f.Show()
    c

Apart from a bit of convolutions to implement a Copy function, this just put the Chart control on a newly created Form. The Create method called inside bar looks like the following.

static let Create (chartType, x, y, isValueShownAsLabel, markerSize, markerStyle, color, xname, yname, seriesName, title) =
    let c = new lc()
    let a = new ChartArea()
    let s = new Series()
    s.ChartType <- chartType
    c.ChartAreas.Add(a)
    c.Series.Add(s)
    match x, y with
        | Some(x), None     -> failwith "You cannot pass only x to a chart drawing function"
        | Some(x), Some(y)  -> s.Points.DataBindXY(x, [|y|])
        | None, Some(y)     -> s.Points.DataBindY([|y|])
        | None, None        -> ()
    s.IsValueShownAsLabel <- defaultArg isValueShownAsLabel s.IsValueShownAsLabel
    s.MarkerSize <- defaultArg markerSize s.MarkerSize
    s.MarkerStyle <- defaultArg markerStyle s.MarkerStyle
    s.Color <- defaultArg color s.Color
    
    a.AxisX.MajorGrid.Enabled <- false
    a.AxisY.MajorGrid.Enabled <- false
    
    match xname with
    | Some(xname) ->
        a.AxisX.Title <- xname
        a.AxisX.TitleFont <- axisFont
        a.AxisX.TitleForeColor <- axisColor
    | _ -> ()
    match yname with
    | Some(yname) ->
        a.AxisY.Title <- yname
        a.AxisY.TitleFont <- axisFont
        a.AxisY.TitleForeColor <- axisColor
    | _ -> ()
    match seriesName with
    | Some(seriesName) -> s.Name <- seriesName
    | _ -> ()
    match title with
    | Some(title) ->
        let t = c.Titles.Add(title: string)
        t.Font <- titleFont
        t.ForeColor <- titleColor
    | _ -> ()
    c

Pretty standard imperative code here. Creating a chart and assigning its properties. Read the documentation for the Chart Control to understand what I’m doing here. I’m not even sure I remember what I’m doing. Given that we have our own lc class (which is a type of Chart) we can then override the ‘+’ operator and ‘++’ operator to do what is needed.

static member (+) (c1:lc, c2:lc) =    
    let c = copyChart(c1)   
    c1.ChartAreas |> Seq.iter (fun a -> addAreaAndSeries c a c1.Series)
    let lastArea = c.ChartAreas |> Seq.nth ((c.ChartAreas |> Seq.length) - 1)
    c2.Series |> Seq.iter(fun s -> c.Series.Add(copySeries s c lastArea.Name))
    let l = c.Legends.Add("")
    l.Font <- legendFont
    c
   
static member (++) (c1:lc, c2:lc) =
    let c = copyChart(c1)   
    c1.ChartAreas |> Seq.iter (fun a -> addAreaAndSeries c a c1.Series)
    let lastArea = c.ChartAreas |> Seq.nth ((c.ChartAreas |> Seq.length) - 1)
    addAreaAndSeries c c2.ChartAreas.[0] c2.Series
    let firstArea = c.ChartAreas |> Seq.nth ((c.ChartAreas |> Seq.length) - 1)
    c2.ChartAreas |> Seq.skip 1 |> Seq.iter (fun a -> addAreaAndSeries c a c2.Series)
    c    

Apart from some other utility functions, this is how it all works. Why do I say that it is wrong? It is my opinion that the right way to do it would be to use ‘+’, ‘++’ and all the lc.XXX functions to create an object model that is completely independent from the Microsoft Chart controls. The display method would then translate it to the appropriate displayable Chart. It would work like a compiler translating to IL and then a Jitter producing native code. This would:

  • Make possible to do more interesting compositions of graphs. Now I’m very constrained in what I can do by the fact that I’m working directly with Chart objects
  • Make possible to change the backend. Using something different than Microsoft Chart controls to draw the chart

Why I have not done it? I didn’t know that was the right design until I used the wrong one. Now that I know, I have no time to do it.

LChart: displaying charts in F# – Part II

In the previous post on my old blog I showed how to display simple charts with LChart. In this one we’ll talk about more complex charts. I wanted to define a little language for graphs for the sake of creating a more complex chart in a single line of code. Remember, the scenario here is: I got some data, I want to display it quickly in the fsi. The language has two operators: ‘+’ and ‘++’.

‘+’ allows you to to superimpose things on a chart as in the following example.

lc.scatter(y) + lc.line(y) |> display

Notice how I can superimpose two graphs of a different type and display the result.

image

Notice on the upper right corner a bizarre (Series1, Series2) legend. What I wanted to do, but didn’t get around to do, was to allow a syntax like

lc.scatter(y) + lc.line(y) + lc.legend(“Players”) |> display

It should be relatively trivial to add it to the code. Also notice that the ‘y’ parameter in the second chart is not needed. Data flows freely from left to right. So you can write the equivalent code below. This is a feature that caused all sort of grief. With hindsight it’s not worth the hassle. That’s why you always need to write your code at least twice to get it right.

lc.scatter(y) + lc.line() |> display 

Some other, more elaborate charts follows. Notice how data flows from left to right until I introduce a new variable (i.e. the two lc.boxplot  instructions plot different boxplots)

lc.scatter(y, markerSize = 10) + lc.column() + lc.boxplot() + lc.line()  + lc.column(x) + lc.boxplot()|> display

image

Things would be better with names for axis, titles and such. I’m not including them for the sake of simplicity.

lc.scatter(y, markerSize = 10) + lc.column() + (lc.line(x)  + lc.column()) + lc.scatter(markerSize = 20) |> display

image

If you remember the previous post, we talked about boxplots and how you generally want to have more than one on a graph. You can do that with the ‘+’ operator and get this ugly chart. More work is needed here.

lc.boxplot(y = y, xname = "Players", yname = "Ratings", title = "Players' Ratings", color = Color.Blue, whiskerPercentile = 5, percentile = 30,
    showAverage = false, showMedian = false, showUnusualValues = true) +  lc.boxplot(y = x) |> display
image 

‘++’ allows you to create new charts below the chart you already have as in:

let h = [1.;2.5;3.1;4.;4.8;6.0;7.5;8.;9.1;15.]
let w = h |> List.map (fun h -> h * 1.2)

lc.line(h) + lc.column() ++ lc.line(w) ++ lc.bubble() |> display

image

Notice the left to right flowing of information here as well. In the next installment we’ll take a look at how things are implemented and why it’s all wrong.