univariate/bivariate option for ElementPenalty plot recipe

[joshday]

@Evizero, how did you make the bivariate parameter plots? It would be great if we could make either version from the recipe.

[Evizero]

The code is here: https://github.com/JuliaML/FileStorage/blob/master/PenaltyFunctions/createplots.jl#L37-L64

Well since you call me out I will have to admit that I do it very inefficiently 😄

Basically the bivariate parameter plot is just slice through the cost surface of the penalty; a single contour of a contourplot in other words. Since the cost grows differently for each penalty, the level at which this slice is taken differs from one penalty to the next. So I do it in two steps:

1. Compute the cost value of interest for the specific penalty, which I do by computing the value at [1., 0.]. I do it there because I want all the paths to go through that point. This is the contour level of the cost surface that we want to trace.

2. Compute a huge grid for the x and y values between -1 and 1, but only keep the coordinates where value(penalty, [xi, yi]) is approximately the value computed in step 1.

As you can see this method is not at all optimal (or precise for that matter). The problem breaks down to computing a specific single contour of a surface. There must be some algorithm around that does that I reckon, but I did not investigate