Provide a set of methods to evidence the powerfulness of the unitary transformations arising from the symmetries of the compact Lie groups
Just one: It is incredibily slow! — Because of the complexity of the algorithm (~ O(N⁴)), this method to compute transformations of 2D images are, unfortunately, the most resources expensive, and truly slow you can find. This challenge isn't for the impatient
At this time (v.0.1.0), there is all set to take a PNG image of N×N pixels, and make a (counterclockwise) rotation given a rotation angle θ.
Fqθ(θ, q₁, q₂, j, imgdat) where j is the size of the representation, thus, N = 2j + 1; θ is the rotation angle; (q₁, q₂) ∈ {-j, j} are the indexes of the two-dimensional array; and, imgdat is the two-dimensional array containing the values of the pixels.
julia> Fqθ(θ, q₁. q₂, j, imgdat)
julia> "Value of the imgdat pixel (q₁, q₂) when rotated θ"
Kindly cheers, from the developer, Alejandro R. Urzúa. 😺