map_x_to_y

map_x_to_y(xi::Int, order::AbstractVector{<:Int}) -> Tuple{Int, Int}

Maps a variable from the systems form (using variables x) back to its original transmission condition form (using variables y). This function is the reverse of map_y_to_x.

Arguments

  • xi::Int: Index of the variable in the systems form.
  • order::AbstractVector{<:Int}: Ordering defined in the transmission matrix.

Returns

  • A tuple (i, t) where i is the index of the variable in the original system and t is its time index.
map_x_to_y(s_x::String, order::AbstractVector{<:Int}) -> String

Transforms a string representing a transmission condition in terms of the systems form variables x back to a string using the original variables y. This function is the reverse of map_y_to_x.

Arguments

  • s_x::String: A string representing the transmission condition using systems form variables x.
  • order::AbstractVector{<:Int}: Ordering defined by the transmission matrix.

Returns

  • A string representing the same transmission question but using variables of the dynamic (original) system (y) rather than those of the systems form (x).

Ex```{julia}le

order = [3, 1, 2]
s_x = "x8 & x4"
map_x_to_y(s_x, order)  # Returns: "y_{1, 2} + y_{3, 1}"