map_y_to_x

map_y_to_x(i::Int, t::Int, K::Int, order::AbstractVector{<:Int}) -> Int

Maps a variable in the original transmission condition (using variables y) to its corresponding systems form (using variables x).

Arguments

  • i::Int: Index of the variable in the original system.
  • t::Int: Time index of the variable in the original system.
  • K::Int: Total number of variables in the system.
  • order::AbstractVector{<:Int}: Vector defining the ordering of variables (defined by the transmission matrix).

Returns

  • An integer representing the index of the corresponding x variable in the systems form.

Notes

  • The contemporaneous period is denoted is period 0.
map_y_to_x(s_y::String, order::AbstractVector{<:Int}) -> String

Transforms a string representing a transmission condition in terms of the original variables y to a string using the systems form variables x based on a specified ordering.

Arguments

  • s_y::String: A string representing the transmission condition using original variables y, e.g. “y{1,0} & !y{2,0}”.
  • order::AbstractVector{<:Int}: Ordering defined in the transmission matrix.

Returns

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

Ex```{julia}le

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