Input Variables
Key Input Variables in Generic Trigger refers to an optional 1D-array of r integers i(1) , i(2) , ... , i(r) that acts as a "filtering mask" on the input variables x₁ , x₂ , ... , xᵤ by allowing only a subset of them to be processed by the function and potentially even change the order by which the selected variables are fed into the function.
Concretely, the r integers i(1) , i(2) , ... , i(r) equal the allowed indices, i.e. the indices of those variables among x₁ , x₂ , ... , xᵤ that must be processed.
Also the ordering of these integers is important.
Formally:
If omitted, the function processes all u elements of the array x₁ , x₂ , ... , xᵤ.
Otherwise, the function processes only the r elements xᵢ₍₁₎ , xᵢ₍₂₎ , ... ,xᵢ₍ᵣ₎ in the given order.
For example, consider the array 1,3,4, i.e. i(1) = 1, i(2) = 3, i(3) = 4.
The meaning of this array is that only the 1ˢᵗ, 3ʳᵈ and 4ᵗʰ elements of the original input variables are processed by the function.
So, if the 4 variables x₁ , x₂ , x₃ , x₄ are fed as input to the function, only the 3 variables x₁ , x₃ , x₄ will be actually processed and the variable x₂ will be fully ignored.
Note, in this example the dimensionality of the function's domain would equal 4, since the function expects as input an array with at least 4 elements, even though it is instructed to ignore the third element.
As a second example, consider the reverse array 4,3,1, i.e. i(1) = 4, i(2) = 3, i(3) = 1.
The effect of this array is similar to the previous case in that only the 3 variables x₁ , x₃ , x₄ will be actually processed and the variable x₂ will be fully ignored.
There is a difference though.
The function will now receive the array x₄ , x₃ , x₁ rather than the array x₁ , x₃ , x₄
It is important to note that any function parameters that act on the input variables relative to those variables' order in the input array will now act on the input variables relative to those variables' order implied by the array here.
For example, the function Linear Fn has the fixed coefficient parameters referred by the key Slope.
These parameters are defined as an array of numbers m₁, m₂, ..., mᵣ so that the first number m₁ is used to multiply the first input variable, the second number m₂ the second input variable and so on.
In the regular case, when the input variables form the array x₁ , x₂ , ... , xᵤ, m₁ should multiply x₁, m₂ should multiply x₂ and so on.
But in the presence of the array discussed here, m₁, m₂, ..., mᵣ will apply on the array xᵢ₍₁₎ , xᵢ₍₂₎ , ... ,xᵢ₍ᵣ₎ in accordance with the ordering in that array.
This means, m₁ will multiply xᵢ₍₁₎, m₂ will multiply xᵢ₍₂₎ annd so on.