Affine Function

Affine functions is a vector-valued functions of the form

f(x_1,…,x_n)=A_1x_1+…+A_nx_n+b

These coefficients can be scalar or dense or sparse matrices. The constant term is a scalar or a column vector.

In geometry, an affine transformation or affine map (from the Latin, affinis, "connected with") between two vector spaces consists of a linear transformation followed by a translation. In a geometric setting, these are precisely the functions that map straight lines to straight lines.

References : https://en.wikipedia.org/wiki/Affine_transformation
https://mathworld.wolfram.com/AffineFunction.html