Floor

Key Floor in Linear Fn refers to an optional lower bound number (floor) F imposed on the function's interim output after the coefficients defined through the keys Slope have been applied and after a likely constant increment defined through the key Intercept has been added.

Formally, let L = m₁x₁ + m₂x₂ + ... + mᵤxᵤ + c be the linear result L derived by applying the coefficients m₁, m₂, ..., mᵤ supplied by the key Slope and the constant c supplied by the key Intercept

Then the formula of the function ƒ is:
ƒ( x₁ , x₂ , ... , xᵤ ) = max{ L , F } if the optional entry Cap does not apply
or
ƒ( x₁ , x₂ , ... , xᵤ ) = max{ min{ L , C } , F } if the optional entry Cap also applies and supplies the cap C

If this entry is missing, no lower bound is imposed and the function ƒ is simply:
ƒ( x₁ , x₂ , ... , xᵤ ) = L if the optional entry Cap does not apply
or
ƒ( x₁ , x₂ , ... , xᵤ ) = min{ L , C } if the optional entry Cap also applies and supplies the cap C