Scheduled Linear Fn
Scheduled Linear Fn is a direct subtype of Timed Real To Real Function
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with functions Scheduled Linear Fn Functions, keys Scheduled Linear Fn keys and example object SchedLinFn
TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE Scheduled Linear Fn
This type represents a function ƒ that acts exactly like the more generic function Scheduled Real Fn, with the additional restriction that the functions defined there through the key Functions are here replaced by functions of type Linear Fn
Look at Scheduled Real Fn for more details.
Another difference from Scheduled Real Fn is that the functions ƒ₁ , ƒ₂ , ... , ƒₙ corresponding to the applicable dates d₁ , d₂ , ... , dₙ are not defined explicitly, but generated implicitly by applying certain step up rules expressed as objects of type Step Up Rule
These rules are applied on the values associated with the keys Slope and Intercept of a given base function ƒ₁
The function ƒ₁ is specified throught the key Fn as an object of type Linear Fn
In summary:
1The given schedule implies a sequence of dates d₁ , d₂ , ... , dₙ
2The given base function ƒ₁ is of type Linear Fn and characterized by certain parameter sets denoted as 𝒫₁
3The given step up rules imply the sequence of stepped-up parameter sets: 𝒫₁ , 𝒫₂ , ... , 𝒫ₙ
4The implied parameters sets 𝒫₁ , 𝒫₂ , ... , 𝒫ₙ lead to the corresponding implied functions: ƒ₁ , ƒ₂ , ... , ƒₙ
5Therefore the dates d₁ , d₂ , ... , dₙ correspond to the functions ƒ₁ , ƒ₂ , ... , ƒₙ
6The function ƒ works by delegation to one of the functions ƒ₁ , ƒ₂ , ... , ƒₙ in the sense that ƒ(dᵢ , x₁ , x₂ , ... , xᵤ) = ƒᵢ(x₁ , x₂ , ... , xᵤ)
7If the first input argument is a date d such that d ∉ d₁ , d₂ , ... , dₙ, the special function 𝘨 alone produces the final result, provided that function is defined, with an error issued on a different occasion.
As an example, below is the chart of a Scheduled Linear Fn function.
The depicted function's domain includes the 3 dates: 21-Mar-2025, 21-Apr-2025, 21-May-2025
The base linear funcion applies at the date 21-Mar-2025, has formula ƒ(x) = x and corresponds to the blue line at the bottom.
The formulas for the linear functions at the next dates of 21-Apr-2025 and 21-May-2025 are calculated from the given step up amounts.
The slope step up is defined as 1 and the intercept step up as 2
It follows that the second function as of 21-Apr-2025 must have formula ƒ(x) = 2x + 2 and corresponds to the orange line in the middle.
The third function as of 21-May-2025 must have formula ƒ(x) = 3x + 4 and corresponds to the green line at the top.
