Left Step Up
Key Left Step Up in Scheduled Number Is Inside Fn refers to a 1D-array of m objects S₁ , S₂ , ... , Sₘ of type Step Up Rule that are used to generate the parameter Left that is part of the Real Interval object embedded in each Number Is Inside Fn function that applies at each and every observation date.
Concretely, let d'₁ , d'₂ , ... be the sequence of adjusted dates implied by the entry in key Step Up Schedule
Note the dates d'₁ , d'₂ , ... may differ from the dates d₁ , d₂ , ... , dᵣ implied by the entry in Schedule
On the first date d'₁, the applicable function is already given and equals the base function ƒ₁ defined in key Fn
Let ƒ₁ be characterized by intervals that are defined by the parameters Left = L₁, L₂, ..., Lᵤ and Right = R₁, R₂, ..., Rᵤ
On the second date d'₂, the applicable function is generated by the new parameters Left = L'₁, L'₂, ..., L'ᵤ and Right = R'₁, R'₂, ..., R'ᵤ
The new parameters L'₁, L'₂, ..., L'ᵤ are constructed by applying the Step Up Rule objects S₁ , S₂ , ... , Sₘ defined in the key here on the base parameters L₁, L₂, ..., Lᵤ
The new parameters R'₁, R'₂, ..., R'ᵤ are constructed similarly, but by applying the Step Up Rule objects defined in the key Right Step Up
Comcretely, S₁ is applied on L₁ and produces the L'₁, then S₂ is applied on L₂ and produces the L'₂ and so on.
If m < u, the sequence S₁ , S₂ , ... , Sₘ is extended based on its last elements, i.e. new elements Sₘ₊₁ , Sₘ₊₂ , ... , Sᵤ₋₁ , Sᵤ are added such that all are equal to Sₘ
If the dates d'₁ , d'₂ , ... differ from the dates d₁ , d₂ , ... , dᵣ, the function applicable on any observation date dᵢ equals the function constructed according to the above procedure at the latest date d' such that d' ≤ dᵢ