dayTable

Linear interpolation in a day table [time of day (s), value], repeated daily

FastSmoothBuildings.Utilities.dayTable, function (source)

Purpose

Linear interpolation in a day table, without the events of a table: rows [time of day (s), value], the time increasing, evaluated at the time of day tod, typically timeOfDay(time).

Equations

With the rows (t_i, v_i), i = 1 … n:

• y = v₁ up to t₁;
• between t_i and t_i+1, the linear interpolation of v_i and v_i+1; where the table repeats an instant, the denominator is bounded by 10⁻⁶ s: a step;
• after t_n, a linear return from v_n to v₁, reached at t₁ + 86400 s.

The result is continuous and piecewise linear (C0) apart from the repeated instants, and continuous across midnight when t₁ = 0. A table of one row is a constant.

Use

The table is a parameter, not a literal matrix in the call, and at the top level of a model the call is an equation, not the binding of a declaration (see Translation into CasADi). The zones read their ventilation schedule with it.

Revisions

• October 2026: moved from trano's FastModel.Utilities.