# Differences

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 interpolation [2013/11/26 13:52] interpolation [2013/11/26 13:52] (current) Line 1: Line 1: + ====== Interpolation ====== + TimEL will interpolate a value when some operation requires a higher granularity than the one provided by the value. + + In this process, TimEL will discriminate between the two numeric data types available: + + * Averages; + * Integrals. + + A variable is an average if the following property follows: + + A = k for ∀a,b,c: a < b < c and ∀t: a ≤ t < c + → + A = k for ∀t: a ≤ t < b + and A = k for ∀t: b ≤ t < c + + An average models correctly any derivate function, such as: + + * The speed a vehicle; + * A price of a stock quote. + + As a practical example, you can think that if a stock price was 100\$ from 09:00 to 15:00, then one can say that the stock price was 100\$ from 09:00 to 12:00 and again 100\$ from 12:00 to 15:00. + + An integral variable is a variable which express a relationship between a value (energy) and a time (its interval), such as: + + * The electricity consumed (kWh) per period; + * The number of calls received per period; + + For an integral variable, TimEL uses linear interpolation,​ so: + + A = k for ∀a,b,c: a < b < c and ∀t: a ≤ t < c + ​→ ​ + A = k * (b - a) / (c - a) for ∀t: a ≤ t < b + and A = k * (c - b) / (c - a) for ∀t: b ≤ t < c + + As a practical example, you can think that if a device consumed 10kWh from 09:00 to 15:00, then one can say that the same device consumed 5kWh from 09:00 to 12:00 and again 5kWh from 12:00 to 15:00. + + Every numeric constant is treated as an average by TimEL, to convert an average into an Integral refer to the [[Integral]] function.
• interpolation.txt