Differences

This shows you the differences between two versions of the page.

Link to this comparison view

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
  • Last modified: 2013/11/26 13:52
  • (external edit)