Differentiated Variables


Differentiated variables creates derivative of variables. The derivatives are computed for each input variable. 

To create a differentiated set of variables:

  1. Click Transform > Differentiated variables in the menu.
  2. Enter a name for the new variable set. 

    Variable set

    Note that Differentiated Variable creates a Variable set, containing several new variables. Therefore, to check your Differentiated variables you can go to the third icon on the left bar.

  3. Enter prefix, default: DIFF_
  4. Enter Step duration. For more information, see Step duration
  5. Select Input variables or variable set. 
  6. Select Differential method. For more information, see Newton, Symmetric and High order
    1. The derivative options are:

      1.  Newton: difference quotient (order 1)
      2. Symmetric: difference quotient (order 2)
      3. High order: five-point stencil

  7. Select the Direction, Left or Right. See below that it is the formula used to derive the variable with the Newton method. 
  8. Click Save.

Differentiated Methods

Formula used to derive the variable:

  • Newton: f'(x) = [f(x + 1 )-f(x)]/Step or f'(x) = [f(x)-f(x - 1)]/Step
  • Symmetric: f'(x) = [f(x + 1) - f(x - 1)] / [2 * Step]
  • High order: f'(x) = [-f(x + 2) + 8f(x + 1) - 8f(x - 1) + f(x - 2)] / [12 * Step]

With:

  • x: the index of the row
  • f(x): the value of the variable for row x
  • f'(x): the value of the derivative for row x
  • Step: Value defined by the field Step duration. It is the duration between two rows of the dataset. If Step duration is missing, the default value is 1.

Direction

Formula used to derive the variable with the Newton method:

  • Left: f'(x) = [f(x)-f(x - 1)]/Step
  • Right: [f(x + 1 )-f(x)]/Step

With :

  • x: the index of the row
  • f(x): the value of the variable for row x
  • f'(x): the value of the derivative for row x
  • Step: Value defined by the field Step duration. It is the duration between two rows of the dataset. If Step duration is missing, the default value is 1.