lisa.datautils.series_integrate

lisa.datautils.series_integrate(y, x=None, sign=None, method='rect', rect_step='post')

Compute the integral of y with respect to x.

Returns:

A scalar \(\int_{x=A}^{x=B} y \, dx\), where x is either the index of y or another series.

Parameters:

• y (pandas.DataFrame) – Series with the data to integrate.

• x (pandas.DataFrame or None) – Series with the x data. If None, the index of y will be used. Note that y and x are expected to have the same index.

• sign (str or None) –

  Clip the data for the area in positive or negative regions. Can be any of:

  • +: ignore negative data

  • -: ignore positive data

  • None: use all data

• method – The method for area calculation. This can be any of the integration methods supported in numpy or rect

• rect_step (str) – The step behaviour for rect method

Rectangular Method

• Step: Post

  Consider the following time series data:

  2            *----*----*----+
               |              |
  1            |              *----*----+
               |
  0  *----*----+
     0    1    2    3    4    5    6    7
  
  import pandas as pd
  a = [0, 0, 2, 2, 2, 1, 1]
  s = pd.Series(a)
  

  The area under the curve is:

  \[\begin{split}\sum_{k=0}^{N-1} (x_{k+1} - {x_k}) \times f(x_k) \\ (2 \times 3) + (1 \times 2) = 8\end{split}\]

• Step: Pre

  2       +----*----*----*
          |              |
  1       |              +----*----*----+
          |
  0  *----*
     0    1    2    3    4    5    6    7
  
  import pandas as pd
  a = [0, 0, 2, 2, 2, 1, 1]
  s = pd.Series(a)
  

  The area under the curve is:

  \[\begin{split}\sum_{k=1}^{N} (x_k - x_{k-1}) \times f(x_k) \\ (2 \times 3) + (1 \times 3) = 9\end{split}\]