[question] AC sensitivity analysis

@rdzman In this comment you shared the makePTDFac.m function. First of all, thanks for that, it really is what I'm looking for! But I have some questions about it:

1. Why isn't the function makePTDFac part of the official distribution? I came across this issue by pure luck as I was looking for ways to analyze sensitivity. Do you have any reservations about the function?
2. Im a bit confused about the resulting two (block)matrices. Is the following interpretation of the first one correct?
   (Ignoring slack just for simplicity)

H^f 
= B^f (B^{bus})^{\ -1}
= B^f J^{\ -1}
=
\left[ 
\begin{array}{c|c} 
  \frac{\delta P_{ij}}{\delta P_{i}} & \frac{\delta P_{ij}}{\delta Q_{i}} \\ 
  \hline 
  \frac{\delta Q_{ij}}{\delta P_{i}} & \frac{\delta Q_{ij}}{\delta Q_{i}}
\end{array} 
\right] 

3. Do you have any detailed explanation of the calculation? The math behind it is not entirely clear to me.

Start with the linked issue comment and the shared makePTDFac.m function, then review how AC sensitivity analysis is represented in the MATPOWER distribution. Resolve whether the function belongs in the official distribution and provide a detailed explanation of the two block matrices and their calculation.