Sorry. Programmer here, not a mathematician.

You're going to have to couch that question in English for me to be able to understand it :)

I'd suggest that you supply a (say) 5x6 3-band matrix as input; and the required output of the inversion.

(Don't forget the <code></code> tags.)

I suspect, that once you have a subroutine that maps the sparse matrix coordinates to the compact rectangular matrix coords, that applying the inversion algorithm in terms of the pre-map coordinates will effect the require transformation upon the compact representation. But I'd need to see it spelt out in english to be sure.