Neither Perl, nor (as far as I'm aware), PDL provides a mechanism for creating banded (sparse) matrices. You could use normal rectangular matrix, and just ignore the zeros, but for large dimensions, that would waste a lot of space.

However, the "normal" way of dealing with them, is to map the active elements to an appropriately sized (smaller) rectangular matrix. The mapping is very simple & regular. A simple sub that maps the original coordinates to the reduced matrix should be pretty simple to write.

Thank you.

Perhaps I should post this as a new question, but I was going to write a spline interpolation code so I could modify it for other forms of interpolation. Hence the reason I wanted to make the band matrix so I could invert it. How might I do that without the matrix itself?

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.

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