In 2008, I had to solve some linear equations of the form
A was a sparse matrix (usually a design matrix for B-splines).
I wrote up a library called
cl-sparsematrix in one afternoon, and
put it on the web.
This was not a sophisticated library. It did three very basic things: it helped construct a sparse matrix using a hash-table, had a function to pack that up in CSC format, and finally, a function to call UMFpack via CFFI to solve the equation mentioned above. This was it. It worked fine for what I wanted to use it, but it was not a sophisticated sparse matrix library.
I didn't have a need for sparse matrices ever since, and the library succumbed to bit rot: some other libraries it depended on moved on, quite substantially in some cases, and now it doesn't even load cleanly. But I still get a few e-mails every month asking about this library. So apparently there is a need in the CL community for a sparse matrix library. I have no time to clean it up at the moment, and you are probably better off writing your own. The library is no longer available online, because it doesn't work and I don't want to mislead people who are looking for a sparse matrix library.
When LLA is finalized, I will include sparse matrix functionality at some point. But LLA is undergoing (yet another) major reorganization now — I think I finally figured out how to interface native Lisp arrays to LAPACK in the implementations that support pinned arrays. So sparse matrices are not on the immediate horizon. Unless, of course, I need to solve sparse systems again, and hack up yet another quick-and-dirty solution.