How can I get the CS decomposition of a matrix?

There seems to be no function in any well-known Julia library to obtain the CS decomposition of a matrix. There is a function CUNCSD in LAPACK, but it is not available in Julia by default. Maybe I can call that function from Julia?

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lapack comes with julia in the module LinearAlgebra.LAPACK, but i can’t find a julia interface to to CUNCSD in particular. in this file are the c calls to the lapack routines:

if you know the conventions of calling directly a lapack routine, maybe you can a direct c call.

Also, this merits an issue on the Julia repo

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Why is it actually that Julia doesn’t have an interface for all of LAPACK? The wrappers must be automatically generated, right?

No, they are hand-written. Writing high-level wrappers for a Fortran library like this is non-trivial to automate, especially since there are four variants of every subroutine (real/complex and single/double precision), sometimes with subtly different calling conventions (e.g. different workspace sizes).

Of course, nothing prevents you from adding a wrapper for any LAPACK routine you want using ccall in user code — there’s nothing special about the code in the Julia standard library.


I see. How would a wrapper for CUNCSD look like?

The specification is here:

Look at the other wrappers in lapack.jl; adapting one for *uncsd shouldn’t be too hard.

There are a lot in LAPACK that are non-standard, for example, QL, LQ, RQ decompositions, that would be quite a bit of work to wrap.

I’ve set up MatrixFactorizations.jl as a home for other matrix factorizations. At the moment it just includes QL and a version of QR that allows more general types.