Compute determinant for MX using CSparse

[nielsvd]

This PRQ adds a determinant computation for large sparse matrices using the LU decomposition of CSparse. This is useful for e.g., optimal experiment design where the D-optimality criterion involves computing the determinant.

Any feedback is welcome, let me know if you want to move the copyright notice.

[GiulioRomualdi]

Hi @jgillis and @jaeandersson is there any plan to merge this PR? It would be a really useful feature

[jaeandersson]

Hi @jgillis and @jaeandersson is there any plan to merge this PR? It would be a really useful feature

Sorry for slow response. I'm a bit questioning whether it should be using CSparse by default like this. A determinant can also be numerically calculated using CasADi's native sparse QR factorization, by just multiplying the diagonal entries of the R factor. That way, it could also support C code generation, which might be useful. We try to avoid having third-party codes (like CSparse) be used without having the user explicitly say that the particular external code is used. Part of the reason is to give the CSparse developers due credit.

So I'd like to at least implement LinsolInternal::det for the LinsolQr plugin (which calls the native QR factorization) and make this the default solver and make CSparse a choice in the public API (cf. MX::inv).

This is a trivial change though, so I could do this myself.

[jaeandersson]

I'll make sure that it's merged (with the minor change mentioned above) before the 3.6 release.