Add Julia API for SuiteSparseQR

[kbatseli]

But needs to be called via its C interface.

It would be nice if it would be possible to just type spqr(A) in Julia to call the SuiteSparseQR command. Or alternatively the command qr(A), where Julia would internally call spqr for when the argument A is a sparse matrix.

[pao]

cc @dmbates

[dmbates]

The C API for SuiteSparseQR is opaque. Essentially you get void* objects that are filled in by the C++ code and need to be accessed only through that code. The definition of the primary struct is

typedef struct SuiteSparseQR_C_factorization_struct
{
    int xtype ;                 /* CHOLMOD_REAL or CHOLMOD_COMPLEX */
    void *factors ;             /* from SuiteSparseQR_factorize <double> or
                                        SuiteSparseQR_factorize <Complex> */

} SuiteSparseQR_C_factorization ;

so essentially the only thing you can do with it at the level of the Julia code is to store a pointer to this struct. There are C routines for the backslash but they don't allow you to save the decomposition.

It is much more difficult to work with SuiteSparseQR than to work with CHOLMOD or UMFPACK. That doesn't mean it shouldn't be done but I have other projects that I need to work on right now.

[StefanKarpinski]

Reasonable. Marking as up for grabs in case anyone wants to take a crack at it.

[ViralBShah]

@andreasnoack implements this in #10180.

[ViralBShah]

Closed by #10180