The other library that scipy uses is SuperLU : 
https://portal.nersc.gov/project/sparse/superlu/
for the function scipy.sparse.linalg.splu : 
https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.splu.html#scipy-sparse-linalg-splu

Scipy supports only factorization for square matrices
the developer asks whether its a limitation or not : 
https://github.com/scipy/scipy/blob/4edfcaa3ce8a387450b6efce968572def71be089/scipy/sparse/linalg/_dsolve/linsolve.py#L424

In reference manual of SuperLU : 
https://portal.nersc.gov/project/sparse/superlu/ug.pdf
In Section 2.4, page 23 we can see code where *"nrow = 5; ncol = 5; *"  are 
defined separately. (  The example intended to solved a 5x5 system )

On Tuesday, January 30, 2024 at 4:21:48 AM UTC+5:30 Nils Bruin wrote:

> By the looks of it, the routines you'd be using would be coming from 
> umfpack. cvxopt has chosen to package the details of LU factorization in 
> opaque objects and instead offer routines to use these decompositions (via 
> taking the opaque object as input). In scipy, umfpack is also used: 
> https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.spsolve.html#scipy.sparse.linalg.spsolve
>  
> . Scipy also offers LU decomposition routines: 
> https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.splu.html#scipy.sparse.linalg.splu
>  
> but that uses a different library. It looks suspicious that two packages 
> offer umfpack for solving sparse problems, but don't give explicit access 
> to LU factorizations produced in the process, when using UMFPACK. Perhaps 
> UMFPACK isn't suited to provide the explicit factorization (but it may be 
> very good at using its internally computed data).
>
>
>
>

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