[Question] Order parameter on solves

[JulianKnodt]

Hello,

What's the parameter order on lusol and qrsol? As far as I can see, it should just be a constant value for each function.

Is there any reason to change it? Also, if it does need to be passed, maybe it would be better to pass it as an enum, rather than an i8.

[RLado]

The order parameter controls the fill-reducing permutation strategy applied to the sparse matrix before factorization. It determines how the matrix is reordered to minimize the number of non-zero elements created during the factorization process ("fill-in").

What does the parameter mean?:

• order = -1:
  No reordering is applied; the matrix columns stay in their original order. It's the fastest option computationally since it skips the reordering calculation entirely, but it typically results in the most fill-in during factorization. Recommended if your matrix already has a favorable structure (banded or nearly triangular).

• order = 0:
  Applies the Approximate Minimum Degree (AMD) ordering algorithm to the pattern of A+A' (the matrix plus its transpose).

• order = 1 or 2:
  Compute the AMD ordering based on A'A (A-transpose times A). Where order=1 is generally recomended for lusol and order=2 is recommended for qrsol (order=1 removes dense rows of A prior to ordering A'A; order=2 does not)

Would it be better to pass an enum rather than an i8?
Yes. I followed the implementation in Davis, T. (2006). Direct Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics and that is why I maintained the parameter as is. But I won't argue an enum would have been the better choice.