Understanding the permutation in QRMumps

[MaxenceGollier]

I am having a hard time to understand what permutation is automatically done in QRMumps.
More precisely, I am trying to implement a QLP factorization in order to solve the least-norm problem

$$\min \|x\| \ \text{subject to } Ax = b.$$

This requires taking a QR factorization with a rank revealing column permutation if I understand correctly.
My question is: are the permutations in QRMumps appropriate for this ?
I have been trying to implement it for a while but can't get it to work on larger problems where specific permutations (I am guessing rank revealing ones) are necessary.

QRMumps.jl/docs/src/control_parameters.md

Lines 22 to 25 in e458114

	## Problem specific parameters
	* **qrm\_ordering**: this parameter specifies what permutation to apply to the columns of the input matrix in order to reduce the fill-in and, consequently, the operation count of the factorization and solve phases. This parameter is used by **qr\_mumps** during the analysis phase and, therefore, has to be set before it starts. The following pre-defined values are accepted:
	* **qrm\_auto** (0) : the choice is automatically made by **qr\_mumps**. This is the default.

In all cases, perhaps the documentation could be a little more specific on the permutations performed ?

[dpo]

@abuttari Would you have a moment to help @MaxenceGollier here? We're trying to compute a complete orthogonal decomposition. Thanks!

[amontoison]

@MaxenceGollier @dpo
A rank-revealing column permutation is computed during the factorization phase because it depends on the values.

The permutation described in the documentation for the analysis phase aims to reduce the fill-in in the factors and is based only on the sparsity pattern of the sparse matrix A.

[abuttari]

yes, @amontoison is right, the column permutation in qrm is only meant to reduce the fill-in generated during the factorization. To the best of my knowledge, there is no sparse QR solver that also does a rank-revealing permutation during the factorization; this is way too complex to implement and, furthermore, as the drawback of increasing the fill-in and thus the operational complexity. SuiteSparseQR does some kind of reank-revealing QR factorization without permuting the columns of $A$ (it simply skips columns where $R$ has diagonal coefficients smaller than a prescribed threshold).
I imagine your $A$ matrix is rank-deficient? If not a plain, non rank-revealing QR factorization will work.

[MaxenceGollier]

Thank you @abuttari !