Pivoting QR decomposition

[loiseaujc]

Following #930, this PR extends the qr interface to enable the computation of the QR factorization with column pivoting. It is based on the xGEQP3 driver from lapack.

Proposed interfaces

• call qr(a, q, r, pivots [, overwrite_a, storage, err])

where a is the matrix to be factorized, q the orthonormal basis for colspan(a), r the upper triangular matrix and pivots an integer array with indices of the pivoted columns.

Progress

• [x] Interface
• [x] Base implementation
• [x] Tests
• [x] In-code documentation
• [x] Specifications
• [x] Example

Ping: @perazz, @jvdp1, @jalvesz

[loiseaujc]

I think this PR is almost ready to be reviewed. I have the specs left to write but this should pretty quick as it mainly is a small modification of the qr specs. I'll try to do that by the end of the week. It seems like there is a small issue with the unbuntu-22.04/cmake/inter-classic 2021.10 setup though. Not sure what it is and I don't have the intel compilers on my laptop so I can't really dig into it at the moment.

[codecov[bot]]

Codecov Report

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Additional details and impacted files

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[loiseaujc]

Modulo the issue with the unbuntu-22.04/cmake/intel-classic 2021.10 setup which I haven't been able to investigate yet, this PR is ready for review.

[loiseaujc]

For the build unbuntu-22.04, cmake, intel-classic 2021-10, it seems the computations are successful (at least according to the linalg_state_type returned) but when comparing A and QR P.T, the test fails. Without having this particular intel compiler on my laptop I unfortunately can't say much more than that.