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Pivoting QR decomposition #1045

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@loiseaujc loiseaujc commented Oct 20, 2025 •
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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

  • Interface
  • Base implementation
  • Tests
  • In-code documentation
  • Specifications
  • Example

Ping: @perazz, @jvdp1, @jalvesz

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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.

@loiseaujc loiseaujc linked an issue Oct 22, 2025 that may be closed by this pull request
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Rank-revealing QR decomposition

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