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Use the truncated QR LAPACK routine geqp3rk as the backend for the partial qr factorization. fixes #60 #61

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@ajinkya-k ajinkya-k commented Dec 10, 2024

The LAPACK routine geqpr3k available starting in v3.12.0 computes the truncated QR factorization based on one of three stopping conditions. This PR adds a backend for pqr that uses the LAPACK routine instead of the Julia native backend in the function geqp3_adap_main!. This backend is faster than using the current implementation.

There is still one unresolved issue that I need help with. When a max rank to truncate at is not provided, the R factor from the lapack backend differs from the current version and I am not sure why. Fixes #60

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Regarding the discrepancy in the factor R, its because of a slightly different order of pivots. See more details in this comment in issue #60

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relevant upstream issue in openBLAS OpenMathLib/OpenBLAS#5013

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Use geqp3rk routine in LAPACK 3.12 for performing pqrfact
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