julia

e70354da - Fix for #48911: Bugfix for the generic left-divide (ldiv!) algorithm with pivoted QR decomposition and wide matrices (#49570)

Fix for #48911: Bugfix for the generic left-divide (ldiv!) algorithm with pivoted QR decomposition and wide matrices (#49570) * Fix for #48911 1. Fix output permutation when A.P is not the identity matrix. 2. Fix the application of the elementary transformation (correct complex conjugation) to the solution as per LAPACK zlarzb https://netlib.org/lapack/explore-html/d5/ddd/zlarzb_8f_source.html 3. Align the final permutation with LAPACK's ZGELSY at https://netlib.org/lapack/explore-html/d8/d6e/zgelsy_8f_source.html 4. Fix a complex conjugate bug in the original solution for #48911, align with LAPACK zlarzb, https://netlib.org/lapack/explore-html/d5/ddd/zlarzb_8f_source.html 5. Improve permutation performance * Integration fix for #48911: Permutation is taken care by ldiv!(QRPivoted, ...) * Tests for #48911: LinearAlgebra/test/qr.jl * Issue #48911: Include original test case mentioned in the issue. --------- Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>