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Implement an in-place `cax_U`
A thin QR decomposition implemented as an V^dag V + Cholesky + Sigma^{-\dag} V requires a large batch of temporary storage unless the Sigma^{-\dag} V, where Sigma^{-\dag} is upper right triangular, is done in place. This has applications in any global orthonormalization workflow, such as in lib/multigrid.cpp.