This is a tracking issue for torch.linalg tasks for PyTorch 1.10. The goals for the 1.10 release are:

• Reviewing the Python Array AP's linalg extension and pursuing consistency with it
• Modernizing linear algebra functions still under the torch namespace to newer torch.linalg versions
• Continuing to deprecate older linear algebra operators (see Deprecations tracking issue #55953)
• Improving CUDA performance (see Linear algebra GPU backend tracking issue [magma/cusolver/cublas] #47953)
• Improving linear algebra gradient computations

Tasks

• Add the "upper" kwarg to linalg.cholesky Enable upper for torch.linalg.cholesky #62434
• Rationalize the kwargs of linalg.eigh, linalg.eigvalsh, linalg.lstsq, and linalg.pinv with each other and the Python Array API
• Add relative and absolute tolerances for matrix_rank, pinv #54151 (comment)
• Add modern versions of lu, lu_unpack, geqrf, orgqr, ormqr, lu_solve, triangular_solve, cholesky_solve, cholesky_inverse, tensordot, matrix_exp, {svd, pca}_lowrank and lobpcg to torch.linalg
• Move matrix_exp into torch.linalg #61648
• Move tensordot into torch.linalg #61649
• Move {svd,pca}_lowrank into torch.linalg #61650
• Move lobpcg into torch.linalg #61653
• Move lu, lu_solve, and lu_unpack into torch.linalg #61657
• Move torch.cholesky_solve into torch.linalg. #61658
• Investigate a common "solver API" to rationalize the various solvers

cc @ezyang @gchanan @zou3519 @bdhirsh @jbschlosser @anjali411 @jianyuh @nikitaved @pearu @mruberry @heitorschueroff @walterddr @IvanYashchuk @xwang233 @lezcano @rgommers @vincentqb @vishwakftw @ssnl