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Summary: Pull Request resolved: https://github.com/pytorch/pytorch/pull/63568 This PR adds the first solver with structure to `linalg`. This solver has an API compatible with that of `linalg.solve` preparing these for a possible future merge of the APIs. The new API: - Just returns the solution, rather than the solution and a copy of `A` - Removes the confusing `transpose` argument and replaces it by a correct handling of conj and strides within the call - Adds a `left=True` kwarg. This can be achieved via transposes of the inputs and the result, but it's exposed for convenience. This PR also implements a dataflow that minimises the number of copies needed before calling LAPACK / MAGMA / cuBLAS and takes advantage of the conjugate and neg bits. This algorithm is implemented for `solve_triangular` (which, for this, is the most complex of all the solvers due to the `upper` parameters). Once more solvers are added, we will factor out this calling algorithm, so that all of them can take advantage of it. Given the complexity of this algorithm, we implement some thorough testing. We also added tests for all the backends, which was not done before. We also add forward AD support for `linalg.solve_triangular` and improve the docs of `linalg.solve_triangular`. We also fix a few issues with those of `torch.triangular_solve`. Resolves https://github.com/pytorch/pytorch/issues/54258 Resolves https://github.com/pytorch/pytorch/issues/56327 Resolves https://github.com/pytorch/pytorch/issues/45734 cc jianyuh nikitaved pearu mruberry walterddr IvanYashchuk xwang233 Lezcano Test Plan: Imported from OSS Reviewed By: jbschlosser Differential Revision: D32588230 Pulled By: mruberry fbshipit-source-id: 69e484849deb9ad7bb992cc97905df29c8915910 |
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