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Move lobpcg into torch.linalg #61653

@lezcano

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@lezcano

In order to move lobpcg into torch.linalg we should:

  • Update the docs: When is this function preferable over eigvals or eigvalsh. Some estimations on the size of the input matrix and its rank would be very helpful to make them more usable (needs benchmarks).
  • Format the docs for them to be in line with the rest of torch.linalg
  • Implement the backwards for non-symmetric matrices (would fix torch.lobpcg always breaks for autograd #38948)
  • Address the performance concerns from [Feature Pitch] Fast extremal eigensolvers #58828
  • Review the API and perhaps split it into two functions, one with a simpler API and a simpler name and a full one (needs some proposals for how to do this).

cc @jianyuh @nikitaved @pearu @mruberry @heitorschueroff @walterddr @IvanYashchuk @xwang233 @lezcano

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    enhancementNot as big of a feature, but technically not a bug. Should be easy to fixmodule: linear algebraIssues related to specialized linear algebra operations in PyTorch; includes matrix multiply matmultriagedThis issue has been looked at a team member, and triaged and prioritized into an appropriate module

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