Handle empty inputs in XLA _linalg_svd

[IvanYashchuk]

In PyTorch/XLA torch.linalg.svd is implemented via _linalg_svd.

The lowering already exists on master; after resolving merge conflicts the only remaining issue is the zero-numel case.

This PR handles empty inputs in _linalg_svd and adds a small C++ test for the output shapes.

Related:

• [PT_BREAK] pinverse test fails when changing the SVD function #2755
• Deprecate torch.svd and change svd -> linalg_svd pytorch#57772

[lezcano]

It would be nice to go over this one again once pytorch/pytorch#69827 is merged.

[Copilot]

Pull request overview

This PR adds a special-case path for torch.linalg.svd lowering on empty XLA tensors, aligning XLA behavior with the newer ATen linalg_svd operator.

Changes:

• Handles self.numel() == 0 inside _linalg_svd.
• Constructs empty-result shapes for U, S, and Vh based on full_matrices and compute_uv.

Comments suppressed due to low confidence (3)

torch_xla/csrc/aten_xla_type.cpp:4185

• The singular values tensor is created with self.options(), so complex inputs produce a complex S. torch.linalg.svd returns real singular values for complex inputs, so this empty-input path should use the corresponding real dtype for s while keeping u/vh in the input dtype.

    auto s = at::zeros(singular_values_sizes, self.options());

torch_xla/csrc/aten_xla_type.cpp:4195

• When full_matrices is true and n == 0, this returns a non-empty zero matrix for U with shape (..., m, m). The SVD contract expects the returned singular vectors to be orthonormal/unitary; a zero square matrix is not, and it will differ from backends that return an identity basis for this empty-dimension case. Populate the full square factor with an identity basis instead of zeros.

    auto u = at::zeros(u_sizes, self.options());

torch_xla/csrc/aten_xla_type.cpp:4200

• When full_matrices is true and m == 0, this returns a non-empty zero matrix for Vh with shape (..., n, n). The full singular-vector factor should be unitary/orthonormal for torch.linalg.svd; use an identity basis for the square factor instead of zeros in this empty-dimension case.

    auto vh = at::zeros(vh_sizes, self.options());

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[IvanYashchuk]

After resolving conflicts against current master, most of the original PR is already upstream: _linalg_svd lowering, codegen registration in codegen/xla_native_functions.yaml, C++ coverage in the split test files, and the OpInfo skip are all present on master already. The only remaining branch delta is the empty-input handling for _linalg_svd, so I renamed the PR to reflect that narrower scope.

[IvanYashchuk]

Added focused C++ coverage in ab18ba0 for empty _linalg_svd inputs across full_matrices and compute_uv, comparing XLA output shapes against CPU. I did not enable the linalg.svd/linalg.svdvals OpInfo entries here because they are currently disabled on XLA for broader dynamic-slice failures, so that would expand this PR beyond the empty-input fix.