submission 870564

"""GPU MODE leaderboard 775 - batched real symmetric eigh on B200.

Submission 1: clean dense baseline.

Recon (see RECON.md) established that EVERY timed benchmark case is a full
dense matrix. There are no diagonal / identity / zero / band-sparse cases in
the benchmark set (the maintainers explicitly removed the one diagonal
benchmark row, and a Triton diagonal fast-path measured *slower* on benchmark:
45.9s vs 28.0s baseline, because structure detection costs on every dense
case for zero benefit). Therefore a structure-dispatch submission cannot move
the geomean and would only add per-batch reduction overhead on the dense path.

So submission 1 is the plain, correct baseline. It exists to:
  * validate the popcorn toolchain end-to-end on the runner, and
  * record our own scored baseline number to compare future work against.

The real lever (beating baseline) requires low-precision / tensor-core spectral
methods -- out of scope for submission 1, see RECON.md "Next step".

Contract: custom_kernel(A: batch x n x n float32 CUDA) -> (Q, L) with
  Q: batch x n x n float32, columns are orthonormal eigenvectors
  L: batch x n float32, eigenvalues ascending
matching torch.linalg.eigh(A) == (L, Q)  ->  we return (Q, L).
"""

import torch
from task import input_t, output_t


def custom_kernel(data: input_t) -> output_t:
    # torch.linalg.eigh returns (eigenvalues ascending, eigenvectors as columns).
    # The task convention wants (Q, L), so we swap the order.
    values, vectors = torch.linalg.eigh(data)
    return vectors, values