⚡ Bolt: Optimize batched covariance functions using broadcasting

[suraj-ranganath]

💡 What: This PR optimizes the core numerical operations for working with covariance matrices (or stacks of them) in src/eegprep/plugins/clean_rawdata/private/covariance.py.

🎯 Why: The previous implementation used explicit diagonal matrix creation and full matrix multiplication even when only row/column scaling was needed. This was inefficient for memory (large intermediate diagonal matrices) and computation (O(N^3) vs O(N^2)).

📊 Impact:

• diag_nd is ~3x faster for typical batch sizes (e.g., 1000 matrices).
• Covariance power functions (like cov_sqrtm) are ~9-10% faster for batch sizes of 1000x64x64 matrices.
• Reduced memory pressure by eliminating intermediate diagonal matrix allocations.

🔬 Measurement: Speedup verified with tools/benchmark_covariance_opt.py (deleted before submission). Correctness verified with the existing test suite (tests/test_utils_covariance.py).

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PR created automatically by Jules for task 18207546850941549272 started by @suraj-ranganath

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PR Review: Optimize batched covariance functions

• Read changed files and diff vs origin/develop
• Verify mathematical equivalence of the broadcasting change
• Check diag_nd rewrite for correctness
• Assess finite_matmul behavioral implications

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Nice, clean optimization. The core change is correct and the numerics are preserved. Summary of my analysis:

✅ Correctness — the broadcasting change is exact

Every rewrite replaces finite_matmul(V, diag_nd(g)) with V * g[..., np.newaxis, :]. This is mathematically identical:

• V @ diag(g) scales the columns of V: (V @ diag(g))[i,j] = V[i,j] * g[j]
• V * g[..., np.newaxis, :] broadcasts g (shape (...,1,N)) across rows: V[i,j] * g[j]

Same result, and it drops the intermediate (...,N,N) diagonal allocation plus one O(N³) matmul per call in favor of an O(N²) elementwise scale. Good win.

✅ diag_nd rewrite (covariance.py:34-42)

The advanced-indexing version (res[..., idx, idx] = M) is correct, preserves dtype, and removes the Python-level list comprehension + np.concatenate. Note diag_nd is still used by cov_shrinkage (target='diag'), so it's not dead code — good that it was kept and improved rather than removed.

🟢 Minor: finite_matmul warning-suppression on the inner product

Worth flagging for the record (not a bug): the old code routed the inner V @ diag(...) through finite_matmul, whose job is to suppress spurious RuntimeWarnings when inputs/result are finite (it does not sanitize values). The new inner step is a plain elementwise *.

This is fine because:

• When D is finite, an elementwise multiply of finite arrays emits no warnings, so nothing is lost.
• When D is non-finite (e.g. cov_rsqrtm/cov_logm on a singular matrix → inf/nan), both the old matmul and the new * produce the same non-finite values, and the outer finite_matmul(..., V.T) still governs warning behavior of the final product.

So no numerical or warning-visibility regression — just noting the intentional narrowing of finite_matmul usage.

🟢 Minor: .jules/bolt.md

The PR adds .jules/bolt.md (a Jules learning log). Just confirm this tracking file is intended to be checked into the repo rather than kept local — it's unrelated to the runtime change.

⚠️ Tests not run here

I couldn't execute tests/test_utils_covariance.py in this environment (sandbox denied the command), so I verified equivalence by reasoning about the code rather than running the suite. Please make sure CI's uv run pytest tests/test_utils_covariance.py is green — the existing tests should fully cover this equivalence.

Verdict: LGTM. Correct, well-scoped, and a genuine perf/memory improvement. No changes requested.