test(linalg): add contract tests for flux-independent QR/LQ isometry

[ultimatile]

Summary

Add contract tests that name flux-independent isometry as the invariant under test for block-sparse QR/LQ. The property — per-sector orthogonality holds regardless of the tensor's overall flux label — was already implicitly exercised by the identity-flux qr_orthogonality / lq_orthogonality tests, but no test name or docstring called it out. Making it an explicitly named contract, pinned by a non-identity flux fixture, keeps a future reader from conflating the overall flux label with the per-sector isometry condition.

Closes #115

Changes

• Add qr_orthogonality_holds_for_nonzero_flux and lq_orthogonality_holds_for_nonzero_flux, driven by the existing sample_u1_nonzero_flux() fixture (flux = U1Sector(1)), asserting $Q^\top Q = I$ / $Q Q^\top = I$ per sector.
• Extract the shared isometry check into assert_orthonormal_columns / assert_orthonormal_rows helpers and route the existing identity-flux orthogonality tests through them, collapsing four near-identical loop bodies into two helpers.

Test plan

• cargo test -p ariadnetor-linalg: 300 passed, 0 failed (the four orthogonality tests, two new and two refactored, all green).
• The new tests use a non-identity flux fixture, so they fail if isometry is ever gated on flux rather than computed per sector.

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[coderabbitai]

📝 Walkthrough

Walkthrough

QR and LQ orthogonality assertions now use shared per-sector isometry helpers, with additional tests covering nonzero-flux tensor fixtures.

Changes

Flux-independent isometry tests

Layer / File(s)	Summary
Per-sector isometry helpers crates/ariadnetor-linalg/src/block_sparse_decomp/tests/mod.rs	Adds shared helpers that verify QR column and LQ row Gram matrices against identity per fused sector.
QR and LQ flux coverage crates/ariadnetor-linalg/src/block_sparse_decomp/tests/mod.rs	Refactors existing orthogonality tests and adds QR/LQ tests using nonzero-flux fixtures.

Estimated code review effort: 3 (Moderate) | ~20 minutes

Poem

I’m a rabbit with matrices bright,
Checking each sector’s shape just right.
QR columns stand tall,
LQ rows answer the call,
Even with flux hopping in sight!

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly matches the main change: new contract tests for flux-independent QR/LQ isometry in linalg.
Linked Issues check	✅ Passed	The changes add nonzero-flux QR/LQ orthogonality tests, reuse the nonzero-flux fixture, and stay within linalg tests as requested.
Out of Scope Changes check	✅ Passed	The PR stays scoped to test refactors and new linalg contract tests, with no production or unrelated-module changes.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.

✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch test/115-flux-independent-isometry

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[Copilot]

Pull request overview

This PR strengthens the block-sparse decomposition test suite by making “flux-independent per-sector isometry” an explicit, named contract for QR/LQ factors in ariadnetor-linalg.

Changes:

• Adds qr_orthogonality_holds_for_nonzero_flux and lq_orthogonality_holds_for_nonzero_flux using the existing sample_u1_nonzero_flux() fixture.
• Extracts shared orthogonality checks into assert_orthonormal_columns / assert_orthonormal_rows and reuses them from the existing identity-flux orthogonality tests.

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Actionable comments posted: 2

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@crates/ariadnetor-linalg/src/block_sparse_decomp/tests/mod.rs`:
- Around line 369-425: Extract the duplicated Gram-matrix accumulation and
identity assertion logic from assert_orthonormal_columns and
assert_orthonormal_rows into a shared test helper. Parameterize the helper as
needed for the row/column multiplication orientation and dimensions, then have
both existing functions delegate to it while preserving their current tolerances
and behavior.
- Around line 369-425: Remove the redundant PartialEq bound from the generic
signatures of assert_orthonormal_columns and assert_orthonormal_rows. Keep S
constrained only by Sector, leaving their existing calls to
compute_fused_sector_groups and assemble_sector_matrix unchanged.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: ASSERTIVE

Plan: Pro Plus

Run ID: 0e710a6c-2f05-4050-a5a5-73f8cbbad874

📥 Commits

Reviewing files that changed from the base of the PR and between f9093ed and 4f3dc25.

📒 Files selected for processing (1)

• crates/ariadnetor-linalg/src/block_sparse_decomp/tests/mod.rs