fix(exact): make the rcond_free conditioning guard opt-out (#32)

[tschm]

Closes #32.

Problem

Exact.solve ran op.rcond_free(idx) — an O(|F|³) symmetric eigendecomposition (np.linalg.eigvalsh) — before every free-block solve. On the plain ActiveSetSolver(Exact()).solve(...) path, every outer step visits a different free set, so the 0.4.1 single-slot memo never hits and the guard fires on every step. For a dense free block it costs several times the Cholesky solve it precedes.

Measured (n=500, κ=1e4, DenseOperator): the guard's eigvalsh is ~3.6× the cholesky_solve, and a full direct solve drops from ~21 ms to ~6 ms (3.5×) with the guard off — identical solution (max|Δx| = 0).

The guard is also redundant when solve_free already fails loudly on a rank-deficient block (cvx.linalg.cholesky_solve's Cholesky→LU fallback).

Change

Add check_conditioning: bool = True on Exact:

• Default unchanged — the guard runs exactly as before (memoised once per free set), so existing callers and the solve_eq amortization from Exact inner solver recomputes rcond_free p+1 times per free set in solve_eq (regression of #18) #30 are untouched.
• Exact(check_conditioning=False) skips the eigendecomposition and lets solve_free surface any singularity itself — for callers who know their free blocks are well-conditioned (e.g. ridged/Gram operators) and want the raw structured solve.

Tests

• New test_exact_check_conditioning_false_skips_rcond_guard: asserts rcond_free is called 0 times when disabled, the solve still converges to the planted optimum, and the result matches the guarded solve bit-for-bit.
• Full suite green (86 passed), coverage gate satisfied, ruff clean.

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[Copilot]

Pull request overview

This PR makes the expensive rcond_free conditioning guard in nncg.inner.Exact optional via a new check_conditioning flag, enabling callers to skip an O(|F|^3) eigendecomposition when they prefer raw solve_free performance.

Changes:

• Add Exact(check_conditioning: bool = True) and gate the conditioning check on this flag.
• Expand Exact’s docstring to explain the performance motivation and how to opt out.
• Add a regression test ensuring rcond_free is never called when check_conditioning=False and that solutions match the guarded path.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 1 comment.

File	Description
src/nncg/inner.py	Adds check_conditioning flag and conditionally skips the rcond_free guard; updates documentation accordingly.
tests/test_operators.py	Adds a test that counts rcond_free calls and verifies correctness when conditioning checks are disabled.

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