Fix: preserve direction and input identity in memoized evaluations

[AHMETHAKANBEZIR1]

MemoizeOperator currently treats a cached forward (x, Ax) pair as an adjoint result, returning x for A.H @ (A @ x). It also matches nearby input vectors with allclose, which can reuse a stale result while an iterative solver is making small updates, and can return a lower-precision cached output for an equal-valued higher-precision input.

For A = Diagonal([2., 3., 4.]) and x = [1., -2., .5], the original cached adjoint returns [1., -2., .5] instead of [4., -18., 8.]. A three-iteration CGLS solve then has solution error about 187.31, whereas the underlying operator recovers the known solution to floating-point precision. After separating directions, a tighter Split Bregman/CGLS integration check exposed a remaining ~2.17e-5 discrepancy from approximate cache hits.

Tag entries by direction and require identical input values and dtype for a hit. Keep the documented (x, y) store entries and shared FIFO max_neval budget. Document the matching rule and add a small executable example. Approximate equality may now result in more operator evaluations, preserving the requested numerical result.

Validation on Windows / Python 3.12.14 / NumPy 2.5.4 / SciPy 1.18.1:

• Final regressions on an untouched base checkout: 27 failures and 3 existing controls passing. Tests cover square/tall/wide real and complex compositions in both orders, repeated hits, cache limits 1/2/infinity, interleaved FIFO eviction, known-solution CGLS, nearby inputs, and output dtype promotion.
• pytest pytests/test_memoizeoperator.py pytests/test_solver.py pytests/test_leastsquares.py: 163 passed. The checkout import path was checked in the same test process.
• Ruff check/format, git diff --check, and the example pass.
• Local integration with Fix: separate Split Bregman inner solver options #820 and Fix: respect model and data ranks in batched TorchOperator #822: a memoized rank-changing TorchOperator layer matches native PyTorch values/gradients; tight-tolerance Split Bregman with a memoized operator now matches the uncached result exactly in this test (previously failed the 1e-8 comparison). This is local composition evidence, not an upstream merge or a requirement to merge these PRs together.

CPU validation only; no CuPy runtime or full repository suite claim.

AI disclosure: code, tests, and this description were prepared by an autonomous AI coding agent at the account owner's request. No independent human code review is claimed.

[codacy-production]

Up to standards ✅

🟢 Issues 0 issues

Results:
0 new issues

View in Codacy

🟢 Metrics 4 complexity · 0 duplication

Metric	Results
Complexity	4
Duplication	0

View in Codacy

_{NEW Get contextual insights on your PRs based on Codacy's metrics, along with PR and Jira context, without leaving GitHub. Enable AI reviewer
TIP This summary will be updated as you push new changes.}