Fix: preserve flat FISTA cost dispatch for ND operators

[mikamikasuki]

FISTA computed its data cost through Op @ x, which reshapes output to Op.dimsd and fails against flattened multidimensional data or multiple right-hand sides. Use the solver's existing Opmatvec dispatch for the cost.

Cover ISTA and FISTA with 16 regression cases across real/complex data, single/multiple right-hand sides, and both preallocation modes. Clarify the input layout in both public docstrings and the deblurring tutorial.

Fixes #801.

Validation: pytest pytests/test_sparsity.py — 92 passed; make lint — passed.

AI assistance: Codex authored the fix, documentation, and regression tests.

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[mrava87]

@mikamikasuki well spotted and thanks for the PR. I left a few minor comments but overall I think is good (including the new test :))

[mrava87]

@claude review.

[claude]

Claude finished @mrava87's task in 22s —— View job

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Review of PR #805

• Read the diff against origin/dev
• Check the fix against ISTA and FISTA in cls_sparsity.py
• Check whether the review comments from @mrava87 have been addressed

The fix is correct and minimal. FISTA.step computed the data cost with self.Op @ x. That reshapes the result to Op.dimsd, so it breaks against a flat y or an (N, nrhs) y. self.Opmatvec(x) is what the iterations already use (matvec or matmat, depending on the shape of y). ISTA.step doesn't have this problem. It reuses the residual it already computed (cls_sparsity.py:1924), so the one-line change is all the solver needs.

Still open from the earlier review

All of the points below are still unaddressed. The branch has only the one commit.

1. ista docstring (pylops/optimization/sparsity.py:71). The Data entry in ista still carries the old text. @mrava87 asked for the same clarification there. The two other Data entries (lines 616 and 742) are for other solvers, so they probably don't need it.
2. Parametrize over ista and fista (pytests/test_sparsity.py). As requested, add @pytest.mark.parametrize("solver", [ista, fista]). The test would pass for ista without a code change, which makes it a useful guard against regressions.
3. Test name and docstring. The suggested wording is along the lines of "Check that ista/fista can handle nd data with flat models". Rename the test to something like test_ISTA_FISTA_flat_model_nd_data.
4. Test placement. Move the test below the tests of the same solvers that check for raised errors, e.g. after test_ISTA_FISTA_unknown_threshkind.

Minor points

• Extra blank line. The new test is followed by three blank lines (see the diff around pytests/test_sparsity.py:366). PEP 8 allows two. ruff format or the linter may flag it.
• Mutating op.dimsd in the test. op.dimsd = (op.shape[0],) modifies the operator in place to build the reference. It works, but it relies on Op.dimsd being writable and on nothing else caching the old shape. Building a second operator, or wrapping the original with a flat Reshape, would be more robust. If you keep it, add a one-line comment that it is deliberate.
• Final cost check. assert_array_almost_equal(cost, expected_cost) compares the two runs. Since the reference run uses a flat dimsd, this is fine. You could also assert that cost is finite and non-increasing in the first few iterations as a sanity check, but that is optional.
• Deblurring tutorial. The added comment is clear. If you want to be thorough, check whether examples/ has other fista calls on a flat model with ND data, for example with SWT2D.

Summary

The core change is good to merge once the four open points above are done. I made no code changes.

[mikamikasuki]

Added the input-layout clarification to ista, parameterized the regression over ISTA/FISTA, clarified its name/docstring, and moved it below the solver error tests. The flat reference uses a shallow copy of the operator; all 92 sparsity tests and lint pass.