Feat: add Lipschitz method to LinearOperator

[Megumi1773]

What

Add a Lipschitz method to LinearOperator that returns the Lipschitz constant of the operator, i.e. its largest singular value:

L = ||A||_2 = sqrt(max eigenvalue of A.H @ A)

A square=True flag returns the squared value (max eigenvalue of A.H @ A) directly.

Why

Closes #812. The issue notes that this exact pattern appears in many examples, tutorials and notebooks (especially with pyproximal solvers):

Op1 = Op.H * Op
L = np.abs(Op1.eigs(1, niter=5, tol=5e-2))[0]
tau = ...  # some formula using L
solver(tau=tau)

Having it as a first-class method avoids re-deriving the step size in every example and gives operators with a closed-form Lipschitz constant (e.g. Diagonal, Restriction, Blending, FFT) a single place to override it.

How

def Lipschitz(self, square=False, backend="numpy", **kwargs_eig):
    Op1 = self.H * self
    if backend == "numpy":
        maxeig = Op1.eigs(neigs=1, symmetric=True, **kwargs_eig)[0]
    else:
        from pylops.optimization.eigs import power_iteration
        maxeig = power_iteration(Op1, dtype=Op1.dtype, backend=backend, **kwargs_eig)[0]
    maxeig = np.abs(maxeig)
    return float(maxeig) if square else float(np.sqrt(maxeig))

• numpy backend: uses LinearOperator.eigs on the Hermitian normal operator (symmetric=True), as suggested in the issue.
• cupy/jax backends: defers to pylops.optimization.eigs.power_iteration, mirroring how pylops.optimization.cls_sparsity already handles non-numpy backends.

Testing

Added test_lipschitz to pytests/test_linearoperator.py, parametrized over real/complex and square/overdetermined operators. It checks:

• a (padded) Diagonal operator, where the largest singular value is the largest diagonal entry;
• square=True equals Lipschitz()**2;
• a dense MatrixMult, compared against np.linalg.svd(M, compute_uv=False)[0].

pytests/test_linearoperator.py::test_lipschitz[par1] PASSED
pytests/test_linearoperator.py::test_lipschitz[par2] PASSED
pytests/test_linearoperator.py::test_lipschitz[par1j] PASSED
pytests/test_linearoperator.py::test_lipschitz[par2j] PASSED

Full pytests/test_linearoperator.py + pytests/test_eigs.py: 54 passed. ruff check on both changed files passes.

Notes

I could not run make tests_gpu, so the cupy/jax branch is written to match the existing power_iteration call convention in cls_sparsity but was not exercised on a GPU here.

[codacy-production]

Up to standards ✅

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