feat(qmc): add Lattice quasi-Monte Carlo sampler

[Samuel-Vangu]

feat(qmc): add Lattice quasi-Monte Carlo sampler

Description

Summary of changes

• Adds a randomly shifted rank-1 lattice quasi-Monte Carlo sampler, shaped like RNG (and mirroring the existing Sobol sampler), that plugs into MonteCarlo.integrate via the existing rng= slot.
• Points are generated from a component-by-component (CBC) generating vector (lattice-33002-1024-1048576.9125, from Frances Y. Kuo's Lattice Rule Generating Vectors collection, order-3 weights, dimensions up to 9125, sample sizes from 1024 to 1048576) as x_i = frac(i * z / N).
• A random shift modulo one is applied on every call to uniform to keep the QMC estimator unbiased. With a fixed seed, the shift is reproducible across calls; without one, each call draws its own independent shift.
• torch backend only for now — the modular arithmetic and shift use torch.Generator/tensor ops directly; there is no SciPy/other-backend path like Sobol's, since scipy.stats.qmc has no rank-1 lattice rule.
• Sample points are constants, so autodiff through the integrand and domain is preserved exactly as with plain Monte Carlo (and with Sobol).
• Exposed as torchquad.Lattice.

Addresses #140 (MonteCarlo path; VEGAS and JIT support to follow). Motivated by the QMC request in #217.

Resolved Issues

• fixes Low Discrepancy Sequences for MonteCarlo and VEGAS #140

How Has This Been Tested?

• Analytic accuracy on a smooth integrand
• Lattice beating plain Monte Carlo at equal N
• Seed reproducibility (fixed seed ⇒ identical result)
• Torch gradient-flow check (autodiff survives through the integral)
• Closed-form check: unshifted points match frac(i*z/N) computed independently from the on-disk generating vector
• Shift behaviour: same seed reproduces the shift across calls; no seed draws an independent shift each call; shift=False ignores the seed entirely
• Input validation: N/dim range checks, power-of-two warning, whole-number/bool type checks

Related Pull Requests

• feat: add Sobol quasi-Monte Carlo sampler #244

[Samuel-Vangu]

Hi @gomezzz, could you please trigger the CI for this PR when you have time? Thank you!

[Samuel-Vangu]

@gomezzz, pushed a few fixes (ruff formatting + moving import torch local to
Lattice.uniform) — could you trigger the CI again when you get a chance? Thanks!

[Samuel-Vangu]

Hi @gomezzz, sorry for the back-and-forth — pushed another fix, could you trigger CI once more when you get a chance? Thanks for your patience!

[Samuel-Vangu]

Hi @gomezzz, pushed pydoclint fixes , could you approve/trigger CI when you get a chance? Thanks!