qmc-sampler

Quasi-Monte Carlo point sampling with spectral exclusion and discrepancy-based criteria.

qmc-sampler is a lightweight wrapper around blue_sampler that provides several sampling methods for generating quasi-Monte Carlo (QMC) point sets.

Installation

Install from PyPI:

pip install qmc-sampler

For the optional KeOps backend:

Available sampling methods

The package provides three sampling methods:

• sample_l2(N, D, **kwargs) — uses a classical isotropic L_2-ball as the spectral exclusion region.
• sample_l1(N, D, **kwargs) — uses an L_1-ball, producing an anisotropic spectral exclusion region that can be useful when exploiting low effective dimensionality.
• sample_wd(N, D, **kwargs) — uses the wrap-around discrepancy (WD), a criterion designed to further exploit low-effective-dimensionality structure.

Here, N denotes the number of points and D the dimension.

Basic usage

from qmc_sampler import sample_l1, sample_l2, sample_wd

N = 1000
D = 2

points_l2 = sample_l2(N, D)
points_l1 = sample_l1(N, D)
points_wd = sample_wd(N, D)

Additional keyword arguments e.g. "chi = 0.4" can be passed to the sampling functions and forwarded to the underlying implementation.

Accelerated L2 sampling with FINUFFT

For supported 2D and 3D problems, blue_sampler provides an accelerated NUFFT-based implementation that can reduce the computational complexity from approximately O(N^2) to O(N\log N).

This backend requires a compatible GPU environment and additional dependencies. Install the appropriate extras supported by your version of blue_sampler, for example:

pip install "blue-sampler[gpu13]"

To use the accelerated backend, overwright the default sample_l2 implementation with:

def sample_l2(N, D, **kwargs):
    from blue_sampler.run.run_nufft import _nufft_pipeline

    kwargs.setdefault("verbose", 0)
    return _nufft_pipeline(N, D, **kwargs)

Note: This uses a private function from blue_sampler (indicated by the leading underscore), so its API may change between versions. The accelerated backend also requires compatible GPU dependencies and is intended for supported 2D and 3D problems.

Plotting utilities

The package also exposes plotting functions from blue_sampler:

from qmc_sampler import plot, plot_structure_factor

plot(...)
plot_structure_factor(...)

Refer to the upstream documentation for the accepted arguments.

Links

• Source code: hyperuniform-samplers on GitHub
• Underlying package: blue_sampler on PyPI
• Upstream repository: Recursive Gaussian Blue Noise
• Documentation: blue-sampler.readthedocs.io

License

MIT