qmc-sampler

Quasi-Monte Carlo point sampling from spectral optimisation.

qmc-sampler is a lightweight wrapper around blue_sampler that provides several sampling methods for generating quasi-Monte Carlo (QMC) point sets, by minimising the spectral loss over all wave vectors within an exclusion region. 3 kinds of exclusion regions, with different geometrical shape, are available: l2, l1, wd.

Installation

Install from PyPI:

pip install qmc-sampler

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)

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