scipy.stats.qmc.Sobol.integers#

Sobol.integers(l_bounds, *, u_bounds=None, n=1, endpoint=False, workers=1)[source]#

Draw n integers from l_bounds (inclusive) to u_bounds (exclusive), or if endpoint=True, l_bounds (inclusive) to u_bounds (inclusive).

Parameters:

l_boundsint or array-like of ints: Lowest (signed) integers to be drawn (unless u_bounds=None, in which case this parameter is 0 and this value is used for u_bounds).
u_boundsint or array-like of ints, optional: If provided, one above the largest (signed) integer to be drawn (see above for behavior if u_bounds=None). If array-like, must contain integer values.
nint, optional: Number of samples to generate in the parameter space. Default is 1.
endpointbool, optional: If true, sample from the interval [l_bounds, u_bounds] instead of the default [l_bounds, u_bounds). Defaults is False.
workersint, optional: Number of workers to use for parallel processing. If -1 is given all CPU threads are used. Only supported when using Halton Default is 1.

Returns:

samplearray_like (n, d): QMC sample.

Notes

It is safe to just use the same [0, 1) to integer mapping with QMC that you would use with MC. You still get unbiasedness, a strong law of large numbers, an asymptotically infinite variance reduction and a finite sample variance bound.

To convert a sample from \([0, 1)\) to \([a, b), b>a\), with \(a\) the lower bounds and \(b\) the upper bounds, the following transformation is used:

\[\text{floor}((b - a) \cdot \text{sample} + a)\]