QMCEngine — SciPy v1.15.2 Manual (original) (raw)

scipy.stats.qmc.

class scipy.stats.qmc.QMCEngine(d, *, optimization=None, rng=None)[source]#

A generic Quasi-Monte Carlo sampler class meant for subclassing.

QMCEngine is a base class to construct a specific Quasi-Monte Carlo sampler. It cannot be used directly as a sampler.

Parameters:

dint

Dimension of the parameter space.

optimization{None, “random-cd”, “lloyd”}, optional

Whether to use an optimization scheme to improve the quality after sampling. Note that this is a post-processing step that does not guarantee that all properties of the sample will be conserved. Default is None.

• random-cd: random permutations of coordinates to lower the centered discrepancy. The best sample based on the centered discrepancy is constantly updated. Centered discrepancy-based sampling shows better space-filling robustness toward 2D and 3D subprojections compared to using other discrepancy measures.
• lloyd: Perturb samples using a modified Lloyd-Max algorithm. The process converges to equally spaced samples.

Added in version 1.10.0.

rngnumpy.random.Generator, optional

Pseudorandom number generator state. When rng is None, a newnumpy.random.Generator is created using entropy from the operating system. Types other than numpy.random.Generator are passed to numpy.random.default_rng to instantiate a Generator.

Changed in version 1.15.0: As part of the SPEC-007transition from use of numpy.random.RandomState tonumpy.random.Generator, this keyword was changed from seed to_rng_. For an interim period, both keywords will continue to work, although only one may be specified at a time. After the interim period, function calls using the seed keyword will emit warnings. Following a deprecation period, the seed keyword will be removed.

Notes

By convention samples are distributed over the half-open interval[0, 1). Instances of the class can access the attributes: d for the dimension; and rng for the random number generator.

Subclassing

When subclassing QMCEngine to create a new sampler, __init__ andrandom must be redefined.

• __init__(d, rng=None): at least fix the dimension. If the sampler does not take advantage of a rng (deterministic methods like Halton), this parameter can be omitted.
• _random(n, *, workers=1): draw n from the engine. workersis used for parallelism. See Halton for example.

Optionally, two other methods can be overwritten by subclasses:

• reset: Reset the engine to its original state.
• fast_forward: If the sequence is deterministic (like Halton sequence), then fast_forward(n) is skipping the n first draw.

Examples

To create a random sampler based on np.random.random, we would do the following:

from scipy.stats import qmc class RandomEngine(qmc.QMCEngine): ... def init(self, d, rng=None): ... super().init(d=d, rng=rng) ... ... ... def _random(self, n=1, *, workers=1): ... return self.rng.random((n, self.d)) ... ... ... def reset(self): ... super().init(d=self.d, rng=self.rng_seed) ... return self ... ... ... def fast_forward(self, n): ... self.random(n) ... return self

After subclassing QMCEngine to define the sampling strategy we want to use, we can create an instance to sample from.

engine = RandomEngine(2) engine.random(5) array([[0.22733602, 0.31675834], # random [0.79736546, 0.67625467], [0.39110955, 0.33281393], [0.59830875, 0.18673419], [0.67275604, 0.94180287]])

We can also reset the state of the generator and resample again.

_ = engine.reset() engine.random(5) array([[0.22733602, 0.31675834], # random [0.79736546, 0.67625467], [0.39110955, 0.33281393], [0.59830875, 0.18673419], [0.67275604, 0.94180287]])

Methods