scipy.stats.qmc.QMCEngine#

class scipy.stats.qmc.QMCEngine(d, *, seed=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.

seed{None, int, numpy.random.Generator}, optional

If seed is None the numpy.random.Generator singleton is used. If seed is an int, a new Generator instance is used, seeded with seed. If seed is already a Generator instance then that instance is used.

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 (used for the seed).

Subclassing

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

  • __init__(d, seed=None): at least fix the dimension. If the sampler does not take advantage of a seed (deterministic methods like Halton), this parameter can be omitted.

  • random(n): draw n from the engine and increase the counter num_generated by n.

Optionally, two other methods can be overwritten by subclasses:

  • reset: Reset the engine to it’s 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, seed=None):
...         super().__init__(d=d, seed=seed)
...
...
...     def random(self, n=1):
...         self.num_generated += n
...         return self.rng.random((n, self.d))
...
...
...     def reset(self):
...         super().__init__(d=self.d, seed=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

fast_forward(n)

Fast-forward the sequence by n positions.

random([n])

Draw n in the half-open interval [0, 1).

reset()

Reset the engine to base state.

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Quasi-Monte Carlo submodule (scipy.stats.qmc)

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