Module « scipy.stats.qmc »

Classe « Halton »

Informations générales

Héritage

builtins.object
    ABC
        QMCEngine
            Halton

Définition

class Halton(QMCEngine):

Description _{[extrait de Halton.__doc__]}

Halton sequence.

    Pseudo-random number generator that generalize the Van der Corput sequence
    for multiple dimensions. The Halton sequence uses the base-two Van der
    Corput sequence for the first dimension, base-three for its second and
    base-:math:`n` for its n-dimension.

    Parameters
    ----------
    d : int
        Dimension of the parameter space.
    scramble : bool, optional
        If True, use Owen scrambling. Otherwise no scrambling is done.
        Default is True.
    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
    -----
    The Halton sequence has severe striping artifacts for even modestly
    large dimensions. These can be ameliorated by scrambling. Scrambling
    also supports replication-based error estimates and extends
    applicabiltiy to unbounded integrands.

    References
    ----------
    .. [1] Halton, "On the efficiency of certain quasi-random sequences of
       points in evaluating multi-dimensional integrals", Numerische
       Mathematik, 1960.
    .. [2] A. B. Owen. "A randomized Halton algorithm in R",
       arXiv:1706.02808, 2017.

    Examples
    --------
    Generate samples from a low discrepancy sequence of Halton.

    >>> from scipy.stats import qmc
    >>> sampler = qmc.Halton(d=2, scramble=False)
    >>> sample = sampler.random(n=5)
    >>> sample
    array([[0.        , 0.        ],
           [0.5       , 0.33333333],
           [0.25      , 0.66666667],
           [0.75      , 0.11111111],
           [0.125     , 0.44444444]])

    Compute the quality of the sample using the discrepancy criterion.

    >>> qmc.discrepancy(sample)
    0.088893711419753

    If some wants to continue an existing design, extra points can be obtained
    by calling again `random`. Alternatively, you can skip some points like:

    >>> _ = sampler.fast_forward(5)
    >>> sample_continued = sampler.random(n=5)
    >>> sample_continued
    array([[0.3125    , 0.37037037],
           [0.8125    , 0.7037037 ],
           [0.1875    , 0.14814815],
           [0.6875    , 0.48148148],
           [0.4375    , 0.81481481]])

    Finally, samples can be scaled to bounds.

    >>> l_bounds = [0, 2]
    >>> u_bounds = [10, 5]
    >>> qmc.scale(sample_continued, l_bounds, u_bounds)
    array([[3.125     , 3.11111111],
           [8.125     , 4.11111111],
           [1.875     , 2.44444444],
           [6.875     , 3.44444444],
           [4.375     , 4.44444444]])

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, d: 'IntNumber', *, scramble: 'bool' = True, seed: 'SeedType' = None) -> 'None'

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe QMCEngine

__init_subclass__, __subclasshook__, fast_forward, reset

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__