Module « scipy.stats.qmc »

Classe « LatinHypercube »

Informations générales

Héritage

builtins.object
    ABC
        QMCEngine
            LatinHypercube

Définition

class LatinHypercube(QMCEngine):

Description _{[extrait de LatinHypercube.__doc__]}

Latin hypercube sampling (LHS).

    A Latin hypercube sample [1]_ generates :math:`n` points in
    :math:`[0,1)^{d}`. Each univariate marginal distribution is stratified,
    placing exactly one point in :math:`[j/n, (j+1)/n)` for
    :math:`j=0,1,...,n-1`. They are still applicable when :math:`n << d`.
    LHS is extremely effective on integrands that are nearly additive [2]_.
    LHS on :math:`n` points never has more variance than plain MC on
    :math:`n-1` points [3]_. There is a central limit theorem for LHS [4]_,
    but not necessarily for optimized LHS.

    Parameters
    ----------
    d : int
        Dimension of the parameter space.
    centered : bool, optional
        Center the point within the multi-dimensional grid. Default is False.
    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.

    References
    ----------
    .. [1] Mckay et al., "A Comparison of Three Methods for Selecting Values
       of Input Variables in the Analysis of Output from a Computer Code",
       Technometrics, 1979.
    .. [2] M. Stein, "Large sample properties of simulations using Latin
       hypercube sampling." Technometrics 29, no. 2: 143-151, 1987.
    .. [3] A. B. Owen, "Monte Carlo variance of scrambled net quadrature."
       SIAM Journal on Numerical Analysis 34, no. 5: 1884-1910, 1997
    .. [4]  Loh, W.-L. "On Latin hypercube sampling." The annals of statistics
       24, no. 5: 2058-2080, 1996.

    Examples
    --------
    Generate samples from a Latin hypercube generator.

    >>> from scipy.stats import qmc
    >>> sampler = qmc.LatinHypercube(d=2)
    >>> sample = sampler.random(n=5)
    >>> sample
    array([[0.1545328 , 0.53664833],  # random
           [0.84052691, 0.06474907],
           [0.52177809, 0.93343721],
           [0.68033825, 0.36265316],
           [0.26544879, 0.61163943]])

    Compute the quality of the sample using the discrepancy criterion.

    >>> qmc.discrepancy(sample)
    0.019558034794794565  # random

    Finally, samples can be scaled to bounds.

    >>> l_bounds = [0, 2]
    >>> u_bounds = [10, 5]
    >>> qmc.scale(sample, l_bounds, u_bounds)
    array([[1.54532796, 3.609945  ],  # random
           [8.40526909, 2.1942472 ],
           [5.2177809 , 4.80031164],
           [6.80338249, 3.08795949],
           [2.65448791, 3.83491828]])

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, d: 'IntNumber', *, centered: 'bool' = False, 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__