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The :class:`torch.quasirandom.SobolEngine` is an engine for generating
(scrambled) Sobol sequences. Sobol sequences are an example of low
discrepancy quasi-random sequences.
This implementation of an engine for Sobol sequences is capable of
sampling sequences up to a maximum dimension of 21201. It uses direction
numbers from https://web.maths.unsw.edu.au/~fkuo/sobol/ obtained using the
search criterion D(6) up to the dimension 21201. This is the recommended
choice by the authors.
References:
- Art B. Owen. Scrambling Sobol and Niederreiter-Xing points.
Journal of Complexity, 14(4):466-489, December 1998.
- I. M. Sobol. The distribution of points in a cube and the accurate
evaluation of integrals.
Zh. Vychisl. Mat. i Mat. Phys., 7:784-802, 1967.
Args:
dimension (Int): The dimensionality of the sequence to be drawn
scramble (bool, optional): Setting this to ``True`` will produce
scrambled Sobol sequences. Scrambling is
capable of producing better Sobol
sequences. Default: ``False``.
seed (Int, optional): This is the seed for the scrambling. The seed
of the random number generator is set to this,
if specified. Otherwise, it uses a random seed.
Default: ``None``
Examples::
>>> # xdoctest: +SKIP("unseeded random state")
>>> soboleng = torch.quasirandom.SobolEngine(dimension=5)
>>> soboleng.draw(3)
tensor([[0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
[0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
[0.7500, 0.2500, 0.2500, 0.2500, 0.7500]])
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Function to draw a sequence of :attr:`n` points from a Sobol sequence.
Note that the samples are dependent on the previous samples. The size
of the result is :math:`(n, dimension)`.
Args:
n (Int, optional): The length of sequence of points to draw.
Default: 1
out (Tensor, optional): The output tensor
dtype (:class:`torch.dtype`, optional): the desired data type of the
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Default: ``None``
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Function to draw a sequence of :attr:`2**m` points from a Sobol sequence.
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of the result is :math:`(2**m, dimension)`.
Args:
m (Int): The (base2) exponent of the number of points to draw.
out (Tensor, optional): The output tensor
dtype (:class:`torch.dtype`, optional): the desired data type of the
returned tensor.
Default: ``None``
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n (Int): The number of steps to fast-forward by.
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