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181 lines
7.4 KiB
181 lines
7.4 KiB
5 months ago
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import torch
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from typing import Optional
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class SobolEngine:
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r"""
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The :class:`torch.quasirandom.SobolEngine` is an engine for generating
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(scrambled) Sobol sequences. Sobol sequences are an example of low
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discrepancy quasi-random sequences.
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This implementation of an engine for Sobol sequences is capable of
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sampling sequences up to a maximum dimension of 21201. It uses direction
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numbers from https://web.maths.unsw.edu.au/~fkuo/sobol/ obtained using the
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search criterion D(6) up to the dimension 21201. This is the recommended
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choice by the authors.
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References:
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- Art B. Owen. Scrambling Sobol and Niederreiter-Xing points.
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Journal of Complexity, 14(4):466-489, December 1998.
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- I. M. Sobol. The distribution of points in a cube and the accurate
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evaluation of integrals.
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Zh. Vychisl. Mat. i Mat. Phys., 7:784-802, 1967.
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Args:
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dimension (Int): The dimensionality of the sequence to be drawn
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scramble (bool, optional): Setting this to ``True`` will produce
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scrambled Sobol sequences. Scrambling is
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capable of producing better Sobol
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sequences. Default: ``False``.
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seed (Int, optional): This is the seed for the scrambling. The seed
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of the random number generator is set to this,
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if specified. Otherwise, it uses a random seed.
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Default: ``None``
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Examples::
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>>> # xdoctest: +SKIP("unseeded random state")
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>>> soboleng = torch.quasirandom.SobolEngine(dimension=5)
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>>> soboleng.draw(3)
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tensor([[0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
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[0.5000, 0.5000, 0.5000, 0.5000, 0.5000],
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[0.7500, 0.2500, 0.2500, 0.2500, 0.7500]])
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"""
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MAXBIT = 30
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MAXDIM = 21201
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def __init__(self, dimension, scramble=False, seed=None):
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if dimension > self.MAXDIM or dimension < 1:
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raise ValueError("Supported range of dimensionality "
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f"for SobolEngine is [1, {self.MAXDIM}]")
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self.seed = seed
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self.scramble = scramble
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self.dimension = dimension
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cpu = torch.device("cpu")
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self.sobolstate = torch.zeros(dimension, self.MAXBIT, device=cpu, dtype=torch.long)
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torch._sobol_engine_initialize_state_(self.sobolstate, self.dimension)
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if not self.scramble:
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self.shift = torch.zeros(self.dimension, device=cpu, dtype=torch.long)
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else:
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self._scramble()
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self.quasi = self.shift.clone(memory_format=torch.contiguous_format)
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self._first_point = (self.quasi / 2 ** self.MAXBIT).reshape(1, -1)
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self.num_generated = 0
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def draw(self, n: int = 1, out: Optional[torch.Tensor] = None,
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dtype: torch.dtype = torch.float32) -> torch.Tensor:
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r"""
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Function to draw a sequence of :attr:`n` points from a Sobol sequence.
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Note that the samples are dependent on the previous samples. The size
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of the result is :math:`(n, dimension)`.
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Args:
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n (Int, optional): The length of sequence of points to draw.
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Default: 1
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out (Tensor, optional): The output tensor
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dtype (:class:`torch.dtype`, optional): the desired data type of the
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returned tensor.
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Default: ``torch.float32``
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"""
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if self.num_generated == 0:
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if n == 1:
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result = self._first_point.to(dtype)
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else:
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result, self.quasi = torch._sobol_engine_draw(
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self.quasi, n - 1, self.sobolstate, self.dimension, self.num_generated, dtype=dtype,
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)
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result = torch.cat((self._first_point, result), dim=-2)
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else:
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result, self.quasi = torch._sobol_engine_draw(
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self.quasi, n, self.sobolstate, self.dimension, self.num_generated - 1, dtype=dtype,
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)
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self.num_generated += n
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if out is not None:
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out.resize_as_(result).copy_(result)
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return out
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return result
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def draw_base2(self, m: int, out: Optional[torch.Tensor] = None,
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dtype: torch.dtype = torch.float32) -> torch.Tensor:
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r"""
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Function to draw a sequence of :attr:`2**m` points from a Sobol sequence.
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Note that the samples are dependent on the previous samples. The size
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of the result is :math:`(2**m, dimension)`.
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Args:
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m (Int): The (base2) exponent of the number of points to draw.
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out (Tensor, optional): The output tensor
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dtype (:class:`torch.dtype`, optional): the desired data type of the
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returned tensor.
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Default: ``torch.float32``
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"""
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n = 2 ** m
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total_n = self.num_generated + n
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if not (total_n & (total_n - 1) == 0):
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raise ValueError("The balance properties of Sobol' points require "
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f"n to be a power of 2. {self.num_generated} points have been "
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f"previously generated, then: n={self.num_generated}+2**{m}={total_n}. "
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"If you still want to do this, please use "
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"'SobolEngine.draw()' instead."
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)
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return self.draw(n=n, out=out, dtype=dtype)
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def reset(self):
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r"""
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Function to reset the ``SobolEngine`` to base state.
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"""
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self.quasi.copy_(self.shift)
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self.num_generated = 0
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return self
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def fast_forward(self, n):
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r"""
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Function to fast-forward the state of the ``SobolEngine`` by
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:attr:`n` steps. This is equivalent to drawing :attr:`n` samples
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without using the samples.
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Args:
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n (Int): The number of steps to fast-forward by.
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"""
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if self.num_generated == 0:
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torch._sobol_engine_ff_(self.quasi, n - 1, self.sobolstate, self.dimension, self.num_generated)
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else:
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torch._sobol_engine_ff_(self.quasi, n, self.sobolstate, self.dimension, self.num_generated - 1)
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self.num_generated += n
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return self
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def _scramble(self):
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g: Optional[torch.Generator] = None
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if self.seed is not None:
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g = torch.Generator()
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g.manual_seed(self.seed)
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cpu = torch.device("cpu")
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# Generate shift vector
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shift_ints = torch.randint(2, (self.dimension, self.MAXBIT), device=cpu, generator=g)
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self.shift = torch.mv(shift_ints, torch.pow(2, torch.arange(0, self.MAXBIT, device=cpu)))
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# Generate lower triangular matrices (stacked across dimensions)
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ltm_dims = (self.dimension, self.MAXBIT, self.MAXBIT)
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ltm = torch.randint(2, ltm_dims, device=cpu, generator=g).tril()
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torch._sobol_engine_scramble_(self.sobolstate, ltm, self.dimension)
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def __repr__(self):
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fmt_string = [f'dimension={self.dimension}']
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if self.scramble:
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fmt_string += ['scramble=True']
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if self.seed is not None:
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fmt_string += [f'seed={self.seed}']
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return self.__class__.__name__ + '(' + ', '.join(fmt_string) + ')'
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