import torch from typing import Optional class SobolEngine(object): r""" 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:: >>> 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]]) """ MAXBIT = 30 MAXDIM = 21201 def __init__(self, dimension, scramble=False, seed=None): if dimension > self.MAXDIM or dimension < 1: raise ValueError("Supported range of dimensionality " f"for SobolEngine is [1, {self.MAXDIM}]") self.seed = seed self.scramble = scramble self.dimension = dimension cpu = torch.device("cpu") self.sobolstate = torch.zeros(dimension, self.MAXBIT, device=cpu, dtype=torch.long) torch._sobol_engine_initialize_state_(self.sobolstate, self.dimension) if not self.scramble: self.shift = torch.zeros(self.dimension, device=cpu, dtype=torch.long) else: self._scramble() self.quasi = self.shift.clone(memory_format=torch.contiguous_format) self._first_point = (self.quasi / 2 ** self.MAXBIT).reshape(1, -1) self.num_generated = 0 def draw(self, n: int = 1, out: Optional[torch.Tensor] = None, dtype: torch.dtype = torch.float32) -> torch.Tensor: r""" 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 returned tensor. Default: ``torch.float32`` """ if self.num_generated == 0: if n == 1: result = self._first_point.to(dtype) else: result, self.quasi = torch._sobol_engine_draw( self.quasi, n - 1, self.sobolstate, self.dimension, self.num_generated, dtype=dtype, ) result = torch.cat((self._first_point, result), dim=-2) else: result, self.quasi = torch._sobol_engine_draw( self.quasi, n, self.sobolstate, self.dimension, self.num_generated - 1, dtype=dtype, ) self.num_generated += n if out is not None: out.resize_as_(result).copy_(result) return out return result def draw_base2(self, m: int, out: Optional[torch.Tensor] = None, dtype: torch.dtype = torch.float32) -> torch.Tensor: r""" Function to draw a sequence of :attr:`2**m` points from a Sobol sequence. Note that the samples are dependent on the previous samples. The size 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: ``torch.float32`` """ n = 2 ** m total_n = self.num_generated + n if not (total_n & (total_n - 1) == 0): raise ValueError("The balance properties of Sobol' points require " "n to be a power of 2. {0} points have been " "previously generated, then: n={0}+2**{1}={2}. " "If you still want to do this, please use " "'SobolEngine.draw()' instead." .format(self.num_generated, m, total_n)) return self.draw(n=n, out=out, dtype=dtype) def reset(self): r""" Function to reset the ``SobolEngine`` to base state. """ self.quasi.copy_(self.shift) self.num_generated = 0 return self def fast_forward(self, n): r""" Function to fast-forward the state of the ``SobolEngine`` by :attr:`n` steps. This is equivalent to drawing :attr:`n` samples without using the samples. Args: n (Int): The number of steps to fast-forward by. """ if self.num_generated == 0: torch._sobol_engine_ff_(self.quasi, n - 1, self.sobolstate, self.dimension, self.num_generated) else: torch._sobol_engine_ff_(self.quasi, n, self.sobolstate, self.dimension, self.num_generated - 1) self.num_generated += n return self def _scramble(self): g: Optional[torch.Generator] = None if self.seed is not None: g = torch.Generator() g.manual_seed(self.seed) cpu = torch.device("cpu") # Generate shift vector shift_ints = torch.randint(2, (self.dimension, self.MAXBIT), device=cpu, generator=g) self.shift = torch.mv(shift_ints, torch.pow(2, torch.arange(0, self.MAXBIT, device=cpu))) # Generate lower triangular matrices (stacked across dimensions) ltm_dims = (self.dimension, self.MAXBIT, self.MAXBIT) ltm = torch.randint(2, ltm_dims, device=cpu, generator=g).tril() torch._sobol_engine_scramble_(self.sobolstate, ltm, self.dimension) def __repr__(self): fmt_string = [f'dimension={self.dimension}'] if self.scramble: fmt_string += ['scramble=True'] if self.seed is not None: fmt_string += [f'seed={self.seed}'] return self.__class__.__name__ + '(' + ', '.join(fmt_string) + ')'