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# SobolEngine

class torch.quasirandom.SobolEngine(dimension, scramble=False, seed=None)

  The `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.

  Parameters:

    - 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]])

  draw(n=1, out=None, dtype=torch.float32)

    Function to draw a sequence of `n` points from a Sobol sequence. Note that the samples are dependent on the previous samples. The size of the result is (n,d i m e n s i o n)(n, dimension)(n,d im e n s i o n).

    Parameters:

      - n (Int, optional) – The length of sequence of points to draw. Default: 1

      - out (Tensor, optional) – The output tensor

      - dtype (`torch.dtype`, optional) – the desired data type of the returned tensor. Default: `torch.float32`

    Return type:

      Tensor

  draw_base2(m, out=None, dtype=torch.float32)

    Function to draw a sequence of `2**m` points from a Sobol sequence. Note that the samples are dependent on the previous samples. The size of the result is (2∗∗m,d i m e n s i o n)(2**m, dimension)(2∗∗m,d im e n s i o n).

    Parameters:

      - m (Int) – The (base2) exponent of the number of points to draw.

      - out (Tensor, optional) – The output tensor

      - dtype (`torch.dtype`, optional) – the desired data type of the returned tensor. Default: `torch.float32`

    Return type:

      Tensor

  fast_forward(n)

    Function to fast-forward the state of the `SobolEngine` by `n` steps. This is equivalent to drawing `n` samples without using the samples.

    Parameters:

      n (Int) – The number of steps to fast-forward by.

  reset()

    Function to reset the `SobolEngine` to base state.

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