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mccube._path

Defines custom paths for performing MCC in diffrax.

See diffrax.AbstractPath for futher information on the path API.

AbstractCubaturePath ¤

Bases: AbstractPath

Abstract base class for paths that define a cubature on Wiener space [@lyons2004].

Reference: [@lyons2004] 
@article{lyons2004,
  title     = {Cubature on Wiener Space},
  author    = {Lyons, Terry and Victoir, Nicolas},
  year      = {2004},
  journal   = {Proceedings: Mathematical, Physical and Engineering Sciences},
  publisher = {The Royal Society},
  number    = {2041},
  volume    = {460},
  pages     = {169--198},
  issn      = {13645021},
  url       = {https://www.jstor.org/stable/4143098}
}

Attributes:

LocalLinearCubaturePath ¤

LocalLinearCubaturePath(gaussian_cubature: AbstractGaussianCubature)

Bases: AbstractCubaturePath

Piecewise linear cubature paths.

The paths \(f(t_0, t_1) = \sqrt{(t_1 - t_0)} M\), where \(M\) is the matrix of cubature points for a given mccube.AbstractGaussianCubature.

Parameters:

Source code in mccube/_path.py 
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def __init__(self, gaussian_cubature: AbstractGaussianCubature):
    """
    Args:
        gaussian_cubature: an instance of an [`mccube.AbstractGaussianCubature`][],
            whose points given the matrix $M$.
    """
    self.gaussian_cubature = gaussian_cubature

weights property ¤

weights: CubatureWeights

Vector of cubature weights associated with the cubature control paths.