Module `ateams.arithmetic.LinBoxWrapper`

Functions

def ComputePercolationEvents(boundary, filtration, homology, p, breaks)

Uses a variant of the Chen/Kerber (2011) and PHAT (2017) twist_reduce algorithm to compute the persistent homology of the complex specified by the flat boundary matrix and the filtration over the field $\mathbb{Z}/p\mathbb{Z}$ .

Args

boundary: Full boundary matrix (i.e. Cubical.matrices.full).
filtration: A list of indices specifying the order in which the cells in the complex will be added. The assumed order is adding cells in order of dimension.
homology: The homology group for which persistence is computed.
p: Characteristic of the field $\mathbb{Z}/p\mathbb{Z}$ .
breaks: Index locations for cells of each degree (i.e. Cubical.breaks).

def LanczosKernelSample(coboundary, zeros, faces, columns, p, maxTries=8)

Uses the LinBox (Block?) Lanczos black-box solver to get a uniform random element of the kernel of the coboundary.

Args

coboundary: Memory-contiguous one-dimensional coboundary array, like that of the Cubical Complex object.
zeros: Memory-contiguous array of row indices that will be included in the coboundary submatrix.
faces: The number of faces per plaquette.
columns: Integer representing the number of columns in the coboundary submatrix; should be the total number of faces in the complex.
p: Characteristic of the field $\mathbb Z/p\mathbb Z$ .
maxTries: How many times do we try to get a nonzero solution from the black-box solver? Default is 8.

Returns

A C++ std::vector with spin assignments.

def SubLanczosKernelSample(coboundary, zeroRows, zeroColumns, p, maxTries=8)

Uses the LinBox (Block?) Lanczos black-box solver to get a uniform random element of the kernel of the coboundary.

Args

coboundary: Memory-contiguous one-dimensional coboundary array, like that of the Cubical Complex object.
zeros: Memory-contiguous array of row indices that will be included in the coboundary submatrix.
p: Characteristic of the field $\mathbb Z/p\mathbb Z$ .
maxTries: How many times do we try to get a nonzero solution from the black-box solver? Default is 8.

Returns

A C++ std::vector with spin assignments.