Abstract Base Classes

The module kernel_abc defines the base class for a hyperbolic graph and a hyperbolic tiling. It may serve as the starting point for the construction of new kernels. Please note that this module is abstract and its classes are intended to be subclassed in the application. It does not provide full implementations.

Tiling Base Class

class hypertiling.kernel_abc.Tiling(p: int, q: int, n: int, mangle: float = 0.0021547274537546575)

This is the abstract base class of a hyperbolic tiling.

p

The first fundamental lattice parameter.

Type:: int

q

The second fundamental lattice parameter.

Type:: int

n

A parameter defining the size of the tiling.

Type:: int

phi

Angle of rotation that leaves the lattice invariant when cell centered.

Type:: float

qhi

Angle of rotation that leaves the lattice invariant when vertex centered.

Type:: float

r

Radius of the fundamental polygon in the Poincare disk.

Type:: float

h

Hyperbolic/geodesic lattice spacing, i.e., the edge length of any cell.

Type:: float

hr

Geodesic radius, i.e., distance between the center and any vertex of cells in a regular p,q tiling.

Type:: float

mangle

Magic angle required for technical reasons.

Type:: float

_nbrs

A placeholder for storing adjacency relations.

Type:: None

abstract get_angle(index: int) → float

Returns the angle to the center of the polygon at index.

Parameters:: index (int) – index of the polygon
Returns:: center of the polygon
Return type:: float

abstract get_center(index: int) → complex128

Returns the center of the polygon at index.

Parameters:: index (int) – index of the polygon
Returns:: center of the polygon
Return type:: np.complex128

abstract get_layer(index: int) → int

Returns the layer to the center of the polygon at index.

Parameters:: index (int) – index of the polygon
Returns:: layer of the polygon
Return type:: int

get_nbrs(i, **kwargs)

Returns the indices of the neighbours of vertex i.

Parameters:: i (int) – the cell index one is interested in.
Returns:: of all neighbour indice
Return type:: list

get_nbrs_list(**kwargs)

Calculates for each vertex the neighbours a returns a list.

Returns:: with neighbour indices
Return type:: List of list

abstract get_sector(index: int) → int

Returns the sector, the polygon at index refers to.

Parameters:: index (int) – index of the polygon
Returns:: number of the sector
Return type:: int

abstract get_vertices(index: int) → array

Returns the p vertices of the polygon at index.

Parameters:: index (int) – index of the polygon
Returns:: vertices of the polygon
Return type:: np.array[np.complex128][p]

Graph Base Class

class hypertiling.kernel_abc.Graph(p: int, q: int, n: int, mangle: float = 0.0021547274537546575)

The abstract base class of a hyperbolic graph.

Parameters:

p (int) – The first fundamental lattice parameter.
q (int) – The second fundamental lattice parameter.
n (int) – A parameter defining the size of the graph.
mangle (float, optional) – Magic angle required for technical reasons, by default MAGICANGLE

Raises: