quimb.tensor.geometry

Some functions for generating the edges of a lattice.

Module Contents

Functions

sort_unique(edges)

Make sure there are no duplicate edges and that for each

check_2d(coo, Lx, Ly, cyclic)

Check coo in inbounds for a maybe cyclic 2D lattice.

edges_2d_square(Lx, Ly[, cyclic, cells])

Return the graph edges of a finite 2D square lattice. The nodes

edges_2d_hexagonal(Lx, Ly[, cyclic, cells])

Return the graph edges of a finite 2D hexagonal lattice. There are two

edges_2d_triangular(Lx, Ly[, cyclic, cells])

Return the graph edges of a finite 2D triangular lattice. There is a

edges_2d_triangular_rectangular(Lx, Ly[, cyclic, cells])

Return the graph edges of a finite 2D triangular lattice tiled in a

edges_2d_kagome(Lx, Ly[, cyclic, cells])

Return the graph edges of a finite 2D kagome lattice. There are

check_3d(coo, Lx, Ly, Lz, cyclic)

Check coo in inbounds for a maybe cyclic 3D lattice.

edges_3d_cubic(Lx, Ly, Lz[, cyclic, cells])

Return the graph edges of a finite 3D cubic lattice. The nodes

edges_3d_pyrochlore(Lx, Ly, Lz[, cyclic, cells])

Return the graph edges of a finite 3D pyorchlore lattice. There are

edges_3d_diamond(Lx, Ly, Lz[, cyclic, cells])

Return the graph edges of a finite 3D diamond lattice. There are

edges_3d_diamond_cubic(Lx, Ly, Lz[, cyclic, cells])

Return the graph edges of a finite 3D diamond lattice tiled in a cubic

edges_tree_rand(n[, max_degree, seed])

Return a random tree with n nodes. This a convenience function for
quimb.tensor.geometry.sort_unique(edges)[source]

Make sure there are no duplicate edges and that for each coo_a < coo_b.

quimb.tensor.geometry.check_2d(coo, Lx, Ly, cyclic)[source]

Check coo in inbounds for a maybe cyclic 2D lattice.

quimb.tensor.geometry.edges_2d_square(Lx, Ly, cyclic=False, cells=None)[source]

Return the graph edges of a finite 2D square lattice. The nodes (sites) are labelled like (i, j).

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly)).

Returns:

edges

Return type:

list[((int, int), (int, int))]

quimb.tensor.geometry.edges_2d_hexagonal(Lx, Ly, cyclic=False, cells=None)[source]

Return the graph edges of a finite 2D hexagonal lattice. There are two sites per cell, and note the cells do not form a square tiling. The nodes (sites) are labelled like (i, j, s) for s in 'AB'.

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly)).

Returns:

edges

Return type:

list[((int, int, str), (int, int, str))]

quimb.tensor.geometry.edges_2d_triangular(Lx, Ly, cyclic=False, cells=None)[source]

Return the graph edges of a finite 2D triangular lattice. There is a single site per cell, and note the cells do not form a square tiling. The nodes (sites) are labelled like (i, j).

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly)).

Returns:

edges

Return type:

list[((int, int), (int, int))]

quimb.tensor.geometry.edges_2d_triangular_rectangular(Lx, Ly, cyclic=False, cells=None)[source]

Return the graph edges of a finite 2D triangular lattice tiled in a rectangular geometry. There are two sites per rectangular cell. The nodes (sites) are labelled like (i, j, s) for s in 'AB'.

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly)).

Returns:

edges

Return type:

list[((int, int, s), (int, int, s))]

quimb.tensor.geometry.edges_2d_kagome(Lx, Ly, cyclic=False, cells=None)[source]

Return the graph edges of a finite 2D kagome lattice. There are three sites per cell, and note the cells do not form a square tiling. The nodes (sites) are labelled like (i, j, s) for s in 'ABC'.

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly)).

Returns:

edges

Return type:

list[((int, int, str), (int, int, str))]

quimb.tensor.geometry.check_3d(coo, Lx, Ly, Lz, cyclic)[source]

Check coo in inbounds for a maybe cyclic 3D lattice.

quimb.tensor.geometry.edges_3d_cubic(Lx, Ly, Lz, cyclic=False, cells=None)[source]

Return the graph edges of a finite 3D cubic lattice. The nodes (sites) are labelled like (i, j, k).

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • Lz (int) – The number of cells along the z-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly), range(Lz)).

Returns:

edges

Return type:

list[((int, int, int), (int, int, int))]

quimb.tensor.geometry.edges_3d_pyrochlore(Lx, Ly, Lz, cyclic=False, cells=None)[source]

Return the graph edges of a finite 3D pyorchlore lattice. There are four sites per cell, and note the cells do not form a cubic tiling. The nodes (sites) are labelled like (i, j, k, s) for s in 'ABCD'.

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • Lz (int) – The number of cells along the z-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly), range(Lz)).

Returns:

edges

Return type:

list[((int, int, int, str), (int, int, int, str))]

quimb.tensor.geometry.edges_3d_diamond(Lx, Ly, Lz, cyclic=False, cells=None)[source]

Return the graph edges of a finite 3D diamond lattice. There are two sites per cell, and note the cells do not form a cubic tiling. The nodes (sites) are labelled like (i, j, k, s) for s in 'AB'.

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • Lz (int) – The number of cells along the z-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly), range(Lz)).

Returns:

edges

Return type:

list[((int, int, int, str), (int, int, int, str))]

quimb.tensor.geometry.edges_3d_diamond_cubic(Lx, Ly, Lz, cyclic=False, cells=None)[source]

Return the graph edges of a finite 3D diamond lattice tiled in a cubic geometry. There are eight sites per cubic cell. The nodes (sites) are labelled like (i, j, k, s) for s in 'ABCDEFGH'.

Parameters:

  • Lx (int) – The number of cells along the x-direction.

  • Ly (int) – The number of cells along the y-direction.

  • Lz (int) – The number of cells along the z-direction.

  • cyclic (bool, optional) – Whether to use periodic boundary conditions.

  • cells (list, optional) – A list of cells to use. If not given the cells used are itertools.product(range(Lx), range(Ly), range(Lz)).

Returns:

edges

Return type:

list[((int, int, int, str), (int, int, int, str))]

quimb.tensor.geometry.edges_tree_rand(n, max_degree=None, seed=None)[source]

Return a random tree with n nodes. This a convenience function for testing purposes and the trees generated are not guaranteed to be uniformly random (for that see networkx.random_tree).

Parameters:

  • n (int) – The number of nodes.

  • max_degree (int, optional) – The maximum degree of the nodes. For example max_degree=3 means generate a binary tree.

  • seed (int, optional) – The random seed.

Returns:

edges

Return type:

list[(int, int)]