graphframes (version 0.1.2)

gf_grid_ising_model: Generate a grid Ising model with random parameters

Description

Generate a grid Ising model with random parameters

Usage

gf_grid_ising_model(sc, n, v_std = 1, e_std = 1)

Arguments

sc

A Spark connection.

n

Length of one side of the grid. The grid will be of size n x n.

v_std

Standard deviation of normal distribution used to generate vertex factors "a". Default of 1.0.

e_std

Standard deviation of normal distribution used to generate edge factors "b". Default of 1.0.

Value

GraphFrame. Vertices have columns "id" and "a". Edges have columns "src", "dst", and "b". Edges are directed, but they should be treated as undirected in any algorithms run on this model. Vertex IDs are of the form "i,j". E.g., vertex "1,3" is in the second row and fourth column of the grid.

Details

This method generates a grid Ising model with random parameters. Ising models are probabilistic graphical models over binary variables xi. Each binary variable xi corresponds to one vertex, and it may take values -1 or +1. The probability distribution P(X) (over all xi) is parameterized by vertex factors ai and edge factors bij:

$$P(X) = (1/Z) * exp[ \sum_i a_i x_i + \sum_{ij} b_{ij} x_i x_j ]$$

Examples

# NOT RUN {
gf_grid_ising_model(sc, 5)
# }