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import itertools
from pyspark.sql import functions as sqlfunctions
from graphframes import GraphFrame
__all__ = ['Graphs']
[docs]class Graphs(object):
"""Example GraphFrames for testing the API
:param spark: SparkSession
"""
def __init__(self, spark):
self._spark = spark
self._sc = spark._sc
[docs] def friends(self):
"""A GraphFrame of friends in a (fake) social network."""
# Vertex DataFrame
v = self._spark.createDataFrame([
("a", "Alice", 34),
("b", "Bob", 36),
("c", "Charlie", 30),
("d", "David", 29),
("e", "Esther", 32),
("f", "Fanny", 36)
], ["id", "name", "age"])
# Edge DataFrame
e = self._spark.createDataFrame([
("a", "b", "friend"),
("b", "c", "follow"),
("c", "b", "follow"),
("f", "c", "follow"),
("e", "f", "follow"),
("e", "d", "friend"),
("d", "a", "friend")
], ["src", "dst", "relationship"])
# Create a GraphFrame
return GraphFrame(v, e)
[docs] def gridIsingModel(self, n, vStd=1.0, eStd=1.0):
"""Grid Ising model with random parameters.
Ising models are probabilistic graphical models over binary variables x\ :sub:`i`.
Each binary variable x\ :sub:`i` corresponds to one vertex, and it may take values -1 or +1.
The probability distribution P(X) (over all x\ :sub:`i`) is parameterized by vertex factors
a\ :sub:`i` and edge factors b\ :sub:`ij`:
P(X) = (1/Z) * exp[ \sum_i a_i x_i + \sum_{ij} b_{ij} x_i x_j ]
where Z is the normalization constant (partition function). See `Wikipedia
<https://en.wikipedia.org/wiki/Ising_model>`__ for more information on Ising models.
Each vertex is parameterized by a single scalar a\ :sub:`i`.
Each edge is parameterized by a single scalar b\ :sub:`ij`.
:param n: Length of one side of the grid. The grid will be of size n x n.
:param vStd: Standard deviation of normal distribution used to generate vertex factors "a".
Default of 1.0.
:param eStd: Standard deviation of normal distribution used to generate edge factors "b".
Default of 1.0.
:return: 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.
"""
# check param n
if n < 1:
raise ValueError(
"Grid graph must have size >= 1, but was given invalid value n = {}"
.format(n))
# create coodinates grid
coordinates = self._spark.createDataFrame(
itertools.product(range(n), range(n)),
schema=('i', 'j'))
# create SQL expression for converting coordinates (i,j) to a string ID "i,j"
# avoid Cartesian join due to SPARK-15425: use generator since n should be small
toIDudf = sqlfunctions.udf(lambda i, j: '{},{}'.format(i,j))
# create the vertex DataFrame
# create SQL expression for converting coordinates (i,j) to a string ID "i,j"
vIDcol = toIDudf(sqlfunctions.col('i'), sqlfunctions.col('j'))
# add random parameters generated from a normal distribution
seed = 12345
vertices = (coordinates.withColumn('id', vIDcol)
.withColumn('a', sqlfunctions.randn(seed) * vStd))
# create the edge DataFrame
# create SQL expression for converting coordinates (i,j+1) and (i+1,j) to string IDs
rightIDcol = toIDudf(sqlfunctions.col('i'), sqlfunctions.col('j') + 1)
downIDcol = toIDudf(sqlfunctions.col('i') + 1, sqlfunctions.col('j'))
horizontalEdges = (coordinates.filter(sqlfunctions.col('j') != n - 1)
.select(vIDcol.alias('src'), rightIDcol.alias('dst')))
verticalEdges = (coordinates.filter(sqlfunctions.col('i') != n - 1)
.select(vIDcol.alias('src'), downIDcol.alias('dst')))
allEdges = horizontalEdges.unionAll(verticalEdges)
# add random parameters from a normal distribution
edges = allEdges.withColumn('b', sqlfunctions.randn(seed + 1) * eStd)
# create the GraphFrame
g = GraphFrame(vertices, edges)
# materialize graph as workaround for SPARK-13333
g.vertices.cache().count()
g.edges.cache().count()
return g