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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.spark.graphx.lib
import org.apache.spark.SparkFunSuite
import org.apache.spark.graphx._
import org.apache.spark.graphx.util.GraphGenerators
object GridPageRank {
def apply(nRows: Int, nCols: Int, nIter: Int, resetProb: Double): Seq[(VertexId, Double)] = {
val inNbrs = Array.fill(nRows * nCols)(collection.mutable.MutableList.empty[Int])
val outDegree = Array.fill(nRows * nCols)(0)
// Convert row column address into vertex ids (row major order)
def sub2ind(r: Int, c: Int): Int = r * nCols + c
// Make the grid graph
for (r <- 0 until nRows; c <- 0 until nCols) {
val ind = sub2ind(r, c)
if (r + 1 < nRows) {
outDegree(ind) += 1
inNbrs(sub2ind(r + 1, c)) += ind
}
if (c + 1 < nCols) {
outDegree(ind) += 1
inNbrs(sub2ind(r, c + 1)) += ind
}
}
// compute the pagerank
var pr = Array.fill(nRows * nCols)(resetProb)
for (iter <- 0 until nIter) {
val oldPr = pr
pr = new Array[Double](nRows * nCols)
for (ind <- 0 until (nRows * nCols)) {
pr(ind) = resetProb + (1.0 - resetProb) *
inNbrs(ind).map( nbr => oldPr(nbr) / outDegree(nbr)).sum
}
}
(0L until (nRows * nCols)).zip(pr)
}
}
class PageRankSuite extends SparkFunSuite with LocalSparkContext {
def compareRanks(a: VertexRDD[Double], b: VertexRDD[Double]): Double = {
a.leftJoin(b) { case (id, a, bOpt) => (a - bOpt.getOrElse(0.0)) * (a - bOpt.getOrElse(0.0)) }
.map { case (id, error) => error }.sum()
}
test("Star PageRank") {
withSpark { sc =>
val nVertices = 100
val starGraph = GraphGenerators.starGraph(sc, nVertices).cache()
val resetProb = 0.15
val errorTol = 1.0e-5
val staticRanks1 = starGraph.staticPageRank(numIter = 1, resetProb).vertices
val staticRanks2 = starGraph.staticPageRank(numIter = 2, resetProb).vertices.cache()
// Static PageRank should only take 2 iterations to converge
val notMatching = staticRanks1.innerZipJoin(staticRanks2) { (vid, pr1, pr2) =>
if (pr1 != pr2) 1 else 0
}.map { case (vid, test) => test }.sum()
assert(notMatching === 0)
val staticErrors = staticRanks2.map { case (vid, pr) =>
val p = math.abs(pr - (resetProb + (1.0 - resetProb) * (resetProb * (nVertices - 1)) ))
val correct = (vid > 0 && pr == resetProb) || (vid == 0L && p < 1.0E-5)
if (!correct) 1 else 0
}
assert(staticErrors.sum === 0)
val dynamicRanks = starGraph.pageRank(0, resetProb).vertices.cache()
assert(compareRanks(staticRanks2, dynamicRanks) < errorTol)
}
} // end of test Star PageRank
test("Star PersonalPageRank") {
withSpark { sc =>
val nVertices = 100
val starGraph = GraphGenerators.starGraph(sc, nVertices).cache()
val resetProb = 0.15
val errorTol = 1.0e-5
val staticRanks1 = starGraph.staticPersonalizedPageRank(0, numIter = 1, resetProb).vertices
val staticRanks2 = starGraph.staticPersonalizedPageRank(0, numIter = 2, resetProb)
.vertices.cache()
// Static PageRank should only take 2 iterations to converge
val notMatching = staticRanks1.innerZipJoin(staticRanks2) { (vid, pr1, pr2) =>
if (pr1 != pr2) 1 else 0
}.map { case (vid, test) => test }.sum
assert(notMatching === 0)
val staticErrors = staticRanks2.map { case (vid, pr) =>
val correct = (vid > 0 && pr == 0.0) ||
(vid == 0 && pr == resetProb)
if (!correct) 1 else 0
}
assert(staticErrors.sum === 0)
val dynamicRanks = starGraph.personalizedPageRank(0, 0, resetProb).vertices.cache()
assert(compareRanks(staticRanks2, dynamicRanks) < errorTol)
val parallelStaticRanks1 = starGraph
.staticParallelPersonalizedPageRank(Array(0), 1, resetProb).mapVertices {
case (vertexId, vector) => vector(0)
}.vertices.cache()
assert(compareRanks(staticRanks1, parallelStaticRanks1) < errorTol)
val parallelStaticRanks2 = starGraph
.staticParallelPersonalizedPageRank(Array(0, 1), 2, resetProb).mapVertices {
case (vertexId, vector) => vector(0)
}.vertices.cache()
assert(compareRanks(staticRanks2, parallelStaticRanks2) < errorTol)
// We have one outbound edge from 1 to 0
val otherStaticRanks2 = starGraph.staticPersonalizedPageRank(1, numIter = 2, resetProb)
.vertices.cache()
val otherDynamicRanks = starGraph.personalizedPageRank(1, 0, resetProb).vertices.cache()
val otherParallelStaticRanks2 = starGraph
.staticParallelPersonalizedPageRank(Array(0, 1), 2, resetProb).mapVertices {
case (vertexId, vector) => vector(1)
}.vertices.cache()
assert(compareRanks(otherDynamicRanks, otherStaticRanks2) < errorTol)
assert(compareRanks(otherStaticRanks2, otherParallelStaticRanks2) < errorTol)
assert(compareRanks(otherDynamicRanks, otherParallelStaticRanks2) < errorTol)
}
} // end of test Star PersonalPageRank
test("Grid PageRank") {
withSpark { sc =>
val rows = 10
val cols = 10
val resetProb = 0.15
val tol = 0.0001
val numIter = 50
val errorTol = 1.0e-5
val gridGraph = GraphGenerators.gridGraph(sc, rows, cols).cache()
val staticRanks = gridGraph.staticPageRank(numIter, resetProb).vertices.cache()
val dynamicRanks = gridGraph.pageRank(tol, resetProb).vertices.cache()
val referenceRanks = VertexRDD(
sc.parallelize(GridPageRank(rows, cols, numIter, resetProb))).cache()
assert(compareRanks(staticRanks, referenceRanks) < errorTol)
assert(compareRanks(dynamicRanks, referenceRanks) < errorTol)
}
} // end of Grid PageRank
test("Chain PageRank") {
withSpark { sc =>
val chain1 = (0 until 9).map(x => (x, x + 1))
val rawEdges = sc.parallelize(chain1, 1).map { case (s, d) => (s.toLong, d.toLong) }
val chain = Graph.fromEdgeTuples(rawEdges, 1.0).cache()
val resetProb = 0.15
val tol = 0.0001
val numIter = 10
val errorTol = 1.0e-5
val staticRanks = chain.staticPageRank(numIter, resetProb).vertices
val dynamicRanks = chain.pageRank(tol, resetProb).vertices
assert(compareRanks(staticRanks, dynamicRanks) < errorTol)
}
}
test("Chain PersonalizedPageRank") {
withSpark { sc =>
val chain1 = (0 until 9).map(x => (x, x + 1) )
val rawEdges = sc.parallelize(chain1, 1).map { case (s, d) => (s.toLong, d.toLong) }
val chain = Graph.fromEdgeTuples(rawEdges, 1.0).cache()
val resetProb = 0.15
val tol = 0.0001
val numIter = 10
val errorTol = 1.0e-1
val staticRanks = chain.staticPersonalizedPageRank(4, numIter, resetProb).vertices
val dynamicRanks = chain.personalizedPageRank(4, tol, resetProb).vertices
assert(compareRanks(staticRanks, dynamicRanks) < errorTol)
val parallelStaticRanks = chain
.staticParallelPersonalizedPageRank(Array(4), numIter, resetProb).mapVertices {
case (vertexId, vector) => vector(0)
}.vertices.cache()
assert(compareRanks(staticRanks, parallelStaticRanks) < errorTol)
}
}
}
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