Michel Lemay created MAHOUT-1790:
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             Summary: SparkEngine nnz overflow resultSize when reducing.
                 Key: MAHOUT-1790
                 URL: https://issues.apache.org/jira/browse/MAHOUT-1790
             Project: Mahout
          Issue Type: Bug
          Components: spark
    Affects Versions: 0.11.1
            Reporter: Michel Lemay
            Priority: Minor


When counting numNonZeroElementsPerColumn in spark engine with large number of 
columns, we get the following error:

ERROR TaskSetManager: Total size of serialized results of nnn tasks (1031.7 MB) 
is bigger than spark.driver.maxResultSize (1024.0 MB)

and then, the call stack:

org.apache.spark.SparkException: Job aborted due to stage failure: Total size 
of serialized results of 267 tasks (1024.1 MB) is bigger than 
spark.driver.maxResultSize (1024.0 MB)
        at 
org.apache.spark.scheduler.DAGScheduler.org$apache$spark$scheduler$DAGScheduler$$failJobAndIndependentStages(DAGScheduler.scala:1283)
        at 
org.apache.spark.scheduler.DAGScheduler$$anonfun$abortStage$1.apply(DAGScheduler.scala:1271)
        at 
org.apache.spark.scheduler.DAGScheduler$$anonfun$abortStage$1.apply(DAGScheduler.scala:1270)
        at 
scala.collection.mutable.ResizableArray$class.foreach(ResizableArray.scala:59)
        at scala.collection.mutable.ArrayBuffer.foreach(ArrayBuffer.scala:47)
        at 
org.apache.spark.scheduler.DAGScheduler.abortStage(DAGScheduler.scala:1270)
        at 
org.apache.spark.scheduler.DAGScheduler$$anonfun$handleTaskSetFailed$1.apply(DAGScheduler.scala:697)
        at 
org.apache.spark.scheduler.DAGScheduler$$anonfun$handleTaskSetFailed$1.apply(DAGScheduler.scala:697)
        at scala.Option.foreach(Option.scala:236)
        at 
org.apache.spark.scheduler.DAGScheduler.handleTaskSetFailed(DAGScheduler.scala:697)
        at 
org.apache.spark.scheduler.DAGSchedulerEventProcessLoop.doOnReceive(DAGScheduler.scala:1496)
        at 
org.apache.spark.scheduler.DAGSchedulerEventProcessLoop.onReceive(DAGScheduler.scala:1458)
        at 
org.apache.spark.scheduler.DAGSchedulerEventProcessLoop.onReceive(DAGScheduler.scala:1447)
        at org.apache.spark.util.EventLoop$$anon$1.run(EventLoop.scala:48)
        at 
org.apache.spark.scheduler.DAGScheduler.runJob(DAGScheduler.scala:567)
        at org.apache.spark.SparkContext.runJob(SparkContext.scala:1822)
        at org.apache.spark.SparkContext.runJob(SparkContext.scala:1942)
        at org.apache.spark.rdd.RDD$$anonfun$reduce$1.apply(RDD.scala:1003)
        at 
org.apache.spark.rdd.RDDOperationScope$.withScope(RDDOperationScope.scala:147)
        at 
org.apache.spark.rdd.RDDOperationScope$.withScope(RDDOperationScope.scala:108)
        at org.apache.spark.rdd.RDD.withScope(RDD.scala:306)
        at org.apache.spark.rdd.RDD.reduce(RDD.scala:985)
        at 
org.apache.mahout.sparkbindings.SparkEngine$.numNonZeroElementsPerColumn(SparkEngine.scala:86)
        at 
org.apache.mahout.math.drm.CheckpointedOps.numNonZeroElementsPerColumn(CheckpointedOps.scala:37)
        at 
org.apache.mahout.math.cf.SimilarityAnalysis$.sampleDownAndBinarize(SimilarityAnalysis.scala:286)
        at 
org.apache.mahout.math.cf.SimilarityAnalysis$.cooccurrences(SimilarityAnalysis.scala:66)
        at 
org.apache.mahout.math.cf.SimilarityAnalysis$.cooccurrencesIDSs(SimilarityAnalysis.scala:141)

This occurs because it uses a DenseVector and spark seemingly aggregate all of 
them on the driver before reducing.  

I think this could be easily prevented with a treeReduce(_ += _, depth)  
instead of a reduce(_ += _)

'depth' could be computed in function of 'n' and numberOfPartitions.. something 
in the line of:

  val maxResultSize = ....
  val numPartitions = drm.rdd.partitions.size
  val n = drm.ncol
  val bytesPerVector = n * 8 + overhead?
  val maxVectors = maxResultSize / bytes / 2 + 1 // be safe
  val depth = math.ceil(math.log(numPartitions / maxVectors) / 
math.log(2)).toInt






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