[SPARK-16469] enhanced simulate multiply

## What changes were proposed in this pull request?

We have a use case of multiplying very big sparse matrices. we have about 1000x1000 distributed block matrices multiplication and the simulate multiply goes like O(n^4) (n being 1000). it takes about 1.5 hours. We modified it slightly with classical hashmap and now run in about 30 seconds O(n^2).

## How was this patch tested?

We have added a performance test and verified the reduced time.

Author: oraviv <[email protected]>

Closes #14068 from uzadude/master.

Author: uzadude

mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/BlockMatrix.scala

@@ -426,16 +426,21 @@ class BlockMatrix @Since("1.3.0") (
       partitioner: GridPartitioner): (BlockDestinations, BlockDestinations) = {
     val leftMatrix = blockInfo.keys.collect() // blockInfo should already be cached
     val rightMatrix = other.blocks.keys.collect()
+
+    val rightCounterpartsHelper = rightMatrix.groupBy(_._1).mapValues(_.map(_._2))
     val leftDestinations = leftMatrix.map { case (rowIndex, colIndex) =>
-      val rightCounterparts = rightMatrix.filter(_._1 == colIndex)
-      val partitions = rightCounterparts.map(b => partitioner.getPartition((rowIndex, b._2)))
+      val rightCounterparts = rightCounterpartsHelper.getOrElse(colIndex, Array())
+      val partitions = rightCounterparts.map(b => partitioner.getPartition((rowIndex, b)))
       ((rowIndex, colIndex), partitions.toSet)
     }.toMap
+
+    val leftCounterpartsHelper = leftMatrix.groupBy(_._2).mapValues(_.map(_._1))
     val rightDestinations = rightMatrix.map { case (rowIndex, colIndex) =>
-      val leftCounterparts = leftMatrix.filter(_._2 == rowIndex)
-      val partitions = leftCounterparts.map(b => partitioner.getPartition((b._1, colIndex)))
+      val leftCounterparts = leftCounterpartsHelper.getOrElse(rowIndex, Array())
+      val partitions = leftCounterparts.map(b => partitioner.getPartition((b, colIndex)))
       ((rowIndex, colIndex), partitions.toSet)
     }.toMap
+
     (leftDestinations, rightDestinations)
   }