[SPARK-7368] [MLLIB] Add QR decomposition for RowMatrix

jira: https://issues.apache.org/jira/browse/SPARK-7368
Add QR decomposition for RowMatrix.

I'm not sure what's the blueprint about the distributed Matrix from community and whether this will be a desirable feature , so I sent a prototype for discussion. I'll go on polish the code and provide ut and performance statistics if it's acceptable.

The implementation refers to the [paper: https://www.cs.purdue.edu/homes/dgleich/publications/Benson%202013%20-%20direct-tsqr.pdf]
Austin R. Benson, David F. Gleich, James Demmel. "Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures", 2013 IEEE International Conference on Big Data, which is a stable algorithm with good scalability.

Currently I tried it on a 400000 * 500 rowMatrix (16 partitions) and it can bring down the computation time from 8.8 mins (using breeze.linalg.qr.reduced)  to 2.6 mins on a 4 worker cluster. I think there will still be some room for performance improvement.

Any trial and suggestion is welcome.

Author: Yuhao Yang <hhbyyh@gmail.com>

Closes #5909 from hhbyyh/qrDecomposition and squashes the following commits:

cec797b [Yuhao Yang] remove unnecessary qr
0fb1012 [Yuhao Yang] hierarchy R computing
3fbdb61 [Yuhao Yang] update qr to indirect and add ut
0d913d3 [Yuhao Yang] Merge remote-tracking branch 'upstream/master' into qrDecomposition
39213c3 [Yuhao Yang] Merge remote-tracking branch 'upstream/master' into qrDecomposition
c0fc0c7 [Yuhao Yang] Merge remote-tracking branch 'upstream/master' into qrDecomposition
39b0b22 [Yuhao Yang] initial draft for discussion

1 files changed, 17 insertions, 0 deletions

diff --git a/mllib/src/test/scala/org/apache/spark/mllib/linalg/distributed/RowMatrixSuite.scala b/mllib/src/test/scala/org/apache/spark/mllib/linalg/distributed/RowMatrixSuite.scala
index b6cb53d0c7..283ffec1d4 100644
--- a/mllib/src/test/scala/org/apache/spark/mllib/linalg/distributed/RowMatrixSuite.scala
+++ b/mllib/src/test/scala/org/apache/spark/mllib/linalg/distributed/RowMatrixSuite.scala
@@ -19,6 +19,7 @@ package org.apache.spark.mllib.linalg.distributed
 
 import scala.util.Random
 
+import breeze.numerics.abs
 import breeze.linalg.{DenseVector => BDV, DenseMatrix => BDM, norm => brzNorm, svd => brzSvd}
 
 import org.apache.spark.SparkFunSuite
@@ -238,6 +239,22 @@ class RowMatrixSuite extends SparkFunSuite with MLlibTestSparkContext {
       }
     }
   }
+
+  test("QR Decomposition") {
+    for (mat <- Seq(denseMat, sparseMat)) {
+      val result = mat.tallSkinnyQR(true)
+      val expected = breeze.linalg.qr.reduced(mat.toBreeze())
+      val calcQ = result.Q
+      val calcR = result.R
+      assert(closeToZero(abs(expected.q) - abs(calcQ.toBreeze())))
+      assert(closeToZero(abs(expected.r) - abs(calcR.toBreeze.asInstanceOf[BDM[Double]])))
+      assert(closeToZero(calcQ.multiply(calcR).toBreeze - mat.toBreeze()))
+      // Decomposition without computing Q
+      val rOnly = mat.tallSkinnyQR(computeQ = false)
+      assert(rOnly.Q == null)
+      assert(closeToZero(abs(expected.r) - abs(rOnly.R.toBreeze.asInstanceOf[BDM[Double]])))
+    }
+  }
 }
 
 class RowMatrixClusterSuite extends SparkFunSuite with LocalClusterSparkContext {