use specialized axpy in RowMatrix for SVD

After running some more tests on large matrix, found that the BV axpy (breeze/linalg/Vector.scala, axpy) is slower than the BSV axpy (breeze/linalg/operators/SparseVectorOps.scala, sv_dv_axpy), 8s v.s. 2s for each multiplication. The BV axpy operates on an iterator while BSV axpy directly operates on the underlying array. I think the overhead comes from creating the iterator (with a zip) and advancing the pointers.

Author: Li Pu <[email protected]>
Author: Xiangrui Meng <[email protected]>
Author: Li Pu <[email protected]>

Closes apache#1378 from vrilleup/master and squashes the following commits:

6fb01a3 [Li Pu] use specialized axpy in RowMatrix
5255f2a [Li Pu] Merge remote-tracking branch 'upstream/master'
7312ec1 [Li Pu] very minor comment fix
4c618e9 [Li Pu] Merge pull request #1 from mengxr/vrilleup-master
a461082 [Xiangrui Meng] make superscript show up correctly in doc
861ec48 [Xiangrui Meng] simplify axpy
62969fa [Xiangrui Meng] use BDV directly in symmetricEigs change the computation mode to local-svd, local-eigs, and dist-eigs update tests and docs
c273771 [Li Pu] automatically determine SVD compute mode and parameters
7148426 [Li Pu] improve RowMatrix multiply
5543cce [Li Pu] improve svd api
819824b [Li Pu] add flag for dense svd or sparse svd
eb15100 [Li Pu] fix binary compatibility
4c7aec3 [Li Pu] improve comments
e7850ed [Li Pu] use aggregate and axpy
827411b [Li Pu] fix EOF new line
9c80515 [Li Pu] use non-sparse implementation when k = n
fe983b0 [Li Pu] improve scala style
96d2ecb [Li Pu] improve eigenvalue sorting
e1db950 [Li Pu] SPARK-1782: svd for sparse matrix using ARPACK

Author: Li Pu

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

@@ -83,7 +83,13 @@ class RowMatrix(
       seqOp = (U, r) => {
         val rBrz = r.toBreeze
         val a = rBrz.dot(vbr.value)
-        brzAxpy(a, rBrz, U.asInstanceOf[BV[Double]])
+        rBrz match {
+          // use specialized axpy for better performance
+          case _: BDV[_] => brzAxpy(a, rBrz.asInstanceOf[BDV[Double]], U)
+          case _: BSV[_] => brzAxpy(a, rBrz.asInstanceOf[BSV[Double]], U)
+          case _ => throw new UnsupportedOperationException(
+            s"Do not support vector operation from type ${rBrz.getClass.getName}.")
+        }
         U
       },
       combOp = (U1, U2) => U1 += U2