Github user mengxr commented on a diff in the pull request:
https://github.com/apache/spark/pull/964#discussion_r13375801
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/RowMatrix.scala
---
@@ -221,15 +234,20 @@ class RowMatrix(
/**
* Computes the singular value decomposition of this matrix.
- * Denote this matrix by A (m x n), this will compute matrices U, S, V
such that A = U * S * V'.
+ * Denote this matrix by A (m x n), this will compute matrices U, S, V
such that A ~= U * S * V',
+ * where S contains the leading singular values, U and V contain the
corresponding singular
+ * vectors.
*
- * There is no restriction on m, but we require `n^2` doubles to fit in
memory.
- * Further, n should be less than m.
-
- * The decomposition is computed by first computing A'A = V S^2 V',
- * computing svd locally on that (since n x n is small), from which we
recover S and V.
- * Then we compute U via easy matrix multiplication as U = A * (V *
S^-1).
- * Note that this approach requires `O(n^3)` time on the master node.
+ * There is no restriction on m, but we require `n*(6*k+4)` doubles to
fit in memory on the master
+ * node. Further, n should be less than m.
+ *
+ * The decomposition is computed by providing a function that multiples
a vector with A'A to
+ * ARPACK, and iteratively invoking ARPACK-dsaupd on master node, from
which we recover S and V.
+ * Then we compute U via easy matrix multiplication as U = A * (V *
S-1).
--- End diff --
"S-1" -> "S^-1" or "S^{-1}"
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