[SPARK-9656][MLLIB][PYTHON] Add missing methods to PySpark's Distributed Linear Algebra Classes

This PR adds the remaining group of methods to PySpark's distributed linear algebra classes as follows:

* `RowMatrix` <sup>**[1]**</sup>
  1. `computeGramianMatrix`
  2. `computeCovariance`
  3. `computeColumnSummaryStatistics`
  4. `columnSimilarities`
  5. `tallSkinnyQR` <sup>**[2]**</sup>
* `IndexedRowMatrix` <sup>**[3]**</sup>
  1. `computeGramianMatrix`
* `CoordinateMatrix`
  1. `transpose`
* `BlockMatrix`
  1. `validate`
  2. `cache`
  3. `persist`
  4. `transpose`

**[1]**: Note: `multiply`, `computeSVD`, and `computePrincipalComponents` are already part of PR #7963 for SPARK-6227.
**[2]**: Implementing `tallSkinnyQR` uncovered a bug with our PySpark `RowMatrix` constructor.  As discussed on the dev list [here](http://apache-spark-developers-list.1001551.n3.nabble.com/K-Means-And-Class-Tags-td10038.html), there appears to be an issue with type erasure with RDDs coming from Java, and by extension from PySpark.  Although we are attempting to construct a `RowMatrix` from an `RDD[Vector]` in [PythonMLlibAPI](https://github.com/apache/spark/blob/master/mllib/src/main/scala/org/apache/spark/mllib/api/python/PythonMLLibAPI.scala#L1115), the `Vector` type is erased, resulting in an `RDD[Object]`.  Thus, when calling Scala's `tallSkinnyQR` from PySpark, we get a Java `ClassCastException` in which an `Object` cannot be cast to a Spark `Vector`.  As noted in the aforementioned dev list thread, this issue was also encountered with `DecisionTrees`, and the fix involved an explicit `retag` of the RDD with a `Vector` type.  Thus, this PR currently contains that fix applied to the `createRowMatrix` helper function in `PythonMLlibAPI`.  `IndexedRowMatrix` and `CoordinateMatrix` do not appear to have this issue likely due to their related helper functions in `PythonMLlibAPI` creating the RDDs explicitly from DataFrames with pattern matching, thus preserving the types.  However, this fix may be out of scope for this single PR, and it may be better suited in a separate JIRA/PR.  Therefore, I have marked this PR as WIP and am open to discussion.
**[3]**: Note: `multiply` and `computeSVD` are already part of PR #7963 for SPARK-6227.

Author: Mike Dusenberry <mwdusenb@us.ibm.com>

Closes #9441 from dusenberrymw/SPARK-9656_Add_Missing_Methods_to_PySpark_Distributed_Linear_Algebra.

1 files changed, 2 insertions, 1 deletions

diff --git a/mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/IndexedRowMatrix.scala b/mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/IndexedRowMatrix.scala
index 06b9c4ac67..b03b3ecde9 100644
--- a/mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/IndexedRowMatrix.scala
+++ b/mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/IndexedRowMatrix.scala
@@ -188,7 +188,8 @@ class IndexedRowMatrix @Since("1.0.0") (
   }
 
   /**
-   * Computes the Gramian matrix `A^T A`.
+   * Computes the Gramian matrix `A^T A`. Note that this cannot be
+   * computed on matrices with more than 65535 columns.
    */
   @Since("1.0.0")
   def computeGramianMatrix(): Matrix = {