[SPARK-5507] Added documentation for BlockMatrix

Docs for BlockMatrix. mengxr

Author: Burak Yavuz <[email protected]>

Closes apache#4664 from brkyvz/SPARK-5507PR and squashes the following commits:

4db30b0 [Burak Yavuz] [SPARK-5507] Added documentation for BlockMatrix

docs/mllib-data-types.md

@@ -296,6 +296,81 @@ backed by an RDD of its entries.
 The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size.
 In general the use of non-deterministic RDDs can lead to errors.
 
+### BlockMatrix
+
+A `BlockMatrix` is a distributed matrix backed by an RDD of `MatrixBlock`s, where `MatrixBlock` is
+a tuple of `((Int, Int), Matrix)`, where the `(Int, Int)` is the index of the block, and `Matrix` is
+the sub-matrix at the given index with size `rowsPerBlock` x `colsPerBlock`.
+`BlockMatrix` supports methods such as `.add` and `.multiply` with another `BlockMatrix`.
+`BlockMatrix` also has a helper function `.validate` which can be used to debug whether the
+`BlockMatrix` is set up properly.
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+
+A [`BlockMatrix`](api/scala/index.html#org.apache.spark.mllib.linalg.distributed.BlockMatrix) can be
+most easily created from an `IndexedRowMatrix` or `CoordinateMatrix` using `.toBlockMatrix()`.
+`.toBlockMatrix()` will create blocks of size 1024 x 1024. Users may change the sizes of their blocks
+by supplying the values through `.toBlockMatrix(rowsPerBlock, colsPerBlock)`.
+
+{% highlight scala %}
+import org.apache.spark.mllib.linalg.SingularValueDecomposition
+import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
+
+val entries: RDD[MatrixEntry] = ... // an RDD of (i, j, v) matrix entries
+// Create a CoordinateMatrix from an RDD[MatrixEntry].
+val coordMat: CoordinateMatrix = new CoordinateMatrix(entries)
+// Transform the CoordinateMatrix to a BlockMatrix
+val matA: BlockMatrix = coordMat.toBlockMatrix().cache()
+
+// validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
+// Nothing happens if it is valid.
+matA.validate
+
+// Calculate A^T A.
+val AtransposeA = matA.transpose.multiply(matA)
+
+// get SVD of 2 * A
+val A2 = matA.add(matA)
+val svd = A2.toIndexedRowMatrix().computeSVD(20, false, 1e-9)
+{% endhighlight %}
+</div>
+
+<div data-lang="java" markdown="1">
+
+A [`BlockMatrix`](api/scala/index.html#org.apache.spark.mllib.linalg.distributed.BlockMatrix) can be
+most easily created from an `IndexedRowMatrix` or `CoordinateMatrix` using `.toBlockMatrix()`.
+`.toBlockMatrix()` will create blocks of size 1024 x 1024. Users may change the sizes of their blocks
+by supplying the values through `.toBlockMatrix(rowsPerBlock, colsPerBlock)`.
+
+{% highlight java %}
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.SingularValueDecomposition;
+import org.apache.spark.mllib.linalg.distributed.BlockMatrix;
+import org.apache.spark.mllib.linalg.distributed.CoordinateMatrix;
+import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix;
+
+JavaRDD<MatrixEntry> entries = ... // a JavaRDD of (i, j, v) Matrix Entries
+// Create a CoordinateMatrix from a JavaRDD<MatrixEntry>.
+CoordinateMatrix coordMat = new CoordinateMatrix(entries.rdd());
+// Transform the CoordinateMatrix to a BlockMatrix
+BlockMatrix matA = coordMat.toBlockMatrix().cache();
+
+// validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
+// Nothing happens if it is valid.
+matA.validate();
+
+// Calculate A^T A.
+BlockMatrix AtransposeA = matA.transpose().multiply(matA);
+
+// get SVD of 2 * A
+BlockMatrix A2 = matA.add(matA);
+SingularValueDecomposition<IndexedRowMatrix, Matrix> svd =
+  A2.toIndexedRowMatrix().computeSVD(20, false, 1e-9);
+{% endhighlight %}
+</div>
+</div>
+
 ### RowMatrix
 
 A `RowMatrix` is a row-oriented distributed matrix without meaningful row indices, backed by an RDD