Github user yu-iskw commented on a diff in the pull request:
https://github.com/apache/spark/pull/8563#discussion_r43609930
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/BlockMatrix.scala
---
@@ -402,4 +441,474 @@ class BlockMatrix @Since("1.3.0") (
s"A.colsPerBlock: $colsPerBlock, B.rowsPerBlock:
${other.rowsPerBlock}")
}
}
+
+ /**
+ * Schur Complement of a BlockMatrix. For a matrix that is in 4
partitions:
+ * A=[a11, a12; a21; a22], the Schur Complement S is S = a22 - (a21 *
a11^-1 * a12).
+ * The Schur Complement is always (n-1) x (n-1), which is the size of
a22. a11 is expected
+ * to fit into memory so that Breeze inversions can be computed.
+ *
+ * @return BlockMatrix Schur Complement as BlockMatrix
+ * @since 1.6.0
+ */
+ private[mllib] def SchurComplement: BlockMatrix = {
+ require(this.numRowBlocks == this.numColBlocks, "Block Matrix must be
square.")
+ require(this.numRowBlocks > 1, "Block Matrix must be larger than one
block.")
+ val topRange = (0, 0); val botRange = (1, this.numColBlocks - 1)
+ val a11 = this.subBlock(topRange, topRange)
+ val a12 = this.subBlock(topRange, botRange)
+ val a21 = this.subBlock(botRange, topRange)
+ val a22 = this.subBlock(botRange, botRange)
+
+ val a11Brz = inv(a11.toBreeze) // note that intermediate a11 calcs
derive from inv(a11)
+ val a11Mtx = Matrices.dense(a11.numRows.toInt, a11.numCols.toInt,
a11Brz.toArray)
+ val a11RDD = this.blocks.sparkContext.parallelize(Seq(((0, 0),
a11Mtx)))
+ val a11Inv = new BlockMatrix(a11RDD, this.rowsPerBlock,
this.colsPerBlock)
+
+ val S = a22.subtract(a21.multiply(a11Inv.multiply(a12)))
+ S
+ }
+
+ /**
+ * Returns a rectangular (sub)BlockMatrix with block ranges as
specified. Block Ranges
+ * refer to a range of blocks that each contain a matrix. The returned
BlockMatrix
+ * is numbered so that the upper left block is indexed as (0,0).
+ *
+ *
+ * @param blockRowRange The lower and upper row range of blocks, as
(Int,Int)
+ * @param blockColRange The lower and upper col range of blocks, as
(Int, Int)
+ * @return a BlockMatrix with (0,0) as the upper leftmost block index
+ * @since 1.6.0
+ */
+ private [mllib] def subBlock(blockRowRange: (Int, Int), blockColRange:
(Int, Int)):
+ BlockMatrix = {
--- End diff --
fix the style
http://docs.scala-lang.org/style/declarations.html
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