Github user yu-iskw commented on a diff in the pull request:
https://github.com/apache/spark/pull/8563#discussion_r43610049
--- 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 = {
+ // Extracts BlockMatrix elements from a specified range of block
indices
+ // Creating a Sub BlockMatrix of rectangular shape.
+ // Also reindexes so that the upper left block is always (0, 0)
+
+ // TODO: add a require statement ...rowMax<=size..
+ val rowMin = blockRowRange._1; val rowMax = blockRowRange._2
+ val colMin = blockColRange._1 ; val colMax = blockColRange._2
+ val extractedSeq = this.blocks.filter{ case((x, y), matrix) =>
+ x >= rowMin && x<= rowMax && // finding blocks
+ y >= colMin && y<= colMax }.map { // shifting indices
+ case(((x, y), matrix) ) => ((x-rowMin, y-colMin), matrix)
+ }
+ new BlockMatrix(extractedSeq, rowsPerBlock, colsPerBlock)
+ }
+
+ /**
+ * Computes the LU decomposition of a Single Block from BlockMatrix
using the
+ * Breeze LU method. The method (as written) operates -only- on the
upper
+ * left (0,0) corner of the BlockMatrix.
+ *
+ * @return List[BDM[Double]] of Breeze Matrices (BDM) (P,L,U) for
blockLU method.
+ * @since 1.6.0
+ */
+ private [mllib] def singleBlockPLU: List[BDM[Double]] = {
+ // returns PA = LU factorization from Breeze
+ val PLU = LU(this.subBlock((0, 0), (0, 0)).toBreeze)
+ val k = PLU._1.cols
+ val L = lowerTriangular(PLU._1) - diag(diag(PLU._1)) +
diag(DenseVector.fill(k){1.0})
+ val U = upperTriangular(PLU._1);
+ var P = diag(DenseVector.fill(k){1.0})
+ var Pi = diag(DenseVector.fill(k){1.0})
+ // size of square matrix
+ // populating permutation matrix
+ var i = 0
+ while (i < k) {
+ val I = {
+ if (i == 0){k - 1}
+ else {i - 1}
+ }
+ val J = PLU._2(i) -1
+ if (i != J) {
+ Pi(i, J) += 1.0
+ Pi(J, i) += 1.0
+ Pi(i, i) -= 1.0
+ Pi(J, J) -= 1.0
+ }
+ P = Pi * P // constructor Pi*P for PA=LU
+ // resetting Pi for next iteration
+ if (i != J) {
+ Pi(i, J) -= 1.0
+ Pi(J, i) -= 1.0
+ Pi(i, i) += 1.0
+ Pi(J, J) += 1.0
+ }
+ i += 1
+ }
+ List(P, L, U)
+ }
+
+
+ /**
+ * This method reassigns 'absolute' index locations (i,j), to sequences.
This is
+ * designed to reconsitute the orignal block locations that were lost in
the
+ * subBlock method.
+ *
+ * @param rowMin The new lowest row value
+ * @param colMin The new lowest column value
+ * @return an RDD of Sequences with new block indexing
+ * @since 1.6.0
+ *
+ */
+ private [mllib] def shiftIndices(rowMin: Int, colMin: Int): RDD[((Int,
Int), Matrix)] = {
+ // This routine recovers the absolute indexing of the block matrices
for reassembly
+ val extractedSeq = this.blocks.map { // shifting indices
+ case(((x, y), matrix)) => ((x + rowMin, y + colMin), matrix)
+ }
+ extractedSeq
+ }
+
+ /**
+ * A class that contains the 3 main BlockMatrix items to be returned
+ * when calling blockLU.
+ *
+ * @param p The Permutation BlockMatrix
+ * @param l Lower Diagonal BlockMatrix
+ * @param u Upper Diagonal BlockMatrix
+ *
+ */
+
--- End diff --
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