Github user dbtsai commented on a diff in the pull request:
https://github.com/apache/spark/pull/8563#discussion_r41109096
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/BlockMatrix.scala
---
@@ -402,4 +445,402 @@ 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.
+ *
+ * @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)))
+ return S
+ }
+
+ /** Returns a rectangular (sub)BlockMatrix with block ranges as
specified.
+ *
+ * @param blockRowRange The lower and upper row ranges, as (Int,Int)
+ * @param blockColRange The lower and upper col ranges, 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)
+
+ // JNDB: 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)
+ }
+ return 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})
+ val Pi = diag(DenseVector.fill(k){1.0})
+ // size of square matrix
+ for(i <- 0 to (k - 1)) { // i test populating permutation matrix
+ val I = i match {case 0 => k - 1 case _ => 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
+ if (i != J) { Pi(i, J) -= 1.0; Pi(J, i) -= 1.0; Pi(i, i) += 1.0;
Pi(J, J) += 1.0}
+ }
+ return 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)
+ }
+ return extractedSeq
+ }
+
+
+
+ /** Computes the LU Decomposition of a Square Matrix. For a matrix A of
size (n x n)
+ * LU decomposition computes the Lower Triangular Matrix L, the Upper
Triangular
+ * Matrix U, along with a Permutation Matrix P, such that PA=LU. The
Permutation
+ * Matrix addresses cases where zero entries prevent forward
substitution
+ * solution of L or U.
+ *
+ * The BlockMatrix version takes a BlockMatrix as an input and returns
a Tuple
+ * of 5 BlockMatrix objects:
+ * P, L, U (in that order), such that P.multiply(A)-L.multiply(U) = 0
+ * and Li, Ui, which are the inverse of the block diagonal terms for L
and U.
+ *
+ * The blockLU method will return only P,L, and U, but blockLUtoSolver
will return
+ * the extra Li and Ui matrices, which will be used by the solve method
+ * so that it does not need to recompute these values.
+ *
+ * The method follows a procedure similar to the method used in
ScaLAPACK, but
+ * places more emphasis on preparing BlockMatrix objects as inputs to
large
+ * BlockMatrix.multiply operations.
+ *
+ *
+ * @return P,L,U,Li,Ui as a Tuple of BlockMatrix
+ * @since 1.6.0
+ */
+
+ private [mllib] def blockLUtoSolver:
+ (BlockMatrix, BlockMatrix, BlockMatrix, BlockMatrix,
BlockMatrix) = {
--- End diff --
Return a case class for readability.
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