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From dbtsai <...@git.apache.org>
Subject [GitHub] spark pull request: [SPARK-8514] LU factorization on BlockMatrix
Date Mon, 05 Oct 2015 03:34:42 GMT
Github user dbtsai commented on a diff in the pull request:

    https://github.com/apache/spark/pull/8563#discussion_r41108645
  
    --- 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)
    --- End diff --
    
    For scala doc, we use
    
    ```scala
    /**
     * Start from here
     * End here
     */
    
    ```


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