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From mengxr <...@git.apache.org>
Subject [GitHub] spark pull request: [SPARK-1390] Refactoring of matrices backed by...
Date Tue, 08 Apr 2014 23:44:00 GMT
Github user mengxr commented on a diff in the pull request:

    https://github.com/apache/spark/pull/296#discussion_r11417359
  
    --- Diff: mllib/src/main/scala/org/apache/spark/mllib/linalg/distributed/RowMatrix.scala
---
    @@ -0,0 +1,340 @@
    +/*
    + * Licensed to the Apache Software Foundation (ASF) under one or more
    + * contributor license agreements.  See the NOTICE file distributed with
    + * this work for additional information regarding copyright ownership.
    + * The ASF licenses this file to You under the Apache License, Version 2.0
    + * (the "License"); you may not use this file except in compliance with
    + * the License.  You may obtain a copy of the License at
    + *
    + *    http://www.apache.org/licenses/LICENSE-2.0
    + *
    + * Unless required by applicable law or agreed to in writing, software
    + * distributed under the License is distributed on an "AS IS" BASIS,
    + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    + * See the License for the specific language governing permissions and
    + * limitations under the License.
    + */
    +
    +package org.apache.spark.mllib.linalg.distributed
    +
    +import java.util
    +
    +import breeze.linalg.{DenseMatrix => BDM, DenseVector => BDV, svd => brzSvd}
    +import breeze.numerics.{sqrt => brzSqrt}
    +import com.github.fommil.netlib.BLAS.{getInstance => blas}
    +
    +import org.apache.spark.mllib.linalg._
    +import org.apache.spark.rdd.RDD
    +import org.apache.spark.Logging
    +
    +/**
    + * Represents a row-oriented distributed Matrix with no meaningful row indices.
    + *
    + * @param rows rows stored as an RDD[Vector]
    + * @param nRows number of rows. A non-positive value means unknown, and then the number
of rows will
    + *              be determined by the number of records in the RDD `rows`.
    + * @param nCols number of columns. A non-positive value means unknown, and then the number
of
    + *              columns will be determined by the size of the first row.
    + */
    +class RowMatrix(
    +    val rows: RDD[Vector],
    +    private var nRows: Long,
    +    private var nCols: Int) extends DistributedMatrix with Logging {
    +
    +  /** Alternative constructor leaving matrix dimensions to be determined automatically.
*/
    +  def this(rows: RDD[Vector]) = this(rows, 0L, 0)
    +
    +  /** Gets or computes the number of columns. */
    +  override def numCols(): Long = {
    +    if (nCols <= 0) {
    +      // Calling `first` will throw an exception if `rows` is empty.
    +      nCols = rows.first().size
    +    }
    +    nCols
    +  }
    +
    +  /** Gets or computes the number of rows. */
    +  override def numRows(): Long = {
    +    if (nRows <= 0L) {
    +      nRows = rows.count()
    +      if (nRows == 0L) {
    +        sys.error("Cannot determine the number of rows because it is not specified in
the " +
    +          "constructor and the rows RDD is empty.")
    +      }
    +    }
    +    nRows
    +  }
    +
    +  /**
    +   * Computes the Gramian matrix `A^T A`.
    +   */
    +  def computeGramianMatrix(): Matrix = {
    +    val n = numCols().toInt
    +    val nt: Int = n * (n + 1) / 2
    +
    +    // Compute the upper triangular part of the gram matrix.
    +    val GU = rows.aggregate(new BDV[Double](new Array[Double](nt)))(
    +      seqOp = (U, v) => {
    +        RowMatrix.dspr(1.0, v, U.data)
    +        U
    +      },
    +      combOp = (U1, U2) => U1 += U2
    +    )
    +
    +    RowMatrix.triuToFull(n, GU.data)
    +  }
    +
    +  /**
    +   * Computes the singular value decomposition of this matrix.
    +   * Denote this matrix by A (m x n), this will compute matrices U, S, V such that A
= U * S * V'.
    +   *
    +   * There is no restriction on m, but we require `n^2` doubles to fit in memory.
    +   * Further, n should be less than m.
    +
    +   * The decomposition is computed by first computing A'A = V S^2 V',
    +   * computing svd locally on that (since n x n is small), from which we recover S and
V.
    +   * Then we compute U via easy matrix multiplication as U =  A * (V * S^-1).
    +   * Note that this approach requires `O(n^3)` time on the master node.
    +   *
    +   * At most k largest non-zero singular values and associated vectors are returned.
    +   * If there are k such values, then the dimensions of the return will be:
    +   *
    +   * U is a RowMatrix of size m x k that satisfies U'U = eye(k),
    +   * s is a Vector of size k, holding the singular values in descending order,
    +   * and V is a Matrix of size n x k that satisfies V'V = eye(k).
    +   *
    +   * @param k number of singular values to keep. We might return less than k if there
are
    +   *          numerically zero singular values. See rCond.
    +   * @param computeU whether to compute U
    +   * @param rCond the reciprocal condition number. All singular values smaller than rCond
* sigma(0)
    +   *              are treated as zero, where sigma(0) is the largest singular value.
    +   * @return SingularValueDecomposition(U, s, V)
    +   */
    +  def computeSVD(
    +      k: Int,
    +      computeU: Boolean = false,
    +      rCond: Double = 1e-9): SingularValueDecomposition[RowMatrix, Matrix] = {
    +    val n = numCols().toInt
    +    require(k > 0 && k <= n, s"Request up to n singular values k=$k n=$n.")
    +
    +    val G = computeGramianMatrix()
    +
    +    // TODO: Use sparse SVD instead.
    +    val (u: BDM[Double], sigmaSquares: BDV[Double], v: BDM[Double]) =
    +      brzSvd(G.toBreeze.asInstanceOf[BDM[Double]])
    +    val sigmas: BDV[Double] = brzSqrt(sigmaSquares)
    +
    +    // Determine effective rank.
    +    val sigma0 = sigmas(0)
    +    val threshold = rCond * sigma0
    +    var i = 0
    +    while (i < k && sigmas(i) >= threshold) {
    +      i += 1
    +    }
    +    val sk = i
    --- End diff --
    
    Added a warning.


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