如何計算Apache Spark中RowMatrix的逆函數？

Question

我有一個X，分佈矩陣，在RowMatrix形式。我正在使用Spark 1.3.0。我需要能夠計算X逆。

Answer 1

import org.apache.spark.mllib.linalg.{Vectors,Vector,Matrix,SingularValueDecomposition,DenseMatrix,DenseVector} 
import org.apache.spark.mllib.linalg.distributed.RowMatrix 

def computeInverse(X: RowMatrix): DenseMatrix = { 
    val nCoef = X.numCols.toInt 
    val svd = X.computeSVD(nCoef, computeU = true) 
    if (svd.s.size < nCoef) { 
    sys.error(s"RowMatrix.computeInverse called on singular matrix.") 
    } 

    // Create the inv diagonal matrix from S 
    val invS = DenseMatrix.diag(new DenseVector(svd.s.toArray.map(x => math.pow(x,-1)))) 

    // U cannot be a RowMatrix 
    val U = new DenseMatrix(svd.U.numRows().toInt,svd.U.numCols().toInt,svd.U.rows.collect.flatMap(x => x.toArray)) 

    // If you could make V distributed, then this may be better. However its alreadly local...so maybe this is fine. 
    val V = svd.V 
    // inv(X) = V*inv(S)*transpose(U) --- the U is already transposed. 
    (V.multiply(invS)).multiply(U) 
    } 

Answer 2

我使用這個功能與選項

conf.set("spark.sql.shuffle.partitions", "12") 

在RowMatrix該行得到了洗牌有問題。

下面是一個更新爲我工作

import org.apache.spark.mllib.linalg.{DenseMatrix,DenseVector} 
import org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix 

def computeInverse(X: IndexedRowMatrix) 
: DenseMatrix = 
{ 
    val nCoef = X.numCols.toInt 
    val svd = X.computeSVD(nCoef, computeU = true) 
    if (svd.s.size < nCoef) { 
    sys.error(s"IndexedRowMatrix.computeInverse called on singular matrix.") 
    } 

    // Create the inv diagonal matrix from S 
    val invS = DenseMatrix.diag(new DenseVector(svd.s.toArray.map(x => math.pow(x, -1)))) 

    // U cannot be a RowMatrix 
    val U = svd.U.toBlockMatrix().toLocalMatrix().multiply(DenseMatrix.eye(svd.U.numRows().toInt)).transpose 

    val V = svd.V 
    (V.multiply(invS)).multiply(U) 
} 

Answer 3

矩陣U由X.computeSVD返回的尺寸爲MXK其中米是人們期望米原（分佈式）RowMatrix X的行數很大（可能大於k），所以如果我們希望我們的代碼縮放到非常大的值m，則不建議將它收集在驅動程序中。

我想說下面的兩個解決方案都會遇到這個缺陷。由@Alexander Kharlamov給出的答案叫做val U = svd.U.toBlockMatrix().toLocalMatrix()，它收集驅動程序中的矩陣。 @Climbs_lika_Spyder給出的答案也是一樣（順便說一句，你的暱稱是岩石!!），它叫svd.U.rows.collect.flatMap(x => x.toArray)。我寧願建議依靠分佈式矩陣乘法，例如發佈了here的Scala代碼。