How to compute the inverse of a RowMatrix in Apache Spark?

Question

I have a X, distributed matrix, in RowMatrix form. I am using Spark 1.3.0. I need to be able to calculate X inverse.

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

I had problems using this function with option

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

The rows in RowMatrix got shuffled.

Here is an update that worked for me

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

Matrix U returned by X.computeSVD has dimensions m x k where m is the number of rows of the original (distributed) RowMatrix X. One would expect m to be large (possibly larger than k), so it is not advisable to collect it in the driver if we want our code to scale to really large values of m.

I would say both of the solutions below suffer from this flaw. The answer given by @Alexander Kharlamov calls val U = svd.U.toBlockMatrix().toLocalMatrix() which collects the matrix in the driver. The same happens with the answer given by @Climbs_lika_Spyder (btw your nick rocks!!), which calls svd.U.rows.collect.flatMap(x => x.toArray). I would rather suggest to rely on a distributed matrix multiplication such as the Scala code posted here.