Inverse of a spark RowMatrix - scala

Question

I am trying to inverse a spark rowmatrix. The function I am using is below.
def computeInverse(matrix: RowMatrix): BlockMatrix = {
val numCoefficients = matrix.numCols.toInt
val svd = matrix.computeSVD(numCoefficients, computeU = true)
val indexed_U = new IndexedRowMatrix(svd.U.rows.zipWithIndex.map(r => new IndexedRow(r._2, r._1)))
val invS = DenseMatrix.diag(new DenseVector(svd.s.toArray.map(x => if(x == 0) 0 else math.pow(x,-1))))
val V_inv = svd.V.multiply(invS)
val inverse = indexed_U.multiply(V_inv.transpose)
inverse.toBlockMatrix.transpose
}
The logic I am implementing is through SVD. An explanation of the process is
U, Σ, V = svd(A)
A = U * Σ * V.transpose
A.inverse = (U * Σ * V.transpose).inverse
= (V.transpose).inverse * Σ.inverse * U.inverse
Now U and V are orthogonal matrix
Therefore,
M * M.transpose = 1
Applying the above,
A.inverse = V * Σ.inverse * U.transpose
Let V * Σ.inverse be X
A.inverse = X * U.transpose
Now, A * B = ((A * B).transpose).transpose
= (B.transpose * A.transpose).transpose
Applying the same, to keep U as a row matrix, not a local matrix
A.inverse = X * U.transpose
= (U.transpose.transpose * X.transpose).transpose
= (U * X.transpose).transpose
The problem is with the input row matrix. For example
1, 2, 3
4, 5, 6
7, 8, 9
10,11,12
the inverse from the above code snippet and on using python numpy is different. I am unable to find out why is it so? Is it because of some underlying assumption made during svd calculation? Any help will be greatly appreciated. Thanks.

Answer 1

The above code works properly. The reason I was getting this error was that I made the RowMatrix with a RDD[Vector]. Now, in spark things are sorted column wise to form a matrix, whereas in the case of numpy, array is converted row wise to a matrix
Array(1,2,3,4,5,6,7,8,9)
In Spark
1 4 7
2 5 8
3 6 9
In python, it is interpreted as
1 2 3
4 5 6
7 8 9
So, the test case was failing :|