QR Rank-Revealing Diagonal

Problem

Estimate the rank of a matrix from the diagonal of its R factor: count the diagonal entries of R whose absolute value exceeds 1e-9.

R is square, as produced by QR with column pivoting where rank-deficient directions show up as tiny diagonal entries.

Hint

Column pivoting pushes dependent directions to the end, making tiny diagonal entries visible.

case 1

in: [[[1,2],[0,3]]]

expected: 2

case 2

in: [[[1,2],[0,0]]]

expected: 1

case 3

in: [[[0,2],[0,0]]]

expected: 0

case 4

in: [[[2,0,1],[0,0,3],[0,0,0]]]

expected: 1

Starter codePython

def rrqr_rank(R):
    # Your code here
    pass

4 test cases · run your code against them in the editor