Low-Rank Truncation Error

Problem

Return the Frobenius norm error of the best rank-r approximation of a matrix, from its singular values:

error = sqrt(sum of squares of the singular values after the first r)

This is the Eckart-Young theorem in error form.

Hint

Truncating at r leaves only the tail singular values as error.

case 1

in: [[5,3,1],1]

expected: 3.1622776601683795

case 2

in: [[5,3,1],0]

expected: 5.916079783099616

case 3

in: [[5,3,1],3]

expected: 0

case 4

in: [[4,0,0],1]

expected: 0

Starter codePython

def low_rank_error(singular_values, r):
    # Your code here
    pass

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