Detailed Balance Residual

Problem

Detailed balance requires pi[i] * matrix[i][j] = pi[j] * matrix[j][i] for all i and j. Return the largest absolute violation, max over i and j of abs(pi[i] * matrix[i][j] - pi[j] * matrix[j][i]). Return -1.0 for malformed input.

Hint

Compare every off-diagonal flow in both directions and keep the worst mismatch.

Test cases

case 1

in: [[0.5,0.5],[[0.5,0.5],[0.5,0.5]]]

expected: 0

case 2

in: [[0.5,0.5],[[0.8,0.2],[0.2,0.8]]]

expected: 0

case 3

in: [[0.3,0.7],[[0.5,0.5],[0.5,0.5]]]

expected: 0.19999999999999998

case 4

in: [[0.25,0.75],[[0.9,0.1],[0.3,0.7]]]

expected: 0.19999999999999998

case 5

in: [[0.5,0.5],[[0.5,0.5]]]

expected: -1

Starter codePython

def detailed_balance_residual(pi, matrix):
    # Your code here
    pass

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