MediumProbabilitypr-128

Detailed Balance Check

Problem

Check that pi satisfies detailed balance with respect to the transition matrix:

pi[i] * matrix[i][j] = pi[j] * matrix[j][i] for all i, j

within a tolerance of 1e-9. Return True or False, and False for malformed input.

Hint

Check both directions of every off-diagonal flow.

case 1

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

expected: true

case 2

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

expected: true

case 3

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

expected: false

case 4

in: [[0.5,0.5],[[0.9,0.1],[0.2,0.8]]]

expected: false

Starter codePython

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

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