Ising Gibbs Conditional Probability

Problem

For an Ising model with local field field, couplings couplings[j] to neighboring spins, and current neighbor spin values, the Gibbs conditional probability that the node equals 1 is sigmoid(2 * (field + sum of couplings[j] * neighbors[j])). Neighbor spins must be 0 or 1. Return 0.0 for mismatched lengths or an invalid spin.

Hint

Collect the field and the coupling-weighted neighbor spins into a single local field.

Test cases

case 1

in: [0,[0.5],[1]]

expected: 0.7310585786300049

case 2

in: [-0.2,[0.3,0.4],[0.5,0.5]]

expected: 0

case 3

in: [0,[0.5],[0]]

expected: 0.5

case 4

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

expected: 0.8807970779778823

case 5

in: [0.5,[0.5,0.5],[1,0]]

expected: 0.8807970779778823

Starter codePython

import math


def ising_gibbs_conditional_probability(field, couplings, neighbors):
    # Your code here
    pass

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