def PDF(size):
    b = np.random.randn(size)
    J = np.random.randn(size, size)

    density_func = np.zeros(2**size)
    states = dec2bin(2**size)

    for i in range(2**size):
        density_func[i] = np.exp((np.dot(b, states[i,:]) + np.dot(np.dot(states[i],J),states[i])))

    Z = np.sum(density_func)
    density_func = density_func / Z

    return density_func

def bitfield(n,size):
    x = [int(x) for x in  bin(n) [ 2 :]]
    x = [0] * (size - len(x)) + x
    return x

def dec2bin(size):
    states = []
    for i in range(size):
        binary = bitfield(i, int(np.sqrt(size)))
        states.append(binary)
    return np.array(states)