def computeQUI(distSXY,
eps=1e-7,
DEBUG=False,
IPmethod="GIS",
maxiter=100000,
maxiter2=100000):
'''
Compute an optimizer Q
distSXY : A joint distribution of three variables (as a dit.Distribution).
eps : The precision of the outer loop. The precision of the inner loop will be eps / (20 |S|).
DEBUG : Print output for debugging.
The computation is carried out using computeQUI_numpy
'''
# Prepare distributions
QSXYd = distSXY.copy() # make a copy, to not overwrite the argument
QSXYd.set_rv_names('SXY')
QSXYd.make_dense() # the set of outcomes should be Cartesian
# collect state spaces / cardinalities
suppS = QSXYd.alphabet[0]
nS = len(suppS)
suppX = QSXYd.alphabet[1]
nX = len(suppX)
suppY = QSXYd.alphabet[2]
nY = len(suppY)
# to do: take relevant subset of suppS
samplespace = QSXYd.outcomes
QSXYa = QSXYd.pmf.reshape(nS, nX, nY)
PS = QSXYd.marginal('S').pmf.reshape(
nS, 1) # PS is a column vector, for convenience
PXgSa = numpy.array(
list(map(lambda x: x.pmf,
QSXYd.condition_on('S', rvs='X')[1]))).transpose()
PYgSa = numpy.array(
list(map(lambda x: x.pmf,
QSXYd.condition_on('S', rvs='Y')[1]))).transpose()
# print(1e-6 * numpy.ones((nX, nY)) / (nX * nY) + (1 - 1e-6) * QSXYd.marginal('X').pmf.reshape(nX, 1) * QSXYd.marginal('Y').pmf.reshape(1, nY))
QSXYa = computeQUI_numpy(PXgSa,
PYgSa,
PS,
eps=eps,
DEBUG=DEBUG,
IPmethod=IPmethod,
maxiter=maxiter,
maxiter2=maxiter2).reshape(-1)
QSXYd = dit.Distribution(samplespace, QSXYa)
QSXYd.set_rv_names('SXY')
return QSXYd
CI = dit.shannon.mutual_information(d, 'S', 'XY') - UIX - UIY - SI
CIQ = dit.shannon.mutual_information(Q, 'S', 'XY') - UIX - UIY - SI
print("PID(R=", SI, ", U0=", UIX, ", U1=", UIY, ", S=", CI, ")", sep='')
print(Q)
# pid
print("\nRunning dit pid_broja...")
start_time = time.time()
pid = dit.algorithms.pid_broja(d, ['X', 'Y'], 'S')
print("--- %s seconds ---" % (time.time() - start_time))
print(pid)
# Example d12 without using dit
print("\nRunning admUI without dit on example d12...")
ns = 2
nx = 3
ny = 2
P = np.array([
0.0869196091623, 0, 0.0218631235533, 0, 0.133963681059, 0, 0,
0.164924698739, 0.429533105427, 0, 0, 0.16279578206
])
Psxy = np.reshape(P, [ns, nx, ny])
Psx = np.sum(Psxy, axis=2)
Psy = np.sum(Psxy, axis=1)
PS = np.sum(Psx, axis=1)
PXgS = np.divide(np.transpose(Psx), PS)
PYgS = np.divide(np.transpose(Psy), PS)
PS = PS.reshape((-1, 1))
Q = computeQUI_numpy(PXgS, PYgS, PS)
print("p=\n", Q)