def get_eigen_pot(self, fin_nd_list):
"""
This function first marginalizes self to fin_nd_list. Then it
reshapes that marginal to a square array, and calculates the
eigenvalues of that square array. Finally, it returns a Potential
pot such that pot.pot_arr contains the eigenvalues as an array with
shape = [x.size for x in fin_nd_list].
Parameters
----------
fin_nd_list : list[BayesNode]
Returns
-------
Potential
"""
assert self.nodes >= set(fin_nd_list)
sub_dmat = DensityMatrix.new_from_tr_of_mixed_st(self, fin_nd_list)
arr = sub_dmat.dmat_arr
shp = sub_dmat.nd_sizes
num_rows = np.prod(np.array(shp))
arr = np.reshape(arr, (num_rows, num_rows))
evals = np.linalg.eigvalsh(arr)
evals = np.reshape(evals, shp)
return Potential(False, fin_nd_list, pot_arr=evals)
def set_pot_to_one(self, is_quantum):
"""
Sets self.potential to one. Needs to know is_quantum to decide
whether to use a numpy array with float64 or complex128 entries.
Sets pot to one over all states, not just the active ones.
Parameters
----------
is_quantum : bool
Returns
-------
None
"""
# insert subnodes into pot in arbitrary order
self.potential = Potential(is_quantum, list(self.subnodes), bias=1)
def main():
# define some nodes
a_nd = BayesNode(0, name="A", size=2)
b_nd = BayesNode(1, name="B", size=3)
c_nd = BayesNode(2, name="C", size=2)
d_nd = BayesNode(3, name="D", size=3)
print('----------------------classical case')
pot = Potential(False, [a_nd, b_nd, c_nd, d_nd])
pot.set_to_random()
# this normalizes so all entries sum to 1
pot /= pot.get_new_marginal([])
assert pot.is_joint_prob_dist()
Entropy.ent_c(pot, [a_nd], verbose=True)
Entropy.ent_c(pot, [a_nd, c_nd], verbose=True)
Entropy.ent_c(pot, [c_nd, a_nd], verbose=True)
Entropy.cond_info_c(pot, [a_nd, b_nd], [c_nd], verbose=True)
Entropy.mut_info_c(pot, [a_nd, b_nd], [c_nd], verbose=True)
Entropy.cond_mut_info_c(pot,
[a_nd], [b_nd, d_nd], [c_nd],
verbose=True)
print('----------------------quantum case')
dmat = DensityMatrix([a_nd, b_nd, c_nd, d_nd])
# dmat = DensityMatrix([a_nd, b_nd])
dmat.set_to_random(normalize=True)
# print(dmat)
assert dmat.is_legal_dmat()
Entropy.ent_q(dmat, [a_nd], verbose=True)
Entropy.ent_q(dmat, [a_nd, c_nd], verbose=True)
Entropy.ent_q(dmat, [c_nd, a_nd], verbose=True)
Entropy.cond_info_q(dmat, [a_nd, b_nd], [c_nd], verbose=True)
Entropy.mut_info_q(dmat, [a_nd, b_nd], [c_nd], verbose=True)
Entropy.cond_mut_info_q(dmat,
[a_nd], [b_nd, d_nd], [c_nd],
verbose=True)
new_abc = cp.deepcopy(rho_abc)
new_abc.set_to_transpose([b_node, a_node, c_node])
new_abc -= rho_bc
assert new_abc == rho_abc - rho_bc
print("\n-----------------try tracing ops and normalize")
new_abc = cp.deepcopy(rho_abc)
new_abc.tr_normalize_self()
# print('new_abc', new_abc)
print('tr new_abc', new_abc.trace())
fin_nd_list = [b_node, a_node]
new_ba = DensityMatrix.new_from_tr_of_mixed_st(new_abc, fin_nd_list)
print("new_ba", new_ba)
new_a = DensityMatrix.new_from_tr_of_mixed_st(new_ba, [a_node])
print('new_a', new_a)
print("\n**************************")
pot = Potential(True, [a_node, b_node, c_node])
pot.set_to_random()
new_bc = DensityMatrix.new_from_tr_of_pure_st(pot, [b_node, c_node])
new_bc.tr_normalize_self()
print("from this pot", pot)
print("_________")
print("new_bc", new_bc)
new_c = DensityMatrix.new_from_tr_of_mixed_st(new_bc, [c_node])
print('new_c', new_c)
def main():
# define some nodes
a_node = BayesNode(0, name="A", size=2)
b_node = BayesNode(1, name="B", size=3)
c_node = BayesNode(2, name="C", size=2)
d_node = BayesNode(3, name="D", size=3)
e_node = BayesNode(4, name="E", size=2)
print("\n-----------------define some density matrices")
rho_ab = DensityMatrix([a_node, b_node])
print("rho_ab:", rho_ab)
rho_ab.set_to_random(max_int=10)
print("rho_ab:", rho_ab)
rho_ab2 = DensityMatrix([a_node, b_node])
rho_bc = DensityMatrix([b_node, c_node])
rho_abc = DensityMatrix([a_node, b_node, c_node])
print("rho_abc:", rho_abc)
rho_abc.set_all_entries_to(2 + 5j)
print("rho_abc:", rho_abc)
rho_abc.set_to_random()
rho_dbc = DensityMatrix([d_node, b_node, c_node])
rho_dbc.set_to_random()
print("\n-----------------try transpose, distance and ==")
new_abc = cp.deepcopy(rho_abc)
new_abc.set_to_transpose([b_node, a_node, c_node])
assert rho_abc == new_abc
assert rho_abc != (new_abc + 5)
print("distance(rho_abc, new_abc)=",
DensityMatrix.distance(new_abc, rho_abc))
print("rho_abc == new_abc?", rho_abc == new_abc)
print("distance(rho_abc, rho_bc)=",
DensityMatrix.distance(rho_abc, rho_bc))
print("rho_abc == rho_bc?", rho_abc == rho_bc)
print("\n-----------------try add, sub, mult")
print("rho_ab:", rho_ab)
print("rho_ab2:", rho_ab2)
print("rho_ab + 5:", rho_ab + 5)
print("rho_ab - 5:", rho_ab - 5)
print("rho_ab * 5:", rho_ab * 5)
print("rho_ab + rho_ab2:", rho_ab + rho_ab2)
print("rho_ab - rho_ab2:", rho_ab - rho_ab2)
print("rho_ab * rho_ab2:", rho_ab * rho_ab2)
print("rho_ab + rho_bc:", rho_ab + rho_bc)
print("rho_ab - rho_bc:", rho_ab - rho_bc)
print("rho_ab * rho_bc:", rho_ab * rho_bc)
print("\n-----------------try iadd, isub")
new_abc = cp.deepcopy(rho_abc)
new_abc.set_to_transpose([b_node, a_node, c_node])
new_abc += 5
assert new_abc == rho_abc + 5
new_abc = cp.deepcopy(rho_abc)
new_abc.set_to_transpose([b_node, a_node, c_node])
new_abc += rho_bc
assert new_abc == rho_abc + rho_bc
new_abc = cp.deepcopy(rho_abc)
new_abc.set_to_transpose([b_node, a_node, c_node])
new_abc -= rho_bc
assert new_abc == rho_abc - rho_bc
print("\n-----------------try tracing ops and normalize")
new_abc = cp.deepcopy(rho_abc)
new_abc.tr_normalize_self()
# print('new_abc', new_abc)
print('tr new_abc', new_abc.trace())
fin_nd_list = [b_node, a_node]
new_ba = DensityMatrix.new_from_tr_of_mixed_st(new_abc, fin_nd_list)
print("new_ba", new_ba)
new_a = DensityMatrix.new_from_tr_of_mixed_st(new_ba, [a_node])
print('new_a', new_a)
print("\n**************************")
pot = Potential(True, [a_node, b_node, c_node])
pot.set_to_random()
new_bc = DensityMatrix.new_from_tr_of_pure_st(pot, [b_node, c_node])
new_bc.tr_normalize_self()
print("from this pot", pot)
print("_________")
print("new_bc", new_bc)
new_c = DensityMatrix.new_from_tr_of_mixed_st(new_bc, [c_node])
print('new_c', new_c)
"""
xyz_nds = x_nds + y_nds + z_nds
pot = dmat.get_eigen_pot(xyz_nds)
return Entropy.cond_mut_info_c(pot, x_nds, y_nds, z_nds, verbose)
if __name__ == "__main__":
# define some nodes
a_nd = BayesNode(0, name="A", size=2)
b_nd = BayesNode(1, name="B", size=3)
c_nd = BayesNode(2, name="C", size=2)
d_nd = BayesNode(3, name="D", size=3)
print('----------------------classical case')
pot = Potential(False, [a_nd, b_nd, c_nd, d_nd])
pot.set_to_random()
pot /= pot.get_new_marginal([]) # this normalizes so all entries sum to 1
assert pot.is_joint_prob_dist()
Entropy.ent_c(pot, [a_nd], verbose=True)
Entropy.ent_c(pot, [a_nd, c_nd], verbose=True)
Entropy.ent_c(pot, [c_nd, a_nd], verbose=True)
Entropy.cond_info_c(pot, [a_nd, b_nd], [c_nd], verbose=True)
Entropy.mut_info_c(pot, [a_nd, b_nd], [c_nd], verbose=True)
Entropy.cond_mut_info_c(pot, [a_nd], [b_nd, d_nd], [c_nd], verbose=True)
print('----------------------quantum case')
dmat = DensityMatrix([a_nd, b_nd, c_nd, d_nd])
# dmat = DensityMatrix([a_nd, b_nd])
dmat.set_to_random(normalize=True)
# print(dmat)