def test_calcProjectionMatrix(self):
Q = projections.calcProjectionMatrix(self.A)
expected_Q = np.array([
[0.5239436 - 0.j, 0.0366197 + 0.3295774j, 0.3661971 + 0.0732394j],
[0.0366197 - 0.3295774j, 0.7690140 + 0.j, -0.0788732 + 0.2478873j],
[0.3661971 - 0.0732394j, -0.0788732 - 0.2478873j, 0.7070422 - 0j]
])
np.testing.assert_array_almost_equal(Q, expected_Q)
def test_calcProjectionMatrix(self):
Q = projections.calcProjectionMatrix(self.A)
expected_Q = np.array(
[
[0.5239436 - 0.0j, 0.0366197 + 0.3295774j, 0.3661971 + 0.0732394j],
[0.0366197 - 0.3295774j, 0.7690140 + 0.0j, -0.0788732 + 0.2478873j],
[0.3661971 - 0.0732394j, -0.0788732 - 0.2478873j, 0.7070422 - 0j],
]
)
np.testing.assert_array_almost_equal(Q, expected_Q)
def test_calc_receive_filter(self):
# Equivalent channel without including stream reduction
Heq_k = randn_c(3, 3)
Re_k = randn_c(3, 2)
Re_k = np.dot(Re_k, Re_k.transpose().conjugate())
P1 = blockdiagonalization._calc_stream_reduction_matrix(Re_k, 1)
P2 = blockdiagonalization._calc_stream_reduction_matrix(Re_k, 2)
P3 = blockdiagonalization._calc_stream_reduction_matrix(Re_k, 3)
# Equivalent channels with the stream reduction
Heq_k_P1 = np.dot(Heq_k, P1)
Heq_k_P2 = np.dot(Heq_k, P2)
Heq_k_P3 = np.dot(Heq_k, P3)
W1 = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k_P1, P1)
W2 = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k_P2, P2)
W3 = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k_P3, P3)
# Note that since P3 is actually including all streams, then the
# performance is the same as if we don't reduce streams. However W3
# and W_full are different matrices, since W3 has to compensate the
# right multiplication of the equivalent channel by P3 and W_full
# does not. The performance is the same because no energy is lost
# due to stream reduction and the Frobenius norms of W3 and W_full
# are equal.
W_full = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k)
np.testing.assert_array_almost_equal(np.dot(W1, np.dot(Heq_k, P1)),
np.eye(1))
np.testing.assert_array_almost_equal(np.dot(W2, np.dot(Heq_k, P2)),
np.eye(2))
np.testing.assert_array_almost_equal(np.dot(W3, np.dot(Heq_k, P3)),
np.eye(3))
np.testing.assert_array_almost_equal(np.dot(W_full, Heq_k),
np.eye(3))
overbar_P2 = calcProjectionMatrix(P2)
expected_W2 = np.dot(
np.linalg.pinv(np.dot(overbar_P2, np.dot(Heq_k, P2))),
overbar_P2)
np.testing.assert_array_almost_equal(expected_W2, W2)
def test_calc_receive_filter(self):
# Equivalent channel without including stream reduction
Heq_k = randn_c(3, 3)
Re_k = randn_c(3, 2)
Re_k = np.dot(Re_k, Re_k.transpose().conjugate())
P1 = blockdiagonalization._calc_stream_reduction_matrix(Re_k, 1)
P2 = blockdiagonalization._calc_stream_reduction_matrix(Re_k, 2)
P3 = blockdiagonalization._calc_stream_reduction_matrix(Re_k, 3)
# Equivalent channels with the stream reduction
Heq_k_P1 = np.dot(Heq_k, P1)
Heq_k_P2 = np.dot(Heq_k, P2)
Heq_k_P3 = np.dot(Heq_k, P3)
W1 = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k_P1, P1)
W2 = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k_P2, P2)
W3 = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k_P3, P3)
# Note that since P3 is actually including all streams, then the
# performance is the same as if we don't reduce streams. However W3
# and W_full are different matrices, since W3 has to compensate the
# right multiplication of the equivalent channel by P3 and W_full
# does not. The performance is the same because no energy is lost
# due to stream reduction and the Frobenius norms of W3 and W_full
# are equal.
W_full = blockdiagonalization.EnhancedBD.calc_receive_filter_user_k(
Heq_k)
np.testing.assert_array_almost_equal(np.dot(W1, np.dot(Heq_k, P1)),
np.eye(1))
np.testing.assert_array_almost_equal(np.dot(W2, np.dot(Heq_k, P2)),
np.eye(2))
np.testing.assert_array_almost_equal(np.dot(W3, np.dot(Heq_k, P3)),
np.eye(3))
np.testing.assert_array_almost_equal(np.dot(W_full, Heq_k), np.eye(3))
overbar_P2 = calcProjectionMatrix(P2)
expected_W2 = np.dot(
np.linalg.pinv(np.dot(overbar_P2, np.dot(Heq_k, P2))), overbar_P2)
np.testing.assert_array_almost_equal(expected_W2, W2)
def test_calcOrthogonalProjectionMatrix(self):
Q = projections.calcProjectionMatrix(self.A)
oQ = projections.calcOrthogonalProjectionMatrix(self.A)
expected_oQ = np.eye(3) - Q
np.testing.assert_array_almost_equal(oQ, expected_oQ)
def test_calcOrthogonalProjectionMatrix(self):
Q = projections.calcProjectionMatrix(self.A)
oQ = projections.calcOrthogonalProjectionMatrix(self.A)
expected_oQ = np.eye(3) - Q
np.testing.assert_array_almost_equal(oQ, expected_oQ)
