def daeg_to_rotational_superoperator(daeg, Rsuper):
"""Convert the frame order matrix (daeg) to the rotational superoperator.
@param daeg: The second degree frame order matrix, daeg. This must be in the Kronecker product layout.
@type daeg: numpy 9D, rank-2 array or numpy 3D, rank-4 array
@param Rsuper: The rotational superoperator structure to be populated.
@type Rsuper: numpy 5D, rank-2 array
"""
# First perform the T23 transpose.
transpose_23(daeg)
# Convert to rank-4.
orig_shape = daeg.shape
daeg.shape = (3, 3, 3, 3)
# First column of the superoperator.
Rsuper[0, 0] = daeg[0, 0, 0, 0] - daeg[2, 0, 2, 0]
Rsuper[1, 0] = daeg[0, 1, 0, 1] - daeg[2, 1, 2, 1]
Rsuper[2, 0] = daeg[0, 0, 0, 1] - daeg[2, 0, 2, 1]
Rsuper[3, 0] = daeg[0, 0, 0, 2] - daeg[2, 0, 2, 2]
Rsuper[4, 0] = daeg[0, 1, 0, 2] - daeg[2, 1, 2, 2]
# Second column of the superoperator.
Rsuper[0, 1] = daeg[1, 0, 1, 0] - daeg[2, 0, 2, 0]
Rsuper[1, 1] = daeg[1, 1, 1, 1] - daeg[2, 1, 2, 1]
Rsuper[2, 1] = daeg[1, 0, 1, 1] - daeg[2, 0, 2, 1]
Rsuper[3, 1] = daeg[1, 0, 1, 2] - daeg[2, 0, 2, 2]
Rsuper[4, 1] = daeg[1, 1, 1, 2] - daeg[2, 1, 2, 2]
# Third column of the superoperator.
Rsuper[0, 2] = daeg[0, 0, 1, 0] + daeg[1, 0, 0, 0]
Rsuper[1, 2] = daeg[0, 1, 1, 1] + daeg[1, 1, 0, 1]
Rsuper[2, 2] = daeg[0, 0, 1, 1] + daeg[1, 0, 0, 1]
Rsuper[3, 2] = daeg[0, 0, 1, 2] + daeg[1, 0, 0, 2]
Rsuper[4, 2] = daeg[0, 1, 1, 2] + daeg[1, 1, 0, 2]
# Fourth column of the superoperator.
Rsuper[0, 3] = daeg[0, 0, 2, 0] + daeg[2, 0, 0, 0]
Rsuper[1, 3] = daeg[0, 1, 2, 1] + daeg[2, 1, 0, 1]
Rsuper[2, 3] = daeg[0, 0, 2, 1] + daeg[2, 0, 0, 1]
Rsuper[3, 3] = daeg[0, 0, 2, 2] + daeg[2, 0, 0, 2]
Rsuper[4, 3] = daeg[0, 1, 2, 2] + daeg[2, 1, 0, 2]
# Fifth column of the superoperator.
Rsuper[0, 4] = daeg[1, 0, 2, 0] + daeg[2, 0, 1, 0]
Rsuper[1, 4] = daeg[1, 1, 2, 1] + daeg[2, 1, 1, 1]
Rsuper[2, 4] = daeg[1, 0, 2, 1] + daeg[2, 0, 1, 1]
Rsuper[3, 4] = daeg[1, 0, 2, 2] + daeg[2, 0, 1, 2]
Rsuper[4, 4] = daeg[1, 1, 2, 2] + daeg[2, 1, 1, 2]
# Revert the shape.
daeg.shape = orig_shape
# Undo the T23 transpose.
transpose_23(daeg)
def daeg_to_rotational_superoperator(daeg, Rsuper):
"""Convert the frame order matrix (daeg) to the rotational superoperator.
@param daeg: The second degree frame order matrix, daeg. This must be in the Kronecker product layout.
@type daeg: numpy 9D, rank-2 array or numpy 3D, rank-4 array
@param Rsuper: The rotational superoperator structure to be populated.
@type Rsuper: numpy 5D, rank-2 array
"""
# First perform the T23 transpose.
transpose_23(daeg)
# Convert to rank-4.
orig_shape = daeg.shape
daeg.shape = (3, 3, 3, 3)
# First column of the superoperator.
Rsuper[0, 0] = daeg[0, 0, 0, 0] - daeg[2, 0, 2, 0]
Rsuper[1, 0] = daeg[0, 1, 0, 1] - daeg[2, 1, 2, 1]
Rsuper[2, 0] = daeg[0, 0, 0, 1] - daeg[2, 0, 2, 1]
Rsuper[3, 0] = daeg[0, 0, 0, 2] - daeg[2, 0, 2, 2]
Rsuper[4, 0] = daeg[0, 1, 0, 2] - daeg[2, 1, 2, 2]
# Second column of the superoperator.
Rsuper[0, 1] = daeg[1, 0, 1, 0] - daeg[2, 0, 2, 0]
Rsuper[1, 1] = daeg[1, 1, 1, 1] - daeg[2, 1, 2, 1]
Rsuper[2, 1] = daeg[1, 0, 1, 1] - daeg[2, 0, 2, 1]
Rsuper[3, 1] = daeg[1, 0, 1, 2] - daeg[2, 0, 2, 2]
Rsuper[4, 1] = daeg[1, 1, 1, 2] - daeg[2, 1, 2, 2]
# Third column of the superoperator.
Rsuper[0, 2] = daeg[0, 0, 1, 0] + daeg[1, 0, 0, 0]
Rsuper[1, 2] = daeg[0, 1, 1, 1] + daeg[1, 1, 0, 1]
Rsuper[2, 2] = daeg[0, 0, 1, 1] + daeg[1, 0, 0, 1]
Rsuper[3, 2] = daeg[0, 0, 1, 2] + daeg[1, 0, 0, 2]
Rsuper[4, 2] = daeg[0, 1, 1, 2] + daeg[1, 1, 0, 2]
# Fourth column of the superoperator.
Rsuper[0, 3] = daeg[0, 0, 2, 0] + daeg[2, 0, 0, 0]
Rsuper[1, 3] = daeg[0, 1, 2, 1] + daeg[2, 1, 0, 1]
Rsuper[2, 3] = daeg[0, 0, 2, 1] + daeg[2, 0, 0, 1]
Rsuper[3, 3] = daeg[0, 0, 2, 2] + daeg[2, 0, 0, 2]
Rsuper[4, 3] = daeg[0, 1, 2, 2] + daeg[2, 1, 0, 2]
# Fifth column of the superoperator.
Rsuper[0, 4] = daeg[1, 0, 2, 0] + daeg[2, 0, 1, 0]
Rsuper[1, 4] = daeg[1, 1, 2, 1] + daeg[2, 1, 1, 1]
Rsuper[2, 4] = daeg[1, 0, 2, 1] + daeg[2, 0, 1, 1]
Rsuper[3, 4] = daeg[1, 0, 2, 2] + daeg[2, 0, 1, 2]
Rsuper[4, 4] = daeg[1, 1, 2, 2] + daeg[2, 1, 1, 2]
# Revert the shape.
daeg.shape = orig_shape
# Undo the T23 transpose.
transpose_23(daeg)
def test_transpose_23(self):
"""Check the 2,3 transpose of a rank-4, 3D tensor."""
# Manually create the string rep of the transpose.
daegT = self.string_transpose(2, 3)
print("The real 2,3 transpose:")
self.print_nice(daegT)
# Convert to numpy.
daegT = self.to_numpy(daegT)
# Check.
print("The numerical 2,3 transpose:")
transpose_23(self.daeg)
self.print_nice(self.daeg)
for i in range(9):
for j in range(9):
print("i = %2s, j = %2s, daeg[i,j] = %s" % (i, j, daegT[i, j]))
self.assertEqual(self.daeg[i, j], daegT[i, j])
def test_transpose_23(self):
"""Check the 2,3 transpose of a rank-4, 3D tensor."""
# Manually create the string rep of the transpose.
daegT = self.string_transpose(2, 3)
print("The real 2,3 transpose:")
self.print_nice(daegT)
# Convert to numpy.
daegT = self.to_numpy(daegT)
# Check.
print("The numerical 2,3 transpose:")
transpose_23(self.daeg)
self.print_nice(self.daeg)
for i in range(9):
for j in range(9):
print("i = %2s, j = %2s, daeg[i,j] = %s" % (i, j, daegT[i, j]))
self.assertEqual(self.daeg[i, j], daegT[i, j])
def test_compile_2nd_matrix_pseudo_ellipse_point1(self):
"""Check the operation of the compile_2nd_matrix_pseudo_ellipse() function."""
# The simulated in frame pseudo-ellipse 2nd degree frame order matrix.
real = array(
[[ 0.7901, 0, 0, 0, 0.7118, 0, 0, 0, 0.6851],
[ 0, 0.0816, 0, -0.0606, 0, 0, 0, 0, 0],
[ 0, 0, 0.1282, 0, 0, 0, -0.1224, 0, 0],
[ 0, -0.0606, 0, 0.0708, 0, 0, 0, 0, 0],
[ 0.7118, 0, 0, 0, 0.6756, 0, 0, 0, 0.6429],
[ 0, 0, 0, 0, 0, 0.2536, 0, -0.2421, 0],
[ 0, 0, -0.1224, 0, 0, 0, 0.1391, 0, 0],
[ 0, 0, 0, 0, 0, -0.2421, 0, 0.2427, 0],
[ 0.6851, 0, 0, 0, 0.6429, 0, 0, 0, 0.6182]], float64)
transpose_23(real)
# Init.
x = pi/4.0
y = 3.0*pi/8.0
z = pi/6.0
# The Kronecker product of the eigenframe rotation.
Rx2_eigen = self.calc_Rx2_eigen_full(0.0, 0.0, 0.0)
# Calculate the matrix.
f2 = compile_2nd_matrix_pseudo_ellipse(self.f2_temp, Rx2_eigen, x, y, z)
# Print out.
print_frame_order_2nd_degree(real, "real")
print_frame_order_2nd_degree(f2, "calculated")
print_frame_order_2nd_degree(real-f2, "difference")
# Check the values.
for i in range(9):
for j in range(9):
print("Element %s, %s; diff %s." % (i, j, f2[i, j] - real[i, j]))
self.assert_(abs(f2[i, j] - real[i, j]) < 1e-4)
def test_compile_2nd_matrix_pseudo_ellipse_point1(self):
"""Check the operation of the compile_2nd_matrix_pseudo_ellipse() function."""
# The simulated in frame pseudo-ellipse 2nd degree frame order matrix.
real = array(
[[ 0.7901, 0, 0, 0, 0.7118, 0, 0, 0, 0.6851],
[ 0, 0.0816, 0, -0.0606, 0, 0, 0, 0, 0],
[ 0, 0, 0.1282, 0, 0, 0, -0.1224, 0, 0],
[ 0, -0.0606, 0, 0.0708, 0, 0, 0, 0, 0],
[ 0.7118, 0, 0, 0, 0.6756, 0, 0, 0, 0.6429],
[ 0, 0, 0, 0, 0, 0.2536, 0, -0.2421, 0],
[ 0, 0, -0.1224, 0, 0, 0, 0.1391, 0, 0],
[ 0, 0, 0, 0, 0, -0.2421, 0, 0.2427, 0],
[ 0.6851, 0, 0, 0, 0.6429, 0, 0, 0, 0.6182]], float64)
transpose_23(real)
# Init.
x = pi/4.0
y = 3.0*pi/8.0
z = pi/6.0
# The Kronecker product of the eigenframe rotation.
Rx2_eigen = self.calc_Rx2_eigen_full(0.0, 0.0, 0.0)
# Calculate the matrix.
f2 = compile_2nd_matrix_pseudo_ellipse(self.f2_temp, Rx2_eigen, x, y, z)
# Print out.
print_frame_order_2nd_degree(real, "real")
print_frame_order_2nd_degree(f2, "calculated")
print_frame_order_2nd_degree(real-f2, "difference")
# Check the values.
for i in range(9):
for j in range(9):
print("Element %s, %s; diff %s." % (i, j, f2[i, j] - real[i, j]))
self.assert_(abs(f2[i, j] - real[i, j]) < 1e-4)