# %%
# Notice the shape of the isotropic chemical shift distribution for the
# :math:`\text{Q}^4` sites is skewed, which is expected.
#
#
# Analysis
# --------
#
# For the analysis, we use the
# `statistics <https://csdmpy.readthedocs.io/en/latest/api/statistics.html>`_
# module of the csdmpy package. Following is the moment analysis of the 3D volumes for
# both the :math:`\text{Q}^4` and :math:`\text{Q}^3` regions up to the second moment.
int_Q4 = stats.integral(Q4_region) # volume of the Q4 distribution
mean_Q4 = stats.mean(Q4_region) # mean of the Q4 distribution
std_Q4 = stats.std(Q4_region) # standard deviation of the Q4 distribution
int_Q3 = stats.integral(Q3_region) # volume of the Q3 distribution
mean_Q3 = stats.mean(Q3_region) # mean of the Q3 distribution
std_Q3 = stats.std(Q3_region) # standard deviation of the Q3 distribution
print("Q4 statistics")
print(f"\tpopulation = {100 * int_Q4 / (int_Q4 + int_Q3)}%")
print("\tmean\n\t\tx:\t{}\n\t\ty:\t{}\n\t\tiso:\t{}".format(*mean_Q4))
print("\tstandard deviation\n\t\tx:\t{}\n\t\ty:\t{}\n\t\tiso:\t{}".format(
*std_Q4))
print("Q3 statistics")
print(f"\tpopulation = {100 * int_Q3 / (int_Q4 + int_Q3)}%")
print("\tmean\n\t\tx:\t{}\n\t\ty:\t{}\n\t\tiso:\t{}".format(*mean_Q3))
def test_01():
domain = "https://sandbox.zenodo.org/record/1065347/files"
filename = f"{domain}/8lnwmg0dr7y6egk40c2orpkmmugh9j7c.csdf"
data_object = cp.load(filename)
data_object = data_object.real
_ = [item.to("ppm", "nmr_frequency_ratio") for item in data_object.dimensions]
data_object = data_object.T
data_object_truncated = data_object[:, 155:180]
anisotropic_dimension = data_object_truncated.dimensions[0]
inverse_dimensions = [
cp.LinearDimension(count=25, increment="400 Hz", label="x"),
cp.LinearDimension(count=25, increment="400 Hz", label="y"),
]
lineshape = ShieldingPALineshape(
anisotropic_dimension=anisotropic_dimension,
inverse_dimension=inverse_dimensions,
channel="29Si",
magnetic_flux_density="9.4 T",
rotor_angle="87.14°",
rotor_frequency="14 kHz",
number_of_sidebands=4,
)
K = lineshape.kernel(supersampling=2)
new_system = TSVDCompression(K, data_object_truncated)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
assert new_system.truncation_index == 87
s_lasso = SmoothLasso(
alpha=2.07e-7, lambda1=7.85e-6, inverse_dimension=inverse_dimensions
)
s_lasso.fit(K=compressed_K, s=compressed_s)
f_sol = s_lasso.f
residuals = s_lasso.residuals(K=K, s=data_object_truncated)
# assert np.allclose(residuals.mean().value, 0.00048751)
np.testing.assert_almost_equal(residuals.std().value, 0.00336372, decimal=2)
f_sol /= f_sol.max()
[item.to("ppm", "nmr_frequency_ratio") for item in f_sol.dimensions]
Q4_region = f_sol[0:8, 0:8, 3:18]
Q4_region.description = "Q4 region"
Q3_region = f_sol[0:8, 11:22, 8:20]
Q3_region.description = "Q3 region"
# Analysis
int_Q4 = stats.integral(Q4_region) # volume of the Q4 distribution
mean_Q4 = stats.mean(Q4_region) # mean of the Q4 distribution
std_Q4 = stats.std(Q4_region) # standard deviation of the Q4 distribution
int_Q3 = stats.integral(Q3_region) # volume of the Q3 distribution
mean_Q3 = stats.mean(Q3_region) # mean of the Q3 distribution
std_Q3 = stats.std(Q3_region) # standard deviation of the Q3 distribution
np.testing.assert_almost_equal(
(100 * int_Q4 / (int_Q4 + int_Q3)).value, 60.45388973909665, decimal=1
)
np.testing.assert_almost_equal(
np.asarray([mean_Q4[0].value, mean_Q4[1].value, mean_Q4[2].value]),
np.asarray([8.604842824865958, 9.05845796147297, -103.6976331077773]),
decimal=0,
)
np.testing.assert_almost_equal(
np.asarray([mean_Q3[0].value, mean_Q3[1].value, mean_Q3[2].value]),
np.asarray([10.35036818411856, 79.02481579085152, -90.58326773441284]),
decimal=0,
)
np.testing.assert_almost_equal(
np.asarray([std_Q4[0].value, std_Q4[1].value, std_Q4[2].value]),
np.asarray([4.525457744683861, 4.686253809896416, 5.369228151035292]),
decimal=0,
)
np.testing.assert_almost_equal(
np.asarray([std_Q3[0].value, std_Q3[1].value, std_Q3[2].value]),
np.asarray([6.138761032132587, 7.837190479891721, 4.210912435356488]),
decimal=0,
)