def test_MAF_lineshape_kernel():
for dim in anisotropic_dims:
ns_obj = ShieldingPALineshape(
anisotropic_dimension=dim,
inverse_dimension=inverse_dimension,
channel="29Si",
magnetic_flux_density="9.4 T",
rotor_angle="90 deg",
rotor_frequency="14 kHz",
number_of_sidebands=1,
)
zeta, eta = ns_obj._get_zeta_eta(supersampling=1)
K = ns_obj.kernel(supersampling=1)
sim_lineshape = generate_shielding_kernel(zeta, eta, np.pi / 2, 14000,
1).T
assert np.allclose(K, sim_lineshape, rtol=1.0e-3, atol=1e-3)
ns_obj = MAF(
anisotropic_dimension=dim,
inverse_dimension=inverse_dimension,
channel="29Si",
magnetic_flux_density="9.4 T",
)
zeta, eta = ns_obj._get_zeta_eta(supersampling=1)
K = ns_obj.kernel(supersampling=1)
sim_lineshape = generate_shielding_kernel(zeta, eta, np.pi / 2, 14000,
1).T
assert np.allclose(K, sim_lineshape, rtol=1.0e-3, atol=1e-3)
_ = TSVDCompression(K, s=np.arange(96))
assert _.truncation_index == 15
def test_spinning_sidebands_kernel():
# 1
for dim in anisotropic_dims:
ns_obj = ShieldingPALineshape(
anisotropic_dimension=dim,
inverse_dimension=inverse_dimension,
channel="29Si",
magnetic_flux_density="9.4 T",
rotor_angle="54.735 deg",
rotor_frequency="100 Hz",
number_of_sidebands=96,
)
zeta, eta = ns_obj._get_zeta_eta(supersampling=1)
K = ns_obj.kernel(supersampling=1)
sim_lineshape = generate_shielding_kernel(zeta, eta,
0.9553059660790962, 100,
96).T
assert np.allclose(K, sim_lineshape, rtol=1.0e-3, atol=1e-3)
# 2
ns_obj = ShieldingPALineshape(
anisotropic_dimension=dim,
inverse_dimension=inverse_dimension_ppm,
channel="29Si",
magnetic_flux_density="9.4 T",
rotor_angle="54.735 deg",
rotor_frequency="100 Hz",
number_of_sidebands=96,
)
zeta, eta = ns_obj._get_zeta_eta(supersampling=1)
K = ns_obj.kernel(supersampling=1)
sim_lineshape = generate_shielding_kernel(zeta,
eta,
0.9553059660790962,
100,
96,
to_ppm=False).T
assert np.allclose(K, sim_lineshape, rtol=1.0e-3, atol=1e-3)
# 3
ns_obj = SpinningSidebands(
anisotropic_dimension=dim,
inverse_dimension=inverse_dimension,
channel="29Si",
magnetic_flux_density="9.4 T",
)
zeta, eta = ns_obj._get_zeta_eta(supersampling=1)
K = ns_obj.kernel(supersampling=1)
sim_lineshape = generate_shielding_kernel(zeta, eta,
0.9553059660790962, 208.33,
96).T
assert np.allclose(K, sim_lineshape, rtol=1.0e-3, atol=1e-3)
_ = TSVDCompression(K, s=np.arange(96))
assert _.truncation_index == 15
def test_inversion():
domain = "https://www.ssnmr.org/sites/default/files/mrsimulator"
filename = f"{domain}/MAS_SE_PIETA_5%25Li2O_FT.csdf"
data_object = cp.load(filename)
# Inversion only requires the real part of the complex dataset.
data_object = data_object.real
sigma = 1110.521 # data standard deviation
# Convert the MAS dimension from Hz to ppm.
data_object.dimensions[0].to("ppm", "nmr_frequency_ratio")
data_object = data_object.T
data_object_truncated = data_object[:, 1220:-1220]
data_object_truncated.dimensions[0].to("s") # set coordinates to 's'
kernel_dimension = data_object_truncated.dimensions[0]
relaxT2 = relaxation.T2(
kernel_dimension=kernel_dimension,
inverse_dimension=dict(
count=32,
minimum="1e-3 s",
maximum="1e4 s",
scale="log",
label="log (T2 / s)",
),
)
inverse_dimension = relaxT2.inverse_dimension
K = relaxT2.kernel(supersampling=20)
new_system = TSVDCompression(K, data_object_truncated)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
assert new_system.truncation_index == 18
# setup the pre-defined range of alpha and lambda values
lambdas = 10 ** (-4 + 5 * (np.arange(32) / 31))
# setup the smooth lasso cross-validation class
s_lasso = LassoFistaCV(
lambdas=lambdas, # A numpy array of lambda values.
sigma=sigma, # data standard deviation
folds=5, # The number of folds in n-folds cross-validation.
inverse_dimension=inverse_dimension, # previously defined inverse dimensions.
)
# run the fit method on the compressed kernel and compressed data.
s_lasso.fit(K=compressed_K, s=compressed_s)
np.testing.assert_almost_equal(s_lasso.hyperparameters["lambda"], 0.116, decimal=1)
s_lasso.cv_plot()
residuals = s_lasso.residuals(K=K, s=data_object_truncated)
np.testing.assert_almost_equal(residuals.std().value, 1538.48, decimal=1)
def generate_kernel(n, data, count0, inc0, count1, inc1, channel, B0, theta,
n_su, d_range, k_typ):
if data is None:
raise PreventUpdate
if d_range is None:
d_range = [[0, -1], [0, -1]]
data = cp.parse_dict(data)
anisotropic_dimension = data.dimensions[0]
inverse_dimensions = [
cp.LinearDimension(count=count0, increment=f"{inc0} Hz", label="x"),
cp.LinearDimension(count=count1, increment=f"{inc1} Hz", label="y"),
]
vr = 0
ns = 1
if k_typ == "sideband-correlation":
vr = anisotropic_dimension.increment.to("Hz")
ns = anisotropic_dimension.count
if k_typ == "MAF":
vr = "1 GHz"
ns = 1
K = ShieldingPALineshape(
anisotropic_dimension=anisotropic_dimension,
inverse_dimension=inverse_dimensions,
channel=channel,
magnetic_flux_density=f"{B0} T",
rotor_angle=f"{theta} °",
rotor_frequency=f"{vr}",
number_of_sidebands=ns,
).kernel(supersampling=int(n_su))
ranges = slice(d_range[1][0], d_range[1][1], None)
data_truncated = data[:, ranges]
new_system = TSVDCompression(K, data_truncated)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
return {
"kernel": compressed_K,
"signal": compressed_s.dict(),
"inverse_dimensions": [item.dict() for item in inverse_dimensions],
}
def test_fista():
domain = "https://sandbox.zenodo.org/record/1065394/files"
filename = f"{domain}/test1_signal.csdf"
signal = cp.load(filename)
sigma = 0.0008
datafile = f"{domain}/test1_t2.csdf"
true_dist = cp.load(datafile)
kernel_dimension = signal.dimensions[0]
relaxT2 = relaxation.T2(
kernel_dimension=kernel_dimension,
inverse_dimension=dict(
count=64,
minimum="1e-2 s",
maximum="1e3 s",
scale="log",
label="log (T2 / s)",
),
)
inverse_dimension = relaxT2.inverse_dimension
K = relaxT2.kernel(supersampling=1)
new_system = TSVDCompression(K, signal)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
assert new_system.truncation_index == 29
lambdas = 10 ** (-5 + 4 * (np.arange(16) / 15))
f_lasso_cv = LassoFistaCV(
lambdas=lambdas, # A numpy array of lambda values.
folds=5, # The number of folds in n-folds cross-validation.
sigma=sigma, # noise standard deviation
inverse_dimension=inverse_dimension, # previously defined inverse dimensions.
)
f_lasso_cv.fit(K=compressed_K, s=compressed_s)
sol = f_lasso_cv.f
assert np.argmax(sol.y[0].components[0]) == np.argmax(true_dist.y[0].components[0])
residuals = f_lasso_cv.residuals(K=K, s=signal)
std = residuals.std()
np.testing.assert_almost_equal(std.value, sigma, decimal=3)
# instance to generate the MAF line-shape kernel.
K = lineshape.kernel(supersampling=1)
print(K.shape)
# %%
# The kernel ``K`` is a NumPy array of shape (128, 625), where the axes with 128 and
# 625 points are the anisotropic dimension and the features (x-y coordinates)
# corresponding to the :math:`25\times 25` `x`-`y` grid, respectively.
# %%
# Data Compression
# ''''''''''''''''
#
# Data compression is optional but recommended. It may reduce the size of the
# inverse problem and, thus, further computation time.
new_system = TSVDCompression(K, data_object_truncated)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
print(f"truncation_index = {new_system.truncation_index}")
# %%
# Solving the inverse problem
# ---------------------------
#
# Smooth LASSO cross-validation
# '''''''''''''''''''''''''''''
#
# Solve the smooth-lasso problem. Ordinarily, one should use the statistical learning
# method to solve the inverse problem over a range of α and λ values and then determine
# the best nuclear shielding tensor parameter distribution for the given 2D MAF
relaxT2 = relaxation.T2(
kernel_dimension=kernel_dimension,
inverse_dimension=dict(count=64,
minimum="1e-2 s",
maximum="1e3 s",
scale="log",
label="log (T2 / s)"),
)
inverse_dimension = relaxT2.inverse_dimension
K = relaxT2.kernel(supersampling=1)
# %%
# Data Compression
# ''''''''''''''''
new_system = TSVDCompression(K, signal)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
print(f"truncation_index = {new_system.truncation_index}")
# %%
# Fista LASSO cross-validation
# '''''''''''''''''''''''''''''
# Create a guess range of values for the :math:`\lambda` hyperparameters.
lambdas = 10**(-5 + 4 * (np.arange(64) / 63))
# setup the smooth lasso cross-validation class
f_lasso_cv = LassoFistaCV(
lambdas=lambdas, # A numpy array of lambda values.
folds=5, # The number of folds in n-folds cross-validation.
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,
)
# and `rotor_frequency`, are set to match the conditions under which the spectrum
# was acquired. The value of the `number_of_sidebands` argument is the number of
# sidebands calculated for each line-shape within the kernel.
#
# Once the ShieldingPALineshape instance is created, use the
# :meth:`~mrinversion.kernel.nmr.ShieldingPALineshape.kernel` method of the
# instance to generate the MAF line-shape kernel.
K = lineshape.kernel(supersampling=1)
# %%
# Data Compression
# ''''''''''''''''
#
# Data compression is optional but recommended. It may reduce the size of the
# inverse problem and, thus, further computation time.
new_system = TSVDCompression(K, data_object)
compressed_K = new_system.compressed_K
compressed_s = new_system.compressed_s
print(f"truncation_index = {new_system.truncation_index}")
# %%
# Solving the inverse problem
# ---------------------------
#
# Smooth-LASSO problem
# ''''''''''''''''''''
#
# Solve the smooth-lasso problem. You may choose to skip this step and proceed to the
# statistical learning method. Usually, the statistical learning method is a
# time-consuming process that solves the smooth-lasso problem over a range of