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 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)
# '''''''''''''''''''''''''' plt.figure(figsize=(4.5, 3.5)) f_lasso_cv.cv_plot() plt.tight_layout() plt.show() # %% # The optimum solution # '''''''''''''''''''' sol = f_lasso_cv.f plt.figure(figsize=(4, 3)) plt.subplot(projection="csdm") plt.plot(true_t2_dist / true_t2_dist.max(), label="true distribution") plt.plot(sol / sol.max(), label="opt solution") plt.legend() plt.grid() plt.tight_layout() plt.show() # %% # Residuals # ''''''''' residuals = f_lasso_cv.residuals(K=K, s=signal) print(residuals.std()) plt.figure(figsize=(4.5, 3.5)) residuals.plot() plt.tight_layout() plt.show()
# %%
# The optimum solution
# ''''''''''''''''''''
f_sol = s_lasso.f
levels = np.arange(15) / 15 + 0.1
plt.figure(figsize=(4, 3))
ax = plt.subplot(projection="csdm")
ax.contour(f_sol / f_sol.max(), levels=levels, cmap="jet_r")
ax.set_ylim(-70, -130)
ax.set_xlim(-3, 2.5)
plt.grid(linestyle="--", alpha=0.75)
plt.tight_layout()
plt.show()
# %%
# The fit residuals
# '''''''''''''''''
residuals = s_lasso.residuals(K=K, s=data_object_truncated)
plot2D(residuals)
# %%
# The standard deviation of the residuals is
residuals.std()
# %%
# Saving the solution
# '''''''''''''''''''
f_sol.save("T2_inverse.csdf") # save the solution
residuals.save("T2_residue.csdf") # save the residuals