1D PASS/MAT sideband order cross-section

This example illustrates the use of mrsimulator and LMFIT modules in fitting the sideband intensity profile across the isotropic chemical shift cross-section from a PASS/MAT dataset.

import csdmpy as cp
import matplotlib.pyplot as plt
from lmfit import Minimizer

from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator.method.lib import BlochDecaySpectrum
from mrsimulator import signal_processor as sp
from mrsimulator.utils import spectral_fitting as sf
from mrsimulator.utils import get_spectral_dimensions
from mrsimulator.spin_system.tensors import SymmetricTensor

Import the dataset

name = "https://ssnmr.org/sites/default/files/mrsimulator/LHistidine_cross_section.csdf"
pass_cross_section = cp.load(name)

# standard deviation of noise from the dataset
sigma = 4.640351

# For the spectral fitting, we only focus on the real part of the complex dataset.
pass_cross_section = pass_cross_section.real

# Convert the coordinates along each dimension from Hz to ppm.
_ = [item.to("ppm", "nmr_frequency_ratio") for item in pass_cross_section.dimensions]


# The plot of the dataset.
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(pass_cross_section, "k", alpha=0.5)
ax.invert_xaxis()
plt.grid()
plt.tight_layout()
plt.show()
plot 2 PASS cross sections

Create a fitting model

Guess model

Create a guess list of spin systems. For fitting the sideband profile at an isotropic chemical shift cross-section from PASS/MAT datasets, set the isotropic_chemical_shift parameter of the site object as zero.

site = Site(
    isotope="13C",
    isotropic_chemical_shift=0,  #
    shielding_symmetric=SymmetricTensor(zeta=-70, eta=0.8),
)
spin_systems = [SpinSystem(sites=[site])]

Method

For the sideband-only cross-section, use the BlochDecaySpectrum method.

# Get the dimension information from the experiment.
spectral_dims = get_spectral_dimensions(pass_cross_section)

PASS = BlochDecaySpectrum(
    channels=["13C"],
    magnetic_flux_density=9.395,  # in T
    rotor_frequency=1500,  # in Hz
    spectral_dimensions=spectral_dims,
    experiment=pass_cross_section,  # also add the measurement to the method.
)

# Optimize the script by pre-setting the transition pathways for each spin system from
# the method.
for sys in spin_systems:
    sys.transition_pathways = PASS.get_transition_pathways(sys)

Guess Spectrum

# Simulation
# ----------
sim = Simulator(spin_systems=spin_systems, methods=[PASS])
sim.run()

# Post Simulation Processing
# --------------------------
processor = sp.SignalProcessor(operations=[sp.Scale(factor=2000)])
processed_dataset = processor.apply_operations(dataset=sim.methods[0].simulation).real

# Plot of the guess Spectrum
# --------------------------
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(pass_cross_section, color="k", linewidth=1, label="Experiment")
ax.plot(processed_dataset, color="r", alpha=0.75, linewidth=1, label="guess spectrum")
plt.grid()
ax.invert_xaxis()
plt.legend()
plt.tight_layout()
plt.show()
plot 2 PASS cross sections

Least-squares minimization with LMFIT

First, create the fitting parameters. Use the make_LMFIT_params() for a quick setup.

params = sf.make_LMFIT_params(sim, processor)

# Fix the value of the isotropic chemical shift to zero for pure anisotropic sideband
# amplitude simulation.
params["sys_0_site_0_isotropic_chemical_shift"].vary = False
print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"]))

Out:

Name                                      Value      Min      Max     Vary     Expr
SP_0_operation_0_Scale_factor              2000     -inf      inf     True     None
sys_0_abundance                             100        0      100    False      100
sys_0_site_0_isotropic_chemical_shift         0     -inf      inf    False     None
sys_0_site_0_shielding_symmetric_eta        0.8        0        1     True     None
sys_0_site_0_shielding_symmetric_zeta       -70     -inf      inf     True     None
None

Run the minimization using LMFIT

Fit Statistics

fitting methodleastsq
# function evals37
# data points16
# variables3
chi-square 56.5116594
reduced chi-square 4.34705072
Akaike info crit. 26.1897321
Bayesian info crit. 28.5074983

Variables

name value standard error relative error initial value min max vary expression
sys_0_site_0_isotropic_chemical_shift 0.00000000 0.00000000 0.0 -inf inf False
sys_0_site_0_shielding_symmetric_zeta -85.1018616 1.52031973 (1.79%) -70.0 -inf inf True
sys_0_site_0_shielding_symmetric_eta 0.46192317 0.03083963 (6.68%) 0.8 0.00000000 1.00000000 True
sys_0_abundance 100.000000 0.00000000 (0.00%) 100 0.00000000 100.000000 False 100
SP_0_operation_0_Scale_factor 1850.35094 48.9743313 (2.65%) 2000.0 -inf inf True

Correlations (unreported correlations are < 0.100)

sys_0_site_0_shielding_symmetric_zetasys_0_site_0_shielding_symmetric_eta0.3743
sys_0_site_0_shielding_symmetric_zetaSP_0_operation_0_Scale_factor-0.2312
sys_0_site_0_shielding_symmetric_etaSP_0_operation_0_Scale_factor0.2063


The best fit solution

best_fit = sf.bestfit(sim, processor)[0].real
residuals = sf.residuals(sim, processor)[0].real

# Plot the spectrum
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(pass_cross_section, color="k", linewidth=1, label="Experiment")
ax.plot(best_fit, "r", alpha=0.75, linewidth=1, label="Best Fit")
ax.plot(residuals, alpha=0.75, linewidth=1, label="Residuals")
ax.invert_xaxis()
plt.grid()
plt.legend()
plt.tight_layout()
plt.show()
plot 2 PASS cross sections

Total running time of the script: ( 0 minutes 1.325 seconds)

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