.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "fitting/1D_fitting/plot_1_31P_Na2PO4_MAS.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_fitting_1D_fitting_plot_1_31P_Na2PO4_MAS.py: ³¹P MAS NMR of crystalline Na2PO4 (CSA) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 7-20 In this example, we illustrate the use of the mrsimulator objects to - create a CSA fitting model using Simulator and SignalProcessor objects, - use the fitting model to perform a least-squares analysis, and - extract the fitting parameters from the model. We use the `LMFIT `_ library to fit the spectrum. The following example shows the least-squares fitting procedure applied to the :math:`^{31}\text{P}` MAS NMR spectrum of :math:`\text{Na}_{2}\text{PO}_{4}`. The following experimental dataset is a part of DMFIT [#f1]_ examples. We thank Dr. Dominique Massiot for sharing the dataset. Start by importing the relevant modules. .. GENERATED FROM PYTHON SOURCE LINES 20-33 .. code-block:: Python import csdmpy as cp import numpy as np 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 .. GENERATED FROM PYTHON SOURCE LINES 35-41 Import the dataset ------------------ Import the experimental data. We use dataset file serialized with the CSDM file-format, using the `csdmpy `_ module. .. GENERATED FROM PYTHON SOURCE LINES 41-60 .. code-block:: Python host = "https://nmr.cemhti.cnrs-orleans.fr/Dmfit/Help/csdm/" filename = "31P Phosphate 6kHz.csdf" experiment = cp.load(host + filename) # For spectral fitting, we only focus on the real part of the complex dataset experiment = experiment.real # Convert the dimension coordinates from Hz to ppm. experiment.x[0].to("ppm", "nmr_frequency_ratio") # plot of the dataset. plt.figure(figsize=(4.25, 3.0)) ax = plt.subplot(projection="csdm") ax.plot(experiment, color="black", linewidth=0.5, label="Experiment") ax.set_xlim(150, -150) plt.grid() plt.tight_layout() plt.show() .. image-sg:: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_001.png :alt: plot 1 31P Na2PO4 MAS :srcset: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 61-62 Estimate noise statistics from the dataset .. GENERATED FROM PYTHON SOURCE LINES 62-77 .. code-block:: Python coords = experiment.dimensions[0].coordinates noise_region = np.where(coords < -100e-6) noise_data = experiment[noise_region] plt.figure(figsize=(3.75, 2.5)) ax = plt.subplot(projection="csdm") ax.plot(noise_data, label="noise") plt.title("Noise section") plt.axis("off") plt.tight_layout() plt.show() noise_mean, sigma = experiment[noise_region].mean(), experiment[noise_region].std() noise_mean, sigma .. image-sg:: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_002.png :alt: Noise section :srcset: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none (, ) .. GENERATED FROM PYTHON SOURCE LINES 78-84 Create a fitting model ---------------------- A fitting model is a composite of ``Simulator`` and ``SignalProcessor`` objects. **Step 1:** Create initial guess sites and spin systems .. GENERATED FROM PYTHON SOURCE LINES 84-92 .. code-block:: Python P_31 = Site( isotope="31P", isotropic_chemical_shift=5.0, # in ppm, shielding_symmetric=SymmetricTensor(zeta=-80, eta=0.5), # zeta in Hz ) spin_systems = [SpinSystem(sites=[P_31])] .. GENERATED FROM PYTHON SOURCE LINES 93-105 **Step 2:** Create the method object. Create an appropriate method object that closely resembles the technique used in acquiring the experimental dataset. The attribute values of this method must meet the experimental conditions, including the acquisition channels, the magnetic flux density, rotor angle, rotor frequency, and the spectral/spectroscopic dimension. In the following example, we set up a Bloch decay spectrum method where the spectral/spectroscopic dimension information, i.e., count, spectral_width, and the reference_offset, is extracted from the CSDM dimension metadata using the :func:`~mrsimulator.utils.get_spectral_dimensions` utility function. The remaining attribute values are set to the experimental conditions. .. GENERATED FROM PYTHON SOURCE LINES 105-117 .. code-block:: Python # get the count, spectral_width, and reference_offset information from the experiment. spectral_dims = get_spectral_dimensions(experiment) MAS = BlochDecaySpectrum( channels=["31P"], magnetic_flux_density=9.395, # in T rotor_frequency=6000, # in Hz spectral_dimensions=spectral_dims, experiment=experiment, # experimental dataset ) .. GENERATED FROM PYTHON SOURCE LINES 118-119 **Step 3:** Create the Simulator object and add the method and spin system objects. .. GENERATED FROM PYTHON SOURCE LINES 119-122 .. code-block:: Python sim = Simulator(spin_systems=spin_systems, methods=[MAS]) sim.run() .. GENERATED FROM PYTHON SOURCE LINES 123-125 **Step 4:** Create a SignalProcessor class object and apply the post-simulation signal processing operations. .. GENERATED FROM PYTHON SOURCE LINES 125-136 .. code-block:: Python processor = sp.SignalProcessor( operations=[ sp.IFFT(), sp.apodization.Exponential(FWHM="0.3 kHz"), sp.FFT(), sp.Scale(factor=3000), sp.baseline.ConstantOffset(offset=-2), ] ) processed_dataset = processor.apply_operations(dataset=sim.methods[0].simulation).real .. GENERATED FROM PYTHON SOURCE LINES 137-138 **Step 5:** The plot of the dataset and the guess spectrum. .. GENERATED FROM PYTHON SOURCE LINES 138-149 .. code-block:: Python plt.figure(figsize=(4.25, 3.0)) ax = plt.subplot(projection="csdm") ax.plot(experiment, color="black", linewidth=0.5, label="Experiment") ax.plot(processed_dataset, linewidth=2, alpha=0.6, label="Guess Spectrum") ax.set_xlim(150, -150) plt.legend() plt.grid() plt.tight_layout() plt.show() .. image-sg:: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_003.png :alt: plot 1 31P Na2PO4 MAS :srcset: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 150-166 Least-squares minimization with LMFIT ------------------------------------- Once you have a fitting model, you need to create the list of parameters to use in the least-squares minimization. For this, you may use the `Parameters `_ class from *LMFIT*, as described in the previous example. Here, we make use of a utility function, :func:`~mrsimulator.utils.spectral_fitting.make_LMFIT_params`, to simplifies the LMFIT parameters generation process. By default, the function only creates parameters from the SpinSystem and SignalProcessor objects. Often, in spectrum with sidebands, spinning speed may not be accurately known; and is, therefore, included as a fitting parameter. To include a keyword from the method object, use the *include* argument of the function, as follows, **Step 6:** Create a list of parameters. .. GENERATED FROM PYTHON SOURCE LINES 166-168 .. code-block:: Python params = sf.make_LMFIT_params(sim, processor, include={"rotor_frequency"}) .. GENERATED FROM PYTHON SOURCE LINES 169-175 The `make_LMFIT_params` parses the instances of the ``Simulator`` and the ``PostSimulator`` objects for parameters and returns a LMFIT `Parameters` object. **Customize the Parameters:** You may customize the parameters list, ``params``, as desired. Here, we remove the abundance parameter. .. GENERATED FROM PYTHON SOURCE LINES 175-178 .. code-block:: Python params.pop("sys_0_abundance") print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"])) .. rst-class:: sphx-glr-script-out .. code-block:: none Name Value Min Max Vary Expr SP_0_operation_1_Exponential_FWHM 0.3 -inf inf True None SP_0_operation_3_Scale_factor 3000 -inf inf True None SP_0_operation_4_ConstantOffset_offset -2 -inf inf True None mth_0_rotor_frequency 6000 5900 6100 True None sys_0_site_0_isotropic_chemical_shift 5 -inf inf True None sys_0_site_0_shielding_symmetric_eta 0.5 0 1 True None sys_0_site_0_shielding_symmetric_zeta -80 -inf inf True None None .. GENERATED FROM PYTHON SOURCE LINES 179-194 **Step 7:** Perform the least-squares minimization. A method object queries every spin system for a list of transition pathways that are relevant to the given method. Since the method and the number of spin systems remains unchanged during the least-squares analysis, a one-time query is sufficient. To avoid querying for the transition pathways at every iteration in a least-squares fitting, call the :py:meth:`~mrsimulator.Simulator.optimize()` method to pre-compute the pathways. For the user's convenience, we also provide a utility function, :func:`~mrsimulator.utils.spectral_fitting.LMFIT_min_function`, for evaluating the difference vector between the simulation and experiment, based on the parameters update. You may use this function directly to instantiate the LMFIT Minimizer class where `fcn_args` and `fcn_kws` are arguments passed to the function, as follows, .. GENERATED FROM PYTHON SOURCE LINES 194-204 .. code-block:: Python opt = sim.optimize() # Pre-compute transition pathways minner = Minimizer( sf.LMFIT_min_function, params, fcn_args=(sim, processor, sigma), fcn_kws={"opt": opt}, ) result = minner.minimize() result .. raw:: html

Fit Result



.. GENERATED FROM PYTHON SOURCE LINES 205-206 **Step 8:** The plot of the fit, measurement, and residuals. .. GENERATED FROM PYTHON SOURCE LINES 206-223 .. code-block:: Python # Best fit spectrum best_fit = sf.bestfit(sim, processor)[0].real residuals = sf.residuals(sim, processor)[0].real plt.figure(figsize=(4.25, 3.0)) ax = plt.subplot(projection="csdm") ax.plot(experiment, color="black", linewidth=0.5, label="Experiment") ax.plot(residuals, color="gray", linewidth=0.5, label="Residual") ax.plot(best_fit, linewidth=2, alpha=0.6, label="Best Fit") ax.set_xlabel(r"$^{31}$P frequency / ppm") ax.set_xlim(150, -150) plt.legend() plt.grid() plt.tight_layout() plt.show() .. image-sg:: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_004.png :alt: plot 1 31P Na2PO4 MAS :srcset: /fitting/1D_fitting/images/sphx_glr_plot_1_31P_Na2PO4_MAS_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 224-228 .. [#f1] D.Massiot, F.Fayon, M.Capron, I.King, S.Le Calvé, B.Alonso, J.O.Durand, B.Bujoli, Z.Gan, G.Hoatson, 'Modelling one and two-dimensional solid-state NMR spectra.', Magn. Reson. Chem. **40** 70-76 (2002) `DOI: 10.1002/mrc.984 `_ .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.006 seconds) .. _sphx_glr_download_fitting_1D_fitting_plot_1_31P_Na2PO4_MAS.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_1_31P_Na2PO4_MAS.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_1_31P_Na2PO4_MAS.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_