.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/1D_simulation(crystalline)/plot_7_CAS_dipolar_J.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_1D_simulation(crystalline)_plot_7_CAS_dipolar_J.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_1D_simulation(crystalline)_plot_7_CAS_dipolar_J.py:


Coupled spin-1/2 (CSA + heteronuclear dipolar + J-couplings)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

¹³C-¹H sideband simulation

.. GENERATED FROM PYTHON SOURCE LINES 9-14

The following simulation is an example by Edén [#f1]_ from `Computer Simulations in
Solid-State NMR.III.Powder Averaging`. The simulation consists of sideband spectra
from a 13C-1H coupled spin system computed at various spinning frequencies with
different relative tensor orientations between the nuclear shielding and dipolar
interaction tensors.

.. GENERATED FROM PYTHON SOURCE LINES 14-24

.. code-block:: Python

    import numpy as np
    import matplotlib.pyplot as plt

    from mrsimulator import Simulator, SpinSystem, Site, Coupling
    from mrsimulator.method.lib import BlochDecaySpectrum
    from mrsimulator import signal_processor as sp
    from mrsimulator.spin_system.tensors import SymmetricTensor
    from mrsimulator.method import SpectralDimension









.. GENERATED FROM PYTHON SOURCE LINES 26-29

Here, we create three 13C-1H spin systems with different relative orientations
between the shielding and dipolar tensors. The Euler angle orientations
:math:`\alpha=\gamma=0` and :math:`\beta` values are listed below.

.. GENERATED FROM PYTHON SOURCE LINES 29-58

.. code-block:: Python

    beta_orientation = [np.pi / 6, 5 * np.pi / 18, np.pi / 2]

    # The `variable` spin_systems is a list of three coupled 13C-1H spin systems with
    # different relative shielding and dipolar tensor orientation.
    spin_systems = [
        SpinSystem(
            sites=[
                Site(
                    isotope="13C",
                    isotropic_chemical_shift=0.0,  # in ppm
                    shielding_symmetric=SymmetricTensor(
                        zeta=18.87562,  # in ppm
                        eta=0.4,
                        beta=beta,
                    ),
                ),
                Site(
                    isotope="1H",
                    isotropic_chemical_shift=0.0,  # in ppm
                ),
            ],
            couplings=[
                Coupling(
                    site_index=[0, 1], isotropic_j=200.0, dipolar=SymmetricTensor(D=-2.1e4)
                )
            ],
        )
        for beta in beta_orientation
    ]







.. GENERATED FROM PYTHON SOURCE LINES 59-61

Next, we create methods to simulate the sideband manifolds for the above spin
systems at four spinning rates: 3 kHz, 5 kHz, 8 kHz, 12 kHz.

.. GENERATED FROM PYTHON SOURCE LINES 61-75

.. code-block:: Python


    spin_rates = [3e3, 5e3, 8e3, 12e3]  # in Hz

    # The variable `methods` is a list of four BlochDecaySpectrum methods.
    methods = [
        BlochDecaySpectrum(
            channels=["13C"],
            magnetic_flux_density=9.4,  # in T
            rotor_frequency=vr,  # in Hz
            spectral_dimensions=[SpectralDimension(count=2048, spectral_width=8.0e4)],
        )
        for vr in spin_rates
    ]








.. GENERATED FROM PYTHON SOURCE LINES 76-77

Create the Simulator object and add the method and the spin system objects.

.. GENERATED FROM PYTHON SOURCE LINES 77-82

.. code-block:: Python

    sim = Simulator(spin_systems=spin_systems, methods=methods)
    sim.config.integration_volume = "hemisphere"  # set averaging to hemisphere
    # config to decompose spectrum to individual spin systems.
    sim.config.decompose_spectrum = "spin_system"








.. GENERATED FROM PYTHON SOURCE LINES 83-85

The run command will simulate twelve spectra corresponding to the three spin systems
evaluated at four different methods (spinning speeds).

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: Python

    sim.run()








.. GENERATED FROM PYTHON SOURCE LINES 88-89

Add post-simulation signal processing.

.. GENERATED FROM PYTHON SOURCE LINES 89-101

.. code-block:: Python

    processor = sp.SignalProcessor(
        operations=[
            sp.IFFT(),
            sp.apodization.Exponential(FWHM="50 Hz"),
            sp.FFT(),
        ]
    )
    # apply the same post-simulation processing to all the twelve simulations.
    processed_dataset = [
        processor.apply_operations(dataset=method.simulation) for method in sim.methods
    ]








.. GENERATED FROM PYTHON SOURCE LINES 102-105

Let's first plot a single simulation, the one corresponding to a relative orientation
of :math:`\beta=30^\circ` between the shielding and dipolar tensors and a spinning
speed of 3 kHz.

.. GENERATED FROM PYTHON SOURCE LINES 105-119

.. code-block:: Python

    plt.figure(figsize=(4.25, 3.0))
    ax = plt.subplot(projection="csdm")
    ax.plot(
        processed_dataset[0].split()[0].real,
        color="black",
        linewidth=1,
        label="$\\nu_r=$3 kHz, \n $\\beta=30^\\circ$",
    )
    ax.legend()
    ax.invert_xaxis()
    plt.tight_layout()
    plt.show()





.. image-sg:: /examples/1D_simulation(crystalline)/images/sphx_glr_plot_7_CAS_dipolar_J_001.png
   :alt: plot 7 CAS dipolar J
   :srcset: /examples/1D_simulation(crystalline)/images/sphx_glr_plot_7_CAS_dipolar_J_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 120-122

The following is a grid plot showing all twelve simulations. For reference, see
Figure 11 from [#f1]_.

.. GENERATED FROM PYTHON SOURCE LINES 122-147

.. code-block:: Python

    fig, ax = plt.subplots(
        nrows=4,
        ncols=3,
        subplot_kw={"projection": "csdm"},
        sharex=True,
        sharey=True,
        figsize=(8, 10.0),
    )
    for i, datum in enumerate(processed_dataset):
        datum_spin_sys = datum.split()  # get simulation from the three spin systems.
        for j, item in enumerate(datum_spin_sys):
            ax[i, j].plot(
                item.real,
                color="black",
                linewidth=1,
                label=(
                    f"$\\nu_r={spin_rates[i]/1e3: .0f}$ kHz \n"
                    f"$\\beta={beta_orientation[j]/np.pi*180: .0f}^\\circ$"
                ),
            )
            ax[i, j].invert_xaxis()
            ax[i, j].legend()
    plt.tight_layout()
    plt.show()




.. image-sg:: /examples/1D_simulation(crystalline)/images/sphx_glr_plot_7_CAS_dipolar_J_002.png
   :alt: plot 7 CAS dipolar J
   :srcset: /examples/1D_simulation(crystalline)/images/sphx_glr_plot_7_CAS_dipolar_J_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 148-151

.. [#f1] Edén, M. Computer Simulations in Solid-State NMR. III. Powder Averaging,
      Concepts in Magnetic Resonance Part A, Vol. 18A(1) 24–55 (2003).
      `DOI: doi.org/10.1002/cmr.a.10065 <https://doi.org/10.1002/cmr.a.10065>`_


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 2.702 seconds)


.. _sphx_glr_download_examples_1D_simulation(crystalline)_plot_7_CAS_dipolar_J.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_7_CAS_dipolar_J.ipynb <plot_7_CAS_dipolar_J.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_7_CAS_dipolar_J.py <plot_7_CAS_dipolar_J.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_