new example

docs/user_guide/spin_system_distributions/czjzek.rst

@@ -55,8 +55,8 @@ In the above example, we draw *50000* random points of the distribution. The out
     import matplotlib.pyplot as plt
 
     plt.scatter(zeta_dist, eta_dist, s=4, alpha=0.02)
-    plt.xlabel("$\zeta$ / ppm")
-    plt.ylabel("$\eta$")
+    plt.xlabel("$\\zeta$ / ppm")
+    plt.ylabel("$\\eta$")
     plt.xlim(-15, 15)
     plt.ylim(0, 1)
     plt.tight_layout()
@@ -146,8 +146,8 @@ on the grid. Below, the distribution is plotted
 
 
     plt.contourf(zeta_grid, eta_grid, amp, levels=10)
-    plt.xlabel("$\zeta$ / ppm")
-    plt.ylabel("$\eta$")
+    plt.xlabel("$\\zeta$ / ppm")
+    plt.ylabel("$\\eta$")
     plt.tight_layout()
     plt.show()
 

docs/user_guide/spin_system_distributions/extended_czjzek.rst

@@ -52,8 +52,8 @@ The scatter plot of these coordinates is shown below.
     import matplotlib.pyplot as plt
 
     plt.scatter(zeta_dist, eta_dist, s=4, alpha=0.01)
-    plt.xlabel("$\zeta$ / ppm")
-    plt.ylabel("$\eta$")
+    plt.xlabel("$\\zeta$ / ppm")
+    plt.ylabel("$\\eta$")
     plt.xlim(60, 100)
     plt.ylim(0, 1)
     plt.tight_layout()
@@ -105,7 +105,7 @@ The plot of the extended Czjzek probability distribution is shown below.
 
     plt.contourf(Cq_grid, eta_grid, amp, levels=10)
     plt.xlabel("$C_q$ / MHz")
-    plt.ylabel("$\eta$")
+    plt.ylabel("$\\eta$")
     plt.tight_layout()
     plt.show()
 
@@ -141,7 +141,7 @@ coordinates.
     fig, ax = plt.subplots(1, 2, figsize=(9, 4), gridspec_kw={"width_ratios": (5, 4)})
     ax[0].contourf(Cq_grid, eta_grid, amp, levels=10)
     ax[0].set_xlabel("$C_q$ / MHz")
-    ax[0].set_ylabel("$\eta$")
+    ax[0].set_ylabel("$\\eta$")
     ax[0].set_title("Cartesian coordinates")
     ax[1].contourf(x_grid, y_grid, amp_polar, levels=10)
     ax[1].set_xlabel("x / MHz")

examples_source/1D_simulation(macro_amorphous)/plot_3_amorphous_like.py

@@ -61,18 +61,18 @@
 
 # isotropic shift v.s. shielding anisotropy
 ax[0].contourf(zeta_range, iso_range, pdf.sum(axis=2))
-ax[0].set_xlabel(r"shielding anisotropy, $\zeta$ / ppm")
+ax[0].set_xlabel("shielding anisotropy, $\\zeta$ / ppm")
 ax[0].set_ylabel("isotropic chemical shift / ppm")
 
 # isotropic shift v.s. shielding asymmetry
 ax[1].contourf(eta_range, iso_range, pdf.sum(axis=1))
-ax[1].set_xlabel(r"shielding asymmetry, $\eta$")
+ax[1].set_xlabel("shielding asymmetry, $\\eta$")
 ax[1].set_ylabel("isotropic chemical shift / ppm")
 
 # shielding anisotropy v.s. shielding asymmetry
 ax[2].contourf(eta_range, zeta_range, pdf.sum(axis=0))
-ax[2].set_xlabel(r"shielding asymmetry, $\eta$")
-ax[2].set_ylabel(r"shielding anisotropy, $\zeta$ / ppm")
+ax[2].set_xlabel("shielding asymmetry, $\\eta$")
+ax[2].set_ylabel("shielding anisotropy, $\\zeta$ / ppm")
 
 plt.tight_layout()
 plt.show()

examples_source/1D_simulation(macro_amorphous)/plot_5_czjzek_distribution.py

@@ -46,8 +46,8 @@
 # The following is the contour plot of the Czjzek distribution.
 plt.figure(figsize=(4.25, 3.0))
 plt.contourf(z_dist, e_dist, amp, levels=10)
-plt.xlabel(r"$\zeta$ / ppm")
-plt.ylabel(r"$\eta$")
+plt.xlabel("$\\zeta$ / ppm")
+plt.ylabel("$\\eta$")
 plt.tight_layout()
 plt.show()
 

examples_source/1D_simulation(macro_amorphous)/plot_6_extended_czjzek.py

@@ -43,8 +43,8 @@
 # The following is the plot of the extended Czjzek distribution.
 plt.figure(figsize=(4.25, 3.0))
 plt.contourf(z_dist, e_dist, amp, levels=10)
-plt.xlabel(r"$\zeta$ / ppm")
-plt.ylabel(r"$\eta$")
+plt.xlabel("$\\zeta$ / ppm")
+plt.ylabel("$\\eta$")
 plt.tight_layout()
 plt.show()
 
@@ -101,8 +101,8 @@
 # The following is the plot of the extended Czjzek distribution.
 plt.figure(figsize=(4.25, 3.0))
 plt.contourf(cq_dist, e_dist, amp, levels=10)
-plt.xlabel(r"$C_q$ / MHz")
-plt.ylabel(r"$\eta$")
+plt.xlabel("$C_q$ / MHz")
+plt.ylabel("$\\eta$")
 plt.tight_layout()
 plt.show()
 

examples_source/2D_simulation(crystalline)/plot_9a1_2D_separated_local_field.py

@@ -0,0 +1,231 @@
+"""
+¹H 2D separated local field powder spectra
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+2D Simulation of polycrystalline methyl formate.
+"""
+
+# %%
+# Equation (14) and (15) of the Linder et al. paper [#f1]_ are:
+#
+# .. math::
+#   \begin{align}
+#   \omega_1^{(1)}(\theta_r, \phi_r, \alpha, \beta) &= \omega_\text{cs}(\theta_r,\phi_r)
+#                         + \frac{1}{\sqrt{3}} \omega_D(\theta_r,\phi_r,\alpha,\beta)\\
+#   \omega_2^{(1)}(\theta_r, \phi_r, \alpha, \beta) &= \omega_\text{cs}(\theta_r,\phi_r)
+#                         - \frac{1}{\sqrt{3}} \omega_D(\theta_r,\phi_r,\alpha,\beta),
+#                         ~\text{and}\\
+#   \omega^{(2)}(\theta_r, \phi_r) &= \omega_\text{cs}(\theta_r,\phi_r)
+#   \end{align}
+#
+# where :math:`\theta_r` and :math:`\phi_r` are the polar coordinates in the principal
+# axis frame of the (asymmetric) nuclear shielding tensor, and :math:`\alpha`,
+# :math:`\beta` are the Euler angles required to orient the dipolar coupling tensor
+# in the nuclear shielding principal axis frame defined with the Mehring convention.
+# The scaling of the dipolar frequency contribution by :math:`1/\sqrt{3}` is due to
+# the use of off-resonance decoupling during the :math:`t_1` period
+# (see Fig. 1 of the paper).
+#
+# The spin interaction tensor values for the carbonyl carbon of methyl formate
+# (H-(C=O)-O-CH3) taken from the paper are :math:`\omega_d/(2 \pi) = 22,630` Hz and
+# :math:`{\sigma_{1} = -126.6}` ppm, :math:`{\sigma_{2} = -7.0}`  ppm, and
+# :math:`{\sigma_{3} = 25.4}`  ppm using the Mehring convention.  However, Mehring uses
+# the symbol :math:`\sigma_{i}` as the chemical shift values read off the spectrum.
+# So, these values should be labeled :math:`\delta_{i}`.
+#
+# Linder et al. use the term "chemical shielding" and the symbol sigma.  The 2D plot
+# dimensions are labeled as chemical shift.
+#
+
+# %%
+# In the Mehring convention, the principal components are ordered according to
+# :math:`\sigma_{1}' \le \sigma_{2}' \le \sigma_{3}'` where
+# :math:`\sigma_{i}' =\sigma_{i} -\sigma_{\text{iso}}^{\text{ref}}`.
+# The angle :math:`\beta` is defined relative to the axis associated with
+# :math:`\sigma_{3}'`.  However, in the Haberlen convention this direction corresponds
+# to the :math:`\lambda_{yy}` direction.  Therefore, we need to change the PAS angles
+# for mrsimulator, which are defined relative to the :math:`\lambda_{zz}` direction.
+#
+
+# %%
+import matplotlib.pyplot as plt
+import numpy as np
+
+from mrsimulator import Simulator, SpinSystem, Site, Coupling
+from mrsimulator.method import Method, SpectralDimension, SpectralEvent
+from mrsimulator import signal_processor as sp
+from mrsimulator.spin_system.tensors import SymmetricTensor
+import mrsimulator.utils.cartesian_tensor as ct
+
+# sphinx_gallery_thumbnail_number = 1
+
+# %%
+D = 22630 * 1 / np.sqrt(3)  # Hz
+
+delta_1 = -126.6  # ppm
+delta_2 = -7.0  # ppm
+delta_3 = 25.4  # ppm
+delta_iso = (delta_1 + delta_2 + delta_3) / 3
+
+mehring_eigenvalues = [-delta_1, -delta_2, -delta_3]  # in ppm
+mehring_euler_angles = [
+    (0, 0, 0),
+    (0, -45, 0),
+    (0, -90, 0),
+    (-90, -45, 0),
+    (-90, -90, 0),
+    (-60, -90, 0),
+]  # in degrees
+
+# Convert angles to radians
+mehring_euler_angles_rad = [
+    (np.radians(alpha), np.radians(beta), np.radians(gamma))
+    for alpha, beta, gamma in mehring_euler_angles
+]
+
+# Convert the tensor to Haeberlen parameters for each set of Euler angles
+haeberlen_euler_angles = []
+for euler_angle in mehring_euler_angles_rad:
+    tensor = ct.from_mehring_params(
+        euler_angles=euler_angle, eigenvalues=mehring_eigenvalues
+    )
+    euler_angles, zeta_sigma, eta_sigma, sigma_iso = ct.to_haeberlen_params(tensor)
+    haeberlen_euler_angles.append(euler_angles)
+
+
+# %%
+site1 = Site(
+    isotope="1H",
+    isotropic_chemical_shift=0,
+)
+
+# Create an empty list to store the spin_system objects
+spin_systems = []
+
+# Iterate through the list
+for angles in haeberlen_euler_angles:
+    alpha, beta, gamma = angles
+
+    site2 = Site(
+        isotope="13C",
+        isotropic_chemical_shift=delta_iso,  # in ppm
+        shielding_symmetric=SymmetricTensor(
+            zeta=zeta_sigma, eta=eta_sigma, alpha=alpha, beta=beta, gamma=gamma
+        ),
+    )
+
+    # Create a Coupling object for each set of Euler angles
+    coupling = Coupling(
+        site_index=[0, 1],
+        dipolar=SymmetricTensor(D=D),  # D in Hz
+    )
+
+    # Add the Coupling object to the list
+    spin_systems.append(SpinSystem(sites=[site1, site2], couplings=[coupling]))
+
+
+# %%
+slf = Method(
+    channels=["13C"],
+    magnetic_flux_density=2.4,  # in T
+    rotor_angle=0,
+    spectral_dimensions=[
+        SpectralDimension(
+            count=512,
+            spectral_width=3.5e4,  # in Hz
+            reference_offset=0,  # in Hz
+            label="Dipolar Coupling +\nChemical Shift",
+            events=[
+                SpectralEvent(
+                    transition_queries=[{"ch1": {"P": [-1]}}],
+                    freq_contrib=["Shielding1_0", "Shielding1_2", "D1_2"],
+                )
+            ],
+        ),
+        SpectralDimension(
+            count=512,
+            spectral_width=5e3,  # in Hz
+            reference_offset=-1e3,  # in Hz
+            label="Chemical Shift",
+            events=[
+                SpectralEvent(
+                    transition_queries=[{"ch1": {"P": [-1]}}],
+                    freq_contrib=["Shielding1_0", "Shielding1_2"],
+                )
+            ],
+        ),
+    ],
+)
+
+# %%
+# Iterate through the list
+simulations = []
+times = []
+for index, angles in enumerate(haeberlen_euler_angles):
+    sim = Simulator(spin_systems=[spin_systems[index]], methods=[slf])
+    sim.config.integration_volume = "hemisphere"
+    sim.run()
+
+    sim.methods[0].simulation.dimensions[1].to("kHz")
+    simulations.append(sim)
+
+# %%
+processor = sp.SignalProcessor(
+    operations=[
+        # Gaussian convolution along both dimensions.
+        sp.IFFT(dim_index=(0, 1)),
+        sp.apodization.Gaussian(FWHM="0.15 kHz", dim_index=0),
+        sp.apodization.Gaussian(FWHM="0.15 kHz", dim_index=1),
+        sp.FFT(dim_index=(0, 1)),
+    ]
+)
+processed_datasets = []
+for index, angles in enumerate(haeberlen_euler_angles):
+    processed_dataset = processor.apply_operations(
+        dataset=simulations[index].methods[0].simulation
+    )
+    processed_dataset /= processed_dataset.max()
+    processed_datasets.append(processed_dataset.real)
+
+# %%
+# First plot
+plt.figure(figsize=(4.25, 3.0))
+ax = plt.subplot(projection="csdm")
+cb = ax.imshow(
+    processed_datasets[0] / processed_datasets[0].max(),
+    aspect="auto",
+    cmap="gist_ncar_r",
+    interpolation="none",
+)
+plt.title(None)
+plt.colorbar(cb)
+plt.tight_layout()
+plt.show()
+
+# %%
+# All plots
+fig, axs = plt.subplots(
+    3, 2, figsize=(6, 7.5), subplot_kw={"projection": "csdm"}, tight_layout=True
+)
+
+index = 0
+for j in range(2):
+    for i in range(3):
+        ax = axs[i, j]
+        data = processed_datasets[index]
+        cb = ax.imshow(data, aspect="auto", cmap="gist_ncar_r")
+        # Get the corresponding Euler angles
+        alpha, beta, gamma = mehring_euler_angles[index]
+        # Set the title to include the Euler angles
+        ax.set_title(f"$\\alpha=$ {-alpha} °, $\\beta=$ {-beta} °")
+        index += 1
+
+# Create a new axes for the colorbar at the specific position
+cbar_ax = fig.add_axes([1, 0.07, 0.015, 0.23])
+fig.colorbar(cb, cax=cbar_ax)
+plt.show()
+
+# %%
+# .. [#f1] M. Linder, A. Höhener, and R. R. Ernst, Orientation of tensorial interactions
+#        determined from 2D NMR powder spectra, J. Chem. Phys. (1980)  **73**, 4959.
+#        `DOI: 10.1063/5.0061611 <https://doi.org/10.1063/1.439973>`_