doc added; reading of isochronal bds

doc/examples/README.rst

@@ -0,0 +1,9 @@
+.. examples-index:
+
+.. _gallery:
+
+========
+Examples
+========
+
+This page contains example plots. Click on any image to see the full image and source code.

doc/examples/distribution/README.rst

@@ -0,0 +1,6 @@
+ .. _distribution_examples:
+
+.. _distribution-examples-index:
+
+Distribution of correlation times
+=================================

doc/examples/distribution/plot_ColeCole.py

@@ -0,0 +1,50 @@
+"""
+=========
+Cole-Cole
+=========
+
+Example for Cole-Cole distributions
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+
+from nmreval.distributions import ColeCole
+
+x = np.logspace(-5, 5, num=101)
+
+cc = ColeCole
+
+alpha_CC = [0.3, 0.5, 0.7]
+
+fig, axes = plt.subplots(2, 3, constrained_layout=True)
+
+lines = []
+for a in alpha_CC:
+    axes[0, 0].plot(np.log10(x), cc.correlation(x, 1, a))
+    axes[1, 0].plot(np.log10(x), np.log10(cc.specdens(x, 1, a)))
+    axes[0, 1].plot(np.log10(x), np.log10(cc.susceptibility(x, 1, a).real))
+    axes[1, 1].plot(np.log10(x), np.log10(cc.susceptibility(x, 1, a).imag))
+    l, = axes[0, 2].plot(np.log10(x), cc.distribution(x, 1, a),
+                         label=rf'$\alpha={a}$')
+    lines.append(l)
+
+fig_titles = ('Correlation function', 'Susceptibility (real)', 'Distribution',
+              'Spectral density', 'Susceptibility (imag)')
+fig_xlabel = (r'$\log(t/\tau_\mathrm{HN})$', r'$\log(\omega\tau_\mathrm{HN})$',
+              r'$\log(\tau/\tau_\mathrm{HN})$', r'$\log(\omega\tau_\mathrm{HN})$',
+              r'$\log(\omega\tau_\mathrm{HN})$')
+fig_ylabel = (r'$C(t)$', r"$\log(\chi'(\omega))$", r'$G(\ln\tau)$',
+              r'$\log(J(\omega))$', r"$\log(\chi''(\omega))$")
+
+for title, xlabel, ylabel, ax in zip(fig_titles, fig_xlabel, fig_ylabel, axes.ravel()):
+    ax.set_title(title)
+    ax.set_xlabel(xlabel)
+    ax.set_ylabel(ylabel)
+
+labels = [l.get_label() for l in lines]
+leg = fig.legend(lines, labels, loc='center left', bbox_to_anchor=(1.05, 0.50),
+                 bbox_transform=axes[1, 1].transAxes)
+
+fig.delaxes(axes[1, 2])
+
+plt.show()

doc/examples/distribution/plot_ColeDavidson.py

@@ -0,0 +1,50 @@
+"""
+=============
+Cole-Davidson
+=============
+
+Example for Cole-Davidson distributions
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+
+from nmreval.distributions import ColeDavidson
+
+x = np.logspace(-5, 5, num=101)
+
+cd = ColeDavidson
+
+gamma_CD = [0.3, 0.5, 0.7]
+
+fig, axes = plt.subplots(2, 3, constrained_layout=True)
+
+lines = []
+for g in gamma_CD:
+    axes[0, 0].plot(np.log10(x), cd.correlation(x, 1, g))
+    axes[1, 0].plot(np.log10(x), np.log10(cd.specdens(x, 1, g)))
+    axes[0, 1].plot(np.log10(x), np.log10(cd.susceptibility(x, 1, g).real))
+    axes[1, 1].plot(np.log10(x), np.log10(cd.susceptibility(x, 1, g).imag))
+    l, = axes[0, 2].plot(np.log10(x), cd.distribution(x, 1, g),
+                         label=rf'$\gamma={g}$')
+    lines.append(l)
+
+fig_titles = ('Correlation function', 'Susceptibility (real)', 'Distribution',
+              'Spectral density', 'Susceptibility (imag)')
+fig_xlabel = (r'$\log(t/\tau_\mathrm{CD})$', r'$\log(\omega\tau_\mathrm{CD})$',
+              r'$\log(\tau/\tau_\mathrm{CD})$', r'$\log(\omega\tau_\mathrm{CD})$',
+              r'$\log(\omega\tau_\mathrm{CD})$')
+fig_ylabel = (r'$C(t)$', r"$\log(\chi'(\omega))$", r'$G(\ln\tau)$',
+              r'$\log(J(\omega))$', r"$\log(\chi''(\omega))$")
+
+for title, xlabel, ylabel, ax in zip(fig_titles, fig_xlabel, fig_ylabel, axes.ravel()):
+    ax.set_title(title)
+    ax.set_xlabel(xlabel)
+    ax.set_ylabel(ylabel)
+
+labels = [l.get_label() for l in lines]
+leg = fig.legend(lines, labels, loc='center left', bbox_to_anchor=(1.05, 0.50),
+                 bbox_transform=axes[1, 1].transAxes)
+
+fig.delaxes(axes[1, 2])
+
+plt.show()

doc/examples/distribution/plot_HavriliakNegami.py

@@ -0,0 +1,53 @@
+"""
+================
+Havriliak-Negami
+================
+
+Example for Havriliak-Negami distributions
+"""
+from itertools import product
+
+import matplotlib.pyplot as plt
+import numpy as np
+
+from nmreval.distributions import HavriliakNegami
+
+x = np.logspace(-5, 5, num=101)
+
+hn = HavriliakNegami
+
+alpha_CC = [0.4, 0.8]
+gamma_CD = [0.3, 0.7]
+
+fig, axes = plt.subplots(2, 3, constrained_layout=True)
+
+lines = []
+for a, g in product(alpha_CC, gamma_CD):
+    axes[0, 0].plot(np.log10(x), hn.correlation(x, 1, a, g))
+    axes[1, 0].plot(np.log10(x), np.log10(hn.specdens(x, 1, a, g)))
+    axes[0, 1].plot(np.log10(x), np.log10(hn.susceptibility(x, 1, a, g).real))
+    axes[1, 1].plot(np.log10(x), np.log10(hn.susceptibility(x, 1, a, g).imag))
+    l, = axes[0, 2].plot(np.log10(x), hn.distribution(x, 1, a, g),
+                         label=rf'$\alpha={a}, \gamma={g}$')
+    lines.append(l)
+
+fig_titles = ('Correlation function', 'Susceptibility (real)', 'Distribution',
+              'Spectral density', 'Susceptibility (imag)')
+fig_xlabel = (r'$\log(t/\tau_\mathrm{HN})$', r'$\log(\omega\tau_\mathrm{HN})$',
+              r'$\log(\tau/\tau_\mathrm{HN})$', r'$\log(\omega\tau_\mathrm{HN})$',
+              r'$\log(\omega\tau_\mathrm{HN})$')
+fig_ylabel = (r'$C(t)$', r"$\log(\chi'(\omega))$", r'$G(\ln\tau)$',
+              r'$\log(J(\omega))$', r"$\log(\chi''(\omega))$")
+
+for title, xlabel, ylabel, ax in zip(fig_titles, fig_xlabel, fig_ylabel, axes.ravel()):
+    ax.set_title(title)
+    ax.set_xlabel(xlabel)
+    ax.set_ylabel(ylabel)
+
+labels = [l.get_label() for l in lines]
+leg = fig.legend(lines, labels, loc='center left', bbox_to_anchor=(1.05, 0.50),
+                 bbox_transform=axes[1, 1].transAxes)
+
+fig.delaxes(axes[1, 2])
+
+plt.show()

doc/examples/distribution/plot_KWW.py

@@ -0,0 +1,50 @@
+"""
+=========================
+Kohlrausch-Williams-Watts
+=========================
+
+Example for KWW distributions
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+
+from nmreval.distributions import KWW
+
+x = np.logspace(-5, 5, num=101)
+
+kww = KWW
+
+beta_KWW = [0.3, 0.5, 0.7]
+
+fig, axes = plt.subplots(2, 3, constrained_layout=True)
+
+lines = []
+for b in beta_KWW:
+    axes[0, 0].plot(np.log10(x), kww.correlation(x, 1, b))
+    axes[1, 0].plot(np.log10(x), np.log10(kww.specdens(x, 1, b)))
+    axes[0, 1].plot(np.log10(x), np.log10(kww.susceptibility(x, 1, b).real))
+    axes[1, 1].plot(np.log10(x), np.log10(kww.susceptibility(x, 1, b).imag))
+    l, = axes[0, 2].plot(np.log10(x), kww.distribution(x, 1, b),
+                         label=rf'$\beta={b}$')
+    lines.append(l)
+
+fig_titles = ('Correlation function', 'Susceptibility (real)', 'Distribution',
+              'Spectral density', 'Susceptibility (imag)')
+fig_xlabel = (r'$\log(t/\tau_\mathrm{KWW})$', r'$\log(\omega\tau_\mathrm{KWW})$',
+              r'$\log(\tau/\tau_\mathrm{KWW})$', r'$\log(\omega\tau_\mathrm{KWW})$',
+              r'$\log(\omega\tau_\mathrm{KWW})$')
+fig_ylabel = (r'$C(t)$', r"$\log(\chi'(\omega))$", r'$G(\ln\tau)$',
+              r'$\log(J(\omega))$', r"$\log(\chi''(\omega))$")
+
+for title, xlabel, ylabel, ax in zip(fig_titles, fig_xlabel, fig_ylabel, axes.ravel()):
+    ax.set_title(title)
+    ax.set_xlabel(xlabel)
+    ax.set_ylabel(ylabel)
+
+labels = [l.get_label() for l in lines]
+leg = fig.legend(lines, labels, loc='center left', bbox_to_anchor=(1.05, 0.50),
+                 bbox_transform=axes[1, 1].transAxes)
+
+fig.delaxes(axes[1, 2])
+
+plt.show()

doc/examples/distribution/plot_LogGaussian.py

@@ -0,0 +1,50 @@
+"""
+============
+Log-Gaussian
+============
+
+Example for Log-Gaussian distributions
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+
+from nmreval.distributions import LogGaussian
+
+x = np.logspace(-5, 5, num=101)
+
+lg = LogGaussian
+
+sigma_lg = [1, 3, 5]
+
+fig, axes = plt.subplots(2, 3, constrained_layout=True)
+
+lines = []
+for s in sigma_lg:
+    axes[0, 0].plot(np.log10(x), lg.correlation(x, 1, s))
+    axes[1, 0].plot(np.log10(x), np.log10(lg.specdens(x, 1, s)))
+    axes[0, 1].plot(np.log10(x), np.log10(lg.susceptibility(x, 1, s).real))
+    axes[1, 1].plot(np.log10(x), np.log10(lg.susceptibility(x, 1, s).imag))
+    l, = axes[0, 2].plot(np.log10(x), lg.distribution(x, 1, s),
+                         label=rf'$\sigma={s}$')
+    lines.append(l)
+
+fig_titles = ('Correlation function', 'Susceptibility (real)', 'Distribution',
+              'Spectral density', 'Susceptibility (imag)')
+fig_xlabel = (r'$\log(t/\tau_\mathrm{LG})$', r'$\log(\omega\tau_\mathrm{LG})$',
+              r'$\log(\tau/\tau_\mathrm{LG})$', r'$\log(\omega\tau_\mathrm{LG})$',
+              r'$\log(\omega\tau_\mathrm{LG})$')
+fig_ylabel = (r'$C(t)$', r"$\log(\chi'(\omega))$", r'$G(\ln\tau)$',
+              r'$\log(J(\omega))$', r"$\log(\chi''(\omega))$")
+
+for title, xlabel, ylabel, ax in zip(fig_titles, fig_xlabel, fig_ylabel, axes.ravel()):
+    ax.set_title(title)
+    ax.set_xlabel(xlabel)
+    ax.set_ylabel(ylabel)
+
+labels = [l.get_label() for l in lines]
+leg = fig.legend(lines, labels, loc='center left', bbox_to_anchor=(1.05, 0.50),
+                 bbox_transform=axes[1, 1].transAxes)
+
+fig.delaxes(axes[1, 2])
+
+plt.show()

doc/examples/nmr/README.rst

@@ -0,0 +1,6 @@
+.. _nmr_examples:
+
+.. _nmr-examples-index:
+
+NMR specifics
+=============

doc/examples/nmr/plot_RelaxationEvaluation.py

@@ -0,0 +1,67 @@
+"""
+=======================
+Spin-lattice relaxation
+=======================
+
+Example for
+"""
+import numpy as np
+from matplotlib import pyplot as plt
+
+from nmreval.distributions import ColeDavidson
+from nmreval.nmr import Relaxation, RelaxationEvaluation
+from nmreval.nmr.coupling import Quadrupolar
+from nmreval.utils.constants import kB
+
+# Define temperature range
+inv_temp = np.linspace(3, 9, num=30)
+temperature = 1000/inv_temp
+
+# spectral density parameter
+ea = 0.45
+tau = 1e-21 * np.exp(ea / kB / temperature)
+gamma_cd = 0.1
+
+# interaction parameter
+omega = 2*np.pi*46e6
+delta = 120e3
+eta = 0
+
+r = Relaxation()
+r.set_distribution(ColeDavidson)  # the only parameter that has to be set beforehand
+
+t1_values = r.t1(omega, tau, gamma_cd, mode='bpp',
+                 prefactor=Quadrupolar.relax(delta, eta))
+# add noise
+rng = np.random.default_rng(123456789)
+noisy = (rng.random(t1_values.size)-0.5) * 0.5 * t1_values + t1_values
+
+# set parameter and data
+r_eval = RelaxationEvaluation()
+r_eval.set_distribution(ColeDavidson)
+r_eval.set_coupling(Quadrupolar, (delta, eta))
+r_eval.data(temperature, noisy)
+r_eval.omega = omega
+
+t1_min_data, _ = r_eval.calculate_t1_min()  # second argument is None
+t1_min_inter, line = r_eval.calculate_t1_min(interpolate=1, trange=(160, 195), use_log=True)
+
+fig, ax = plt.subplots()
+ax.semilogy(1000/t1_min_data[0], t1_min_data[1], 'rx', label='Data minimum')
+ax.semilogy(1000/t1_min_inter[0], t1_min_inter[1], 'r+', label='Parabola')
+ax.semilogy(1000/line[0], line[1])
+
+found_gamma, found_height = r_eval.get_increase(t1_min_inter[1], idx=0, mode='distribution')
+print(found_gamma)
+
+plt.axhline(found_height)
+plt.show()
+
+#%%
+# Now we found temperature and height of the minimum we can calculate the correlation time
+
+plt.semilogy(1000/temperature, tau)
+tau_from_t1, opts = r_eval.correlation_from_t1()
+print(opts)
+plt.semilogy(1000/tau_from_t1[:, 0], tau_from_t1[:, 1], 'o')
+plt.show()