doc added; reading of isochronal bds

doc/examples/distribution/README.rst

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+ .. _distribution_examples:
+
+.. _distribution-examples-index:
+
+Distribution of correlation times
+=================================

doc/examples/distribution/plot_ColeCole.py

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+"""
+=========
+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

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+"""
+=============
+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

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+"""
+================
+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

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+"""
+=========================
+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

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+"""
+============
+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()