doc added; reading of isochronal bds

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()