85 lines
2.6 KiB
Python
85 lines
2.6 KiB
Python
"""
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================================
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Example of apodization functions
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================================
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This file
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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from nmreval.distributions import ColeDavidson
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from nmreval.nmr import Relaxation, RelaxationEvaluation
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from nmreval.nmr.coupling import Quadrupolar
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from nmreval.utils.constants import kB
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# Define temperature range
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inv_temp = np.linspace(3, 9, num=30)
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temperature = 1000/inv_temp
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# spectral density parameter
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ea = 0.45
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tau = 1e-21 * np.exp(ea / kB / temperature)
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gamma_cd = 0.4
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# interaction parameter
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omega = 2*np.pi*46e6
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delta = 120e3
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eta = 0
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r = Relaxation()
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r.set_distribution(ColeDavidson) # the only parameter that set beforehand
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t1_values = r.t1(omega, tau, gamma_cd, mode='bpp',
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prefactor=Quadrupolar.relax(delta, eta))
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# add noise
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rng = np.random.default_rng()
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noisy = (rng.random(t1_values.size)-0.5) * 0.5 * t1_values + t1_values
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ax_t1 = plt.figure().add_subplot()
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ax_t1.semilogy(inv_temp, t1_values, label='Calculated T1')
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ax_t1.semilogy(inv_temp, noisy, 'o', label='Noise')
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ax_t1.legend()
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plt.show()
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# Actual evaluation starts here
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# setting necessary parameter
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r_eval = RelaxationEvaluation()
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r_eval.set_distribution(ColeDavidson)
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r_eval.set_coupling(Quadrupolar, (delta, eta))
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r_eval.set_data(temperature, noisy)
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r_eval.omega = omega
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# Find a T1 minumum
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t1_min_data, _ = r_eval.calculate_t1_min() # second argument is None
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t1_min_inter, line = r_eval.calculate_t1_min(interpolate=1, trange=(160, 195), use_log=True)
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ax_min = plt.figure().add_subplot()
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ax_min.semilogy(inv_temp, noisy, 'o', label='Data')
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ax_min.semilogy(1000/line[0], line[1], '--')
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ax_min.semilogy(1000/t1_min_data[0], t1_min_data[1], 'C2X',label='Data minimum')
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ax_min.semilogy(1000/t1_min_inter[0], t1_min_inter[1], 'C3P',label='Parabola')
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ax_min.set_xlim(4.5, 7)
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ax_min.set_ylim(1e-3, 1e-1)
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ax_min.legend()
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# Vary the first (and for Cole-Davidson, only) parameter of the spectral density
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found_gamma, found_height = r_eval.get_increase(t1_min_inter[1], idx=0, mode='distribution')
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print(f'Minimum at {found_height} for {found_gamma}; input is {gamma_cd}')
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plt.show()
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##################################################################################
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# Calculation of correlation times uses previously parameter for spectral density
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# and prefactor
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tau_from_t1, opts = r_eval.correlation_from_t1(mode='mean')
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print(f'Used options: {opts}')
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ax_tau = plt.figure().add_subplot()
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ax_tau.semilogy(inv_temp, tau*gamma_cd, label='Original input')
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ax_tau.semilogy(1000/tau_from_t1[:, 0], tau_from_t1[:, 1], 'o', label='Calculated')
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ax_tau.legend()
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plt.show()
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