def autocorrelation_function(self, r):
"""compute the real space autocorrelation function for the Gaussian random field model
"""
# compute the cut-level parameter beta
beta = np.sqrt(2) * erfinv(2 * (1-self.frac_volume) - 1)
# the covariance of the GRF
acf_psi = (np.exp(-r/self.corr_length) * (1 + r / self.corr_length)
* np.sinc(2*r/self.repeat_distance))
# integral discretization. henning says: the resolution 1e-2 is ad hoc, test required,
# the integrand has a (integrable) singularity for t=1 and acf_psi = 1, so an adaptive
# discretization seems preferable -> TODO
dt = 1e-2
t = np.arange(0, 1, dt)
# the gridded integrand, via change of integration variable
# compared to the wp-2 docu, to enable array-based computation
t_gridded, acf_psi_gridded = np.meshgrid(t, acf_psi)
integrand_gridded = (acf_psi_gridded / np.sqrt(1 - (t_gridded * acf_psi_gridded)**2)
* np.exp( - beta**2 / (1 + t_gridded * acf_psi_gridded)))
acf = 1.0 / (2 * np.pi) * np.trapz(integrand_gridded, x=t_gridded)
return acf
# ft not known analytically: deligate
# def ft_autocorrelation_function(self, k):
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