The spectrum of a covariance model is given by:
Since the covariance function is radially symmetric, we can calculate this by the hankel-transformation:
Depending on the spectrum, the spectral-density is defined by:
You can access these methods by:
import gstools as gs model = gs.Gaussian(dim=3, var=2.0, len_scale=10) ax = model.plot("spectrum") model.plot("spectral_density", ax=ax)
The spectral-density is given by the radius of the input phase. But it is
not a probability density function for the radius of the phase.
To obtain the pdf for the phase-radius, you can use the methods
CovModel.ln_spectral_rad_pdf for the logarithm.
The user can also provide a cdf (cumulative distribution function) by
defining a method called
and/or a ppf (percent-point function)
Total running time of the script: ( 0 minutes 0.115 seconds)