Note
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Spectral methods¶
The spectrum of a covariance model is given by:
Since the covariance function is radially symmetric, we can calculate this by the hankel-transformation:
Where .
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)
Note
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.spectral_rad_pdf
or CovModel.ln_spectral_rad_pdf
for the logarithm.
The user can also provide a cdf (cumulative distribution function) by
defining a method called spectral_rad_cdf
and/or a ppf (percent-point function)
by spectral_rad_ppf
.
The attributes CovModel.has_cdf
and CovModel.has_ppf
will check for that.
Total running time of the script: ( 0 minutes 0.094 seconds)