Simple kriging assumes a known mean of the data. For simplicity we assume a mean of 0, which can be achieved by subtracting the mean from the observed values and subsequently adding it to the resulting data.
The resulting equation system for is given by:
Thereby is the covariance of the given observations.
Here we use simple kriging in 1D (for plotting reasons) with 5 given observations/conditions. The mean of the field has to be given beforehand.
import numpy as np from gstools import Gaussian, krige # condtions cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7] cond_val = [0.47, 0.56, 0.74, 1.47, 1.74] # resulting grid gridx = np.linspace(0.0, 15.0, 151) # spatial random field class model = Gaussian(dim=1, var=0.5, len_scale=2)
krig = krige.Simple(model, mean=1, cond_pos=cond_pos, cond_val=cond_val) krig(gridx)
Total running time of the script: ( 0 minutes 0.121 seconds)