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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Sketches for automating spatial models
This notebook is for designing the tool box and methods for fitting spatial data.
I´m using the library Geopystats (before spystats)
Requirements
Given a dataset in Geopandas dataframe, create the Variogram object.
And read from the file the variogram data
Step1:  The object new_data has been reprojected to Alberts and a linear model have been fitted with residuals stored as residuals
Step2:  The empirical variogram
The empirical variogram has been calculated already using the HEC. A variogram object has been created which takes the values from the previously calculated in HEC
Step3:  Bonus!
Fitting the model to the empirical variogram
It´s included as a method in the VariogramModel class.
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Python Code:
from external_plugins.spystats import tools
%run ../HEC_runs/fit_fia_logbiomass_logspp_GLS.py
from external_plugins.spystats import tools
hx = np.linspace(0,800000,100)
Explanation: Sketches for automating spatial models
This notebook is for designing the tool box and methods for fitting spatial data.
I´m using the library Geopystats (before spystats)
Requirements
Given a dataset in Geopandas dataframe, create the Variogram object.
And read from the file the variogram data
End of explanation
new_data.residuals[:10]
Explanation: The object new_data has been reprojected to Alberts and a linear model have been fitted with residuals stored as residuals
End of explanation
gvg.plot(refresh=False,legend=False,percentage_trunked=20)
plt.title("Semivariogram of residuals $log(Biomass) ~ log(SppR)$")
## HERE we can cast a model (Whittle) and fit it inside the global variogram
whittle_model = tools.WhittleVariogram(sill=0.345,range_a=100000,nugget=0.33,alpha=1.0)
tt = gvg.fitVariogramModel(whittle_model)
plt.plot(hx,gvg.model.f(hx),'--',lw=4,c='black')
print(whittle_model)
## This section is an example for calculating GLS. Using a small section because of computing intensity
minx = -85
maxx = -80
miny = 30
maxy = 35
section = tools._subselectDataFrameByCoordinates(new_data,'LON','LAT',minx,maxx,miny,maxy)
secvg = tools.Variogram(section,'logBiomass',model=whittle_model)
MMdist = secvg.distance_coordinates.flatten()
CovMat = secvg.model.corr_f(MMdist).reshape(len(section),len(section))
plt.imshow(CovMat)
import statsmodels.regression.linear_model as lm
import statsmodels.api as sm
model1 = results_gls.from_formula(formula='logBiomass ~ logSppN',data=section,sigma=CovMat)
results = model1.fit()
results.summary()
## Without spatial structure
Id = np.identity(len(section))
model2 = results_gls.from_formula(formula='logBiomass ~ logSppN',data=section,sigma=Id)
results = model2.fit()
results.summary()
Explanation: The empirical variogram
The empirical variogram has been calculated already using the HEC. A variogram object has been created which takes the values from the previously calculated in HEC
End of explanation
matm = tools.MaternVariogram(sill=0.34,range_a=100000,nugget=0.33,kappa=0.5)
expmm = tools.ExponentialVariogram(sill=0.34,range_a=100000,nugget=0.33)
gausms = tools.GaussianVariogram(sill=0.34,range_a=100000,nugget=0.33)
sphmm = tools.SphericalVariogram(sill=0.34,range_a=100000,nugget=0.33)
wm = tools.WhittleVariogram(sill=0.34,range_a=100000,nugget=0.33,alpha=1)
map(lambda l : l.fit(gvg), [matm,expmm,gausms,sphmm,wm])
print(matm)
print(expmm)
print(gausms)
print(sphmm)
print(wm)
Explanation: Bonus!
Fitting the model to the empirical variogram
It´s included as a method in the VariogramModel class.
End of explanation
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