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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:
 Spatial Model fitting in GLS
In this exercise we will fit a linear model using a Spatial structure as covariance matrix. 
We will use GLS to get better estimators.
As always we will need to load the necessary libraries.
Step1:  Use this to automate the process. Be carefull it can overwrite current results
run ../HEC_runs/fit_fia_logbiomass_logspp_GLS.py /RawDataCSV/idiv_share/plotsClimateData_11092017.csv /apps/external_plugins/spystats/HEC_runs/results/logbiomas_logsppn_res.csv -85 -80 30 35
Importing data
We will use the FIA dataset and for exemplary purposes we will take a subsample of this data. 
Also important.
The empirical variogram has been calculated for the entire data set using the residuals of an OLS model. 
We will use some auxiliary functions defined in the fit_fia_logbiomass_logspp_GLS.
You can inspect the functions using the ?? symbol.
Step2:  Now we will obtain the data from the calculated empirical variogram.
Step3:  Instantiating the variogram object
Step4:  Instantiating theoretical variogram model
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Python Code:
ls
# Load Biospytial modules and etc.
%matplotlib inline
import sys
sys.path.append('/apps/external_plugins/spystats/spystats/')
sys.path.append('..')
import django
django.setup()
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
## Use the ggplot style
plt.style.use('ggplot')
import tools
Explanation: Spatial Model fitting in GLS
In this exercise we will fit a linear model using a Spatial structure as covariance matrix. 
We will use GLS to get better estimators.
As always we will need to load the necessary libraries.
End of explanation
from HEC_runs.fit_fia_logbiomass_logspp_GLS import prepareDataFrame,loadVariogramFromData,buildSpatialStructure, calculateGLS, initAnalysis, fitGLSRobust
section = initAnalysis("/RawDataCSV/idiv_share/FIA_Plots_Biomass_11092017.csv",
                        "/apps/external_plugins/spystats/HEC_runs/results/variogram/data_envelope.csv",-130,-60,30,40)
#section = initAnalysis("/RawDataCSV/idiv_share/plotsClimateData_11092017.csv",
#                        "/apps/external_plugins/spystats/HEC_runs/results/variogram/data_envelope.csv",
#                       -85,-80,30,35)
# IN HEC
#section = initAnalysis("/home/hpc/28/escamill/csv_data/idiv/FIA_Plots_Biomass_11092017.csv","/home/hpc/28/escamill/spystats/HEC_runs/results/variogram/data_envelope.csv",-85,-80,30,35)
Explanation: Use this to automate the process. Be carefull it can overwrite current results
run ../HEC_runs/fit_fia_logbiomass_logspp_GLS.py /RawDataCSV/idiv_share/plotsClimateData_11092017.csv /apps/external_plugins/spystats/HEC_runs/results/logbiomas_logsppn_res.csv -85 -80 30 35
Importing data
We will use the FIA dataset and for exemplary purposes we will take a subsample of this data. 
Also important.
The empirical variogram has been calculated for the entire data set using the residuals of an OLS model. 
We will use some auxiliary functions defined in the fit_fia_logbiomass_logspp_GLS.
You can inspect the functions using the ?? symbol.
End of explanation
gvg,tt = loadVariogramFromData("/apps/external_plugins/spystats/HEC_runs/results/variogram/data_envelope.csv",section)
gvg.plot(refresh=False,with_envelope=True)
resum,gvgn,resultspd,results = fitGLSRobust(section,gvg,num_iterations=50,distance_threshold=1000000)
variogram_data_path = "/apps/external_plugins/spystats/HEC_runs/results/variogram/data_envelope.csv"
thrs_dist = 100000
emp_var_log_log = pd.read_csv(variogram_data_path)
Explanation: Now we will obtain the data from the calculated empirical variogram.
End of explanation
gvg = tools.Variogram(section,'logBiomass',using_distance_threshold=thrs_dist)
gvg.envelope = emp_var_log_log
gvg.empirical = emp_var_log_log.variogram
gvg.lags = emp_var_log_log.lags
#emp_var_log_log = emp_var_log_log.dropna()
#vdata = gvg.envelope.dropna()
Explanation: Instantiating the variogram object
End of explanation
matern_model = tools.MaternVariogram(sill=0.34,range_a=100000,nugget=0.33,kappa=4)
whittle_model = tools.WhittleVariogram(sill=0.34,range_a=100000,nugget=0.0,alpha=3)
exp_model = tools.ExponentialVariogram(sill=0.34,range_a=100000,nugget=0.33)
gaussian_model = tools.GaussianVariogram(sill=0.34,range_a=100000,nugget=0.33)
spherical_model = tools.SphericalVariogram(sill=0.34,range_a=100000,nugget=0.33)
gvg.model = whittle_model
#gvg.model = matern_model
#models = map(lambda model : gvg.fitVariogramModel(model),[matern_model,whittle_model,exp_model,gaussian_model,spherical_model])
gvg.fitVariogramModel(whittle_model)
import numpy as np
xx = np.linspace(0,1000000,1000)
gvg.plot(refresh=False,with_envelope=True)
plt.plot(xx,whittle_model.f(xx),lw=2.0,c='k')
plt.title("Empirical Variogram with fitted Whittle Model")
def randomSelection(n,p):
    idxs = np.random.choice(n,p,replace=False)
    random_sample = new_data.iloc[idxs]
    return random_sample
#################
n = len(new_data)
p = 3000 # The amount of samples taken (let's do it without replacement)
random_sample = randomSelection(n,100)
Explanation: Instantiating theoretical variogram model
End of explanation
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