# creating the coregionalization model with three gaussian functions
linear_model_co_region<-function(ranges,rhos,shifts){
rho1a12 = gaussian_cov(ranges[1],shifts[1])
rho1a13 = gaussian_cov(ranges[1],shifts[3])
rho1a1213 = gaussian_cov(ranges[1],abs(shifts[1]-shifts[3]))
rho2a23 = gaussian_cov(ranges[2],shifts[2])
lambda12= rhos[1]/rho1a12
lambda13= rhos[3]/rho1a13
lambda23 = rhos[2]-lambda13 * lambda12 *rho1a1213
lambda23 =lambda23 / (sqrt(1-lambda12^2)*rho2a23)
return(lambda12,lambda23,lambda23)
}
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