N=500; # sample size for LHS  

# Create vector of sample values for each parameter 
# Here, all 3 params are taken as Uniform(-1,1)  
x=seq(from=-1,to=1,length=N+1); 
p=(x[-1]+x[-(N+1)])/2; 

## create P matrix 
## create P matrix 
P=rbind(p,p,p);   

## shuffle each of the rows 
P=t(apply(P,1,sample)); 

# Compute Y values for each column of P 
# In real applications, you would run your model N times 
f=function(p) {exp(p[1])+exp(2*p[2])+exp(3*p[3])} 
Y=apply(P,2,f); 

require(mgcv);
par1=P[1,]; par2=P[2,]; par3=P[3,];   

fit1=gam(Y~s(par1)+s(par2)+s(par3)); 
out1=predict(fit1,type="terms"); 
apply(out1,2,var)^0.5; 

# Compute different Y values for each column of P 
f=function(p) {exp(p[1])+exp(2*p[2])+exp(3*p[1]*p[3])} 
Y=apply(P,2,f); 

require(mgcv);
par1=P[1,]; par2=P[2,]; par3=P[3,];   

fit2=gam(Y~s(par1)+s(par2)+s(par3)); 
out2=predict(fit2,type="terms"); 
apply(out2,2,var)^0.5;