##To begin, make sure you have loaded adapt, calibrator, emulator, and
##mvtnorm using the package manager.


x.training<-seq(0,1,0.1) 
dim(x.training) <- c(11,1)
f<-function(x) 
{
1
}

datagenerator<- function(x)
{
exp(-x)*sin((2*pi*x)) + x
}

y.training <- datagenerator(x.training)

##We plot the true function for illustrative purposes

x.pred<-seq(0,1,.01) 
plot(x.pred, datagenerator(x.pred),type="l", ylab="y(x)",col = "green", lwd=1.5)

## Note that the values of scales.start, lower, and upper below are the 
## values of the natural logarithms of the scale parameters.
## You can adjust the start , lower, and upper values to see what effect
## these have on the mle computed by scales.optim

scales.optim <- optimal.scales(val = x.training, scales.start = 10, d = y.training, method="L-BFGS-B", lower=1, upper=100, give=FALSE)

A <- corr.matrix(xold = x.training, scales = scales.optim)
Ainv <- solve(A)

x.pred <-seq(0,1,0.01) 
dim(x.pred)<-c(101,1)

newpreds <- interpolant.quick(x.pred, y.training, x.training, Ainv, scales = scales.optim, func = f, give.Z = TRUE, power = 2)

inputs <- x.pred
predictions <- newpreds$mstar.star
std.errs <- newpreds$Z

results <- data.frame(inputs, predictions, std.errs)

results

lines(inputs, predictions, type="l", lty = 4, col = "red", lwd=1.5)
lines(inputs, predictions + 2*std.errs, lty = 4, lwd=1.5)
lines(inputs, predictions - 2*std.errs, lty = 4, lwd=1.5)