###Use this file to generate results

################################################################################
#Set up parameters for the trials
################################################################################

#source the functions.R file 
source()

#Fixed parameters for the trials
alpha  <- 0.025
lambda <- 0.5
tau	 <- 0.5
info	 <- ((qnorm(1-0.025)+qnorm(0.9))/10)^2
delta  <- c(0,0)

#set sample size to be used in simulations
#n is when simulating trials
n <- 10^6
#m is when computing decision boundary
m <- 10^6

#parameters for displayed decision boundaries
#number of iterations you want
maxit0 <- 9
#number of iterations for decision rule computing Bayes optimal AE expected 
#performance
maxit <- 9

#Prior distribution to be investigated
mu	 <- c(12,4)
sigma  <- c(5,5)
rho <- 0.75

print(noquote(c("mu =",mu," sigma =",sigma," rho =",rho)))

################################################################################
##computing the gain of the fixed sample designs
################################################################################
#draw from the prior, note if you wish to find the gain at given  
#theta, change each to rep(theta,n)

theta1 <- rnorm(n,mu[1],sigma[1])
theta2 <- rnorm(n,mu[2]+(sigma[2]/sigma[1])*rho*(theta1-mu[1]),
                sqrt(1-rho^2)*sigma[2])

#compute the fixed sample gains as given by the parameters
outFS=FEgain(alpha,lambda,info,n,delta,theta1)
outFF=MHgain(alpha,lambda,info,n,delta,theta1,theta2)
print(c("outFS=",outFS))
print(c("outFF=",outFF))

################################################################################
##plotting a Bayes optimal decision
################################################################################

# note thetahat1 and thetahat2 determine the window this shall be computed over, 
# adjust these as necessary
thetahat1 <- c(qnorm(0.05,mu[1],
                     sigma[1]+sqrt(1/(lambda*tau*info))),
               qnorm(0.95,mu[1],
                     sigma[1]+sqrt(1/(lambda*tau*info)))) 
thetahat2 <- c(qnorm(0.05,mu[2],
                     sigma[2]+sqrt(1/((1-lambda)*tau*info))),
               qnorm(0.95,mu[2],
                     sigma[2]+sqrt(1/((1-lambda)*tau*info))))

#repackage the prior and related information
prior.v=array(0,c(2,2))
prior.v[1,1]=sigma[1]^2
prior.v[2,2]=sigma[2]^2
prior.v[1,2]=rho*sigma[1]*sigma[2]
prior.v[2,1]=prior.v[1,2]
var.that=array(0,c(2,2))
var.that[1,1]=1/(lambda*tau*info)
var.that[2,2]=1/((1-lambda)*tau*info)
prior.v.inv=solve(prior.v)
var.that.inv=solve(var.that)
postr.v=solve(prior.v.inv+var.that.inv)
a=postr.v%*%prior.v.inv%*%mu
b=postr.v%*%var.that.inv
c=postr.v


#parameters for the optimisation
dparm <- list(mu,sigma,rho,a,b,c)

#create the decision grid object, called pictab
#set pctd to a positive value to show region within which decisions are within 
#pctd%
pctd <- 0.05
pictab <- cgrid(thetahat1,thetahat2,maxit,pctd,alpha, 
                lambda,tau,info,m,delta,vbayesopt,dparm)

#plot the decision object 
plotdecis(pictab)
leg1 <- c(-10:10)*5
leg2 <- c(-10:10)*5
#add points for legend of decision
leg  <- expand.grid(leg1,leg2)
leg1 <- leg[,1]
leg2 <- leg[,2]
addleg(leg1,leg2,alpha,lambda,tau,info,delta,m,pictab)

################################################################################
##computing expected performance of the Bayes optimal AE trial
################################################################################

# window to create look up table for actual trial create the intial grid by 
# choosing the extreme values, note that the decisions must differ at these 
# points for the algorithm to work
thetahat1 <- c(qnorm(0.0001,mu[1],
                     sigma[1]+sqrt(1/(lambda*tau*info))),
               qnorm(0.9999,mu[1],
                     sigma[1]+sqrt(1/(lambda*tau*info)))) 
thetahat2 <- c(qnorm(0.0001,mu[2],
                     sigma[2]+sqrt(1/((1-lambda)*tau*info))),
               qnorm(0.9999,mu[2],
                     sigma[2]+sqrt(1/((1-lambda)*tau*info))))

#no pctd required here 
pctd <- 0
#create the decision object
decistab <- cgrid(thetahat1,thetahat2,maxit,pctd,alpha,
                  lambda,tau,info,m,delta,vbayesopt,dparm)
##note you may wish to plot this to confirm it has worked as intended

#simulate theta from the prior distribution 
theta1 <- rnorm(n,mu[1],sigma[1])
theta2 <- rnorm(n,mu[2]+(sigma[2]/sigma[1])*rho*(theta1-mu[1]),
                sqrt(1-rho^2)*sigma[2])

#find the expected gain of the Bayes optimal decision
outAE=simAE(alpha,lambda,tau,info,n,delta,theta1,theta2,vdgrid,decistab)
print(c("outAE=",outAE))

################################################################################
##Ouput results in tidy format
################################################################################

prej1=outAE[1]      # Reject H01 only
prej3=outAE[2]      # Reject H03 only
prejb=outAE[3]      # Reject both H01 and H03
prej3b=prej3+prejb  # Reject H03 (with or without H01)
probe=outAE[4]      # P(Enrich)
egain=outAE[5]      # E(gain)

printout=array(" ",c(4,10))
printout[1,]=c("mu1  ","mu2  ","s1   ","s2   ","rho  ",
               "Des  ","P(R1)","P(R3)","P(En)",
               "E(G) ")
printout[2,1]=as.character(mu[1])
printout[2,2]=as.character(mu[2])
printout[2,3]=as.character(sigma[1])
printout[2,4]=as.character(sigma[2])
printout[2,5]=as.character(rho)
printout[2,6]="FS"
printout[2,7]=as.character(round(outFS[[1]]*100)/100)
printout[2,8]="-"
printout[2,9]="-"
printout[2,10]=as.character(round(outFS[[2]]*100)/100)
printout[3,6]="FF"
printout[3,7]=as.character(round(outFF[[1]][1]*100)/100)
printout[3,8]=as.character(round((outFF[[1]][2]+outFF[[1]][3])*100)/100)
printout[3,9]="-"
printout[3,10]=as.character(round(outFF[[2]]*100)/100)
printout[4,6]="AE"
printout[4,7]=as.character(round(prej1*100)/100)
printout[4,8]=as.character(round(prej3b*100)/100)
printout[4,9]=as.character(round(probe*100)/100)
printout[4,10]=as.character(round(egain*100)/100)
print(printout,quote=FALSE)