#Dennis Moskov, Master Thesis
#Split by unique articles and CV
#RT for prediction
#reduced model
#conversion, selectivity and yield
#using "rpart" package

#install.packages("rpart")
#library(rpart)

#packages for fancy plot
#fancy tree plot
#install.packages("rattle")
#install.packages("rpart.plot")
#library(rattle)
#library(rpart.plot)

#use database with article number

#randomly shuffle the data
set.seed(77)                      # seed for reproducibility
DBt<-DB[sample(nrow(DB)),]

#initiate possible results
results<-rbind(c("Conversion","Selectivity","Yield"),c("X.MeOH","S.MeOH","Y.MeOH"),c(length(DBt)-2,length(DBt)-1,length(DBt)))


#loop through different outcomes
for (r in 1:3) {

#use desired outcome
useDB<-DBt[-c(as.numeric(results[3,-r]))]


#initiate results lists
res<-list()
res.names<-c("number","fold","predicted","observed","residuals","residuals_squared")
resreg<-list()
resreg.names<-c("predicted","observed","residuals","residuals_squared")

Anova<-list()
summ<-list()
redVar<-list()

#divide data by article number
ref.num.CV <- unique(useDB[,1])

#choose number of folds
k <- 5	

#build folds with unique article numbers
for(j in 1:k){
  if(j<k){
    change.index <- ref.num.CV[trunc(length(ref.num.CV)/k*(j-1)+1):trunc(length(ref.num.CV)/k*j)]
  }else{
    change.index <- ref.num.CV[trunc(length(ref.num.CV)/k*(j-1)+1):(length(ref.num.CV))]
  }
  for(l in 1:length(change.index)){
    useDB[(DBt[,1]==change.index[l]),1] = j
  }
}


#initiate matrices for regression and prediction values
reg<-matrix(, nrow = 10,ncol = k)
colnames(reg, do.NULL = FALSE)
colnames(reg) <-  colnames(reg, do.NULL = FALSE, prefix = "fold ")
rownames(reg) <- c("Sample","RSS","TSS","MSS","R","R","adj.R","MSE","RMSE","SDEC")
predic<-matrix(,nrow=4,ncol=1)
colnames(predic) <-  "overall"
rownames(predic) <- c("PRESS","Q","PSE","SDEP")

#initiate list for used variables for tree construction
tvar<-vector("list", k)

#initiate matrix for variable importance analysis
vi<-list()



#perform k fold cross validation
for(i in 1:k){
    #segement data by fold  
    testIndexes <- which(useDB[,1]==i,arr.ind=TRUE)
    testData <- useDB[testIndexes, ]               #test data fold k
    testData <- testData[-1]			#remove fold column
    trainData <- useDB[-testIndexes, ]             #training data fold k
    trainData <- trainData[-1]			#remove fold column
 
    #grow tree
    form <- paste(names(trainData)[length(trainData)], "~", paste(names(trainData)[-length(trainData)], collapse=" + "))
    fit<-rpart(form, data=trainData, method="anova")
    
    #use only important variables
    form <- paste(names(useDB)[length(useDB)], "~", paste(names(fit[13][[1]]), collapse=" + "))
    fit<-rpart(form, data=useDB, method="anova")

    #prune tree
    pfit<-prune(fit, cp=fit$cptable[which.min(fit$cptable[,"xerror"]),"CP"] )

    #get model fitness
    predreg <- predict(pfit,trainData)

    #predict 
    pred <- predict(pfit,testData)

    #save results for prediction of each fold
    res$number<-c(res$number,as.numeric(names(pred)))
    res$fold<-c(res$fold,rep(i,length(pred)))
    res$predicted<-c(res$predicted,unname(pred))

    #save results for regression of each fold
    resreg$predicted<-unname(predreg)
    resreg$observed<-trainData[,length(trainData)]
    resreg$residuals<-resreg$observed-resreg$predicted
    resreg$residuals_squared<-(resreg$residuals)^2

    #evaluation values for model fitness for each fold
    reg["Sample",i]<-nrow(trainData)                                #number of datapoints in training set of the fold
    reg["RSS",i]<-sum(resreg$residuals_squared)                     #Residual Sum of Squares
    reg["TSS",i]<- sum((resreg$observed-mean(resreg$observed))^2)   #Total Sum of Squares
    reg["MSS",i]<-reg["TSS",i]-reg["RSS",i]                         #Model Sum of Squares
    reg["R",i]<-reg["MSS",i]/reg["TSS",i]                          #coefficient of determination
    reg["R",i]<-sqrt(reg["R",i])                                   #multiple correlation coefficient
    reg["adj.R",i]<- 1-((1-reg["R",i])*((reg["Sample",i]-1)/(reg["Sample",i]-(length(levels(fit$frame$var))-1))))            
 								    #Adjusted coefficient of determination 
    reg["MSE",i]<-reg["RSS",i]/(reg["Sample",i]-(length(levels(fit$frame$var))-1))                      
    								    #Mean square error
    reg["RMSE",i]<-sqrt(reg["MSE",i])                               #Root Mean square error (residual standard deviation)
    reg["SDEC",i]<-sqrt(reg["RSS",i]/reg["Sample",i])               #Standard Deviation Error in Calculation


#save used variables for each fold
tvar[[i]]<-levels(fit$frame$var)[-1]

#save variable importance for each fold
vi<-cbind(vi,pfit[13])

#save regression trees to file
png(filename=paste(results[1,r]," Tree ",i,".png"))
fancyRpartPlot(pfit,main=paste("Regression Tree for Prediction of MeOH",results[1,r]),sub=paste("Fold: ",i))
dev.off()

redVar<-cbind(redVar,names(fit[13][[1]]))

}


#average values for model fitness
reg<-cbind(reg,rowSums(reg)/k)
colnames(reg)[length(colnames(reg))]<-"overall"

#calculate residuals predicted
res$observed<-useDB[,length(useDB)]
res$residuals<-res$observed-res$predicted
res$residuals_squared<-(res$residuals)^2

#evaluation values for goodness of prediction                                     
predic["PRESS",1]<-sum(res$residuals_squared)                            #Predictive Error Sum of Squares
predic["Q",1]<-1-(predic["PRESS",1]/reg["TSS","overall"])               #Cross-validated predictive R2
predic["PSE",1]<-predic["PRESS",1]/length(res$residuals_squared)         #predictive squared error
predic["SDEP",1]<-sqrt(predic["PSE",1])                                  #standard deviation error in prediction

#matrix of used variables in each fold
max.len <- max(sapply(tvar, length))
corrected.list <- lapply(tvar, function(x) {c(x, rep(NA, max.len - length(x)))})
tvar <- do.call(cbind, corrected.list)
colnames(tvar, do.NULL = FALSE)
colnames(tvar) <-  colnames(tvar, do.NULL = FALSE, prefix = "fold ")


View(reg)
View(predic)

#--------------------------PLOT--------------------------------------------------------
#plot predicted vs. observed
x11()
plot(res$predicted,res$observed,pch=16, col=res$fold, xlim=c(0,1),ylim=c(0,1),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Predicted vs. Observed MeOH",results[1,r]))
abline(0,1)
legend("topleft", legend = c(1:k), lty ="longdash",title = "folds",col=unique(res$fold))

x11()
plot(res$predicted,res$observed,pch=16, col=res$fold,xlim=c(min(0,min(res$predicted)),max(max(res$observed),max(res$predicted))),ylim=c(min(0,min(res$predicted)),max(max(res$observed),max(res$predicted))),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Predicted vs. Observed MeOH",results[1,r]))
abline(0,1)
legend("topleft", legend = c(1:k), lty ="longdash",title = "folds",col=unique(res$fold))

#plot predicted vs. residuals
x11() 
plot(res$predicted,res$residuals, col=res$fold, xlim=c(0,1),ylim=c(-1,1),xlab=paste("Predicted MeOH",results[1,r]), xaxs="i",yaxs="i",ylab="Residuals",main=paste("Predicted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)

x11() 
plot(res$predicted,res$residuals, col=res$fold, xlim=c(min(res$predicted),max(res$predicted)), ylim=c(min(res$residuals),max(res$residuals)),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab="Residuals",main=paste("Predicted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)



#plot residual density
x11()
plot(density(res$residuals),xlab="Residuals", ylab="Density",main=paste("Density Plot of Residuals for",results[1,r]))


#-----------SAVE-----------------------------------------------------------------------------

#regression and prediction results
write.csv(reg, file =paste(results[1,r]," regression_values.csv"))
write.csv(predic, file =paste(results[1,r]," prediction_values.csv"))
write.csv(res, file =paste(results[1,r]," prediction_results.csv"), row.names=FALSE)
write.csv(resreg, file =paste(results[1,r]," regression_results.csv"), row.names=FALSE)
write.csv(tvar,file=paste(results[1,r]," Variables_Tree_Construction.csv"))
write.csv(cbind(names(unlist(vi[1:10])),unlist(vi[1:10])), file =paste(results[1,r]," variable_importance.csv"))

#plot predicted vs. observed
png(filename=paste(results[1,r]," predVSobs full.png"))
par(new=TRUE, pch=16)
plot(res$predicted,res$observed,pch=16, col=res$fold,xlim=c(0,1),ylim=c(0,1),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Predicted vs. Observed MeOH",results[1,r]))
abline(0,1)
legend("topleft", legend = c(1:k), lty ="longdash",title = "folds",col=unique(res$fold))
dev.off()

png(filename=paste(results[1,r]," predVSobs cropped.png"))
par(new=TRUE, pch=16)
plot(res$predicted,res$observed,pch=16, col=res$fold,xlim=c(min(0,min(res$predicted)),max(max(res$observed),max(res$predicted))),ylim=c(min(0,min(res$predicted)),max(max(res$observed),max(res$predicted))),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab=paste("Observed MeOH",results[1,r] ),main=paste("Predicted vs. Observed MeOH",results[1,r]))
abline(0,1)
legend("topleft", legend = c(1:k), lty ="longdash",title = "folds",col=unique(res$fold))
dev.off()


#plot predicted vs. residuals
png(filename=paste(results[1,r]," predVSres full.png"))
plot(res$predicted,res$residuals, col=res$fold,xlim=c(0,1),ylim=c(-1,1),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab="Residuals",main=paste("Predicted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)
dev.off()

png(filename=paste(results[1,r]," predVSres cropped.png"))
plot(res$predicted,res$residuals, col=res$fold,xlim=c(min(res$predicted),max(res$predicted)), ylim=c(min(res$residuals),max(res$residuals)),xaxs="i",yaxs="i",xlab=paste("Predicted MeOH",results[1,r]), ylab="Residuals",main=paste("Predicted MeOH",results[1,r],"vs. Residuals"),pch=16)
abline(h=0)
dev.off()


#plot residual density
png(filename=paste(results[1,r]," resDensity.png"))
plot(density(res$residuals),xlab="Residuals", ylab="Density",main=paste("Density Plot of Residuals for",results[1,r]))
dev.off()

write.csv(redVar, file = paste(results[1,r]," reduction.csv"))

}





