## The TriComp Function:
#  0 Input:
#    0.1 Required:
#       df = input data.frame
#       var1, var2, var3 = Column names of the three input variables
#       VariablesAreLog = {TRUE/FALSE} denotes if the input values are already logarithmised or not
#    0.2 Optional parameters
#       Prefix: Will attach the prefix to all output variables. Useful when performing multiple Tricomp algorithms on the same dataset
#  1 Process
#    1.1 if necessary converts the input variables to logarithmised format
#    1.2 Calculates the logarithmic fold change for each pair
#    1.3 Determines the Highest Absolute Fold Change difference between any pairs
#  2 Calculates two cartesian plotting variables (a and b)
#  3 Converts the two cartesian coordinates into polar coordinates
#    3.1 The radius (r), which corresponds to the relative intensity of the difference between the three input values
#    3.2 The Degree variable (theta, between 0 and 360 degrees) which corresponds to the relationship.
#    3.3 Summarises Degree with a group variable (Group 1:6)
#  4. The original dataframe is returned including the new variables with the chosen prefix attached
#   logFC2over1  ## Calculates relative change from Group 1 to Group 2
#   logFC3over1 ## Calculates relative change from Group 1 to Group 3
#   logFC3over2 ## Calculates relative change from Group 2 to Group 3
#   HighestlogFC ## Calculates the absolute highest logFC between any of the three groups
#   a  ##Coordinate for plotting
#   b  ## Coordinate for plotting
#   Group   ##Category
#   Distance ##Polar coordinate
#   Degree   ##Polar coordinate


TriComp <- function(df, var1, var2, var3, VariablesAreLog = TRUE, Prefix = "TriComp_"){
  save = df
  #1.1
  if (VariablesAreLog == FALSE){
    df$logFC2over1=log(df[,var2],2)-log(df[,var1],2)
    df$logFC3over1=log(df[,var3],2)-log(df[,var1],2)
    df$logFC3over2=log(df[,var3],2)-log(df[,var2],2)
  } else {
    df$logFC2over1=df[,var2]-df[,var1]
    df$logFC3over1=df[,var3]-df[,var1]
    df$logFC3over2=df[,var3]-df[,var2] }
  
  #1.3
  df$HighestlogFC= pmax(abs(df$logFC2over1),abs(df$logFC3over1),abs(df$logFC3over2))
  
  #2
  df$a= - df$logFC3over1 + sin(pi/6)*df$logFC2over1
  df$b= - cos(pi/6)*df$logFC2over1
  
  #3.1
  df$Distance=sqrt(df$a^2 + df$b^2)
  
  #3.2
  df$Degree <- 0
  for (i in 1:nrow(df)){
    if (is.na(df$a[i]) == TRUE) {
      df$Degree[i] <- NA
    }  else if (df$a[i] >= 0 & df$b[i] > 0){
      df$Degree[i] <- atan(abs(df$a[i]/df$b[i]))*180/pi
    } else if (df$a[i] >= 0 & df$b[i] < 0){
      df$Degree[i] <- 180 - atan(abs(df$a[i]/df$b[i]))*180/pi
    } else if (df$a[i] < 0 & df$b[i] > 0){
      df$Degree[i] <- 360 -atan(abs(df$a[i]/df$b[i]))*180/pi
    } else if (df$a[i] < 0 & df$b[i] < 0){
      df$Degree[i] <- 180 + atan(abs(df$a[i]/df$b[i]))*180/pi
    } else if (df$a[i] > 0 & df$b[i] == 0){
      df$Degree[i] <- 90
    } else if (df$a[i] < 0 & df$b[i] == 0){
      df$Degree[i] <- 270
    } else if (df$a[i] == 0 & df$b[i] == 0){
      df$Degree[i] <- NA
    }}
  
  #3.3
  df$Group=floor(df$Degree/60) + 1   ##Category 1-6 based on Degree
  
  #4
  keep <- c("logFC2over1", "logFC3over1", "logFC3over2", "HighestlogFC", "a", "b", "Degree", "Group")
  df <- cbind(save,df[,keep])
  colnames(df)[match(keep,colnames(df))] <- paste0(Prefix, keep)
  return(df) 
}