#' Plot
#'
#' It is a function which plots relevant parameters
#'
#' @param X matrix of covariates (of size n*p)
#' @param Y matrix of responses (of size n*m)
#' @param model the model constructed by valse procedure
#' @param n sample size
#' @return several plots
#'
#' @examples TODO
#'
#' @export
#'
plot_valse = function(X,Y,model,n, comp = FALSE, k1 = NA, k2 = NA){
  require("gridExtra")
  require("ggplot2")
  require("reshape2")
  require("cowplot")
  
  K = length(model$pi)
  ## regression matrices
  gReg = list()
  for (r in 1:K){
    Melt = melt(t((model$phi[,,r])))
    gReg[[r]] = ggplot(data = Melt, aes(x=Var1, y=Var2, fill=value)) +  geom_tile() + 
      scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0,  space = "Lab") +
      ggtitle(paste("Regression matrices in cluster",r))
  }
  print(gReg)
  
  ## Differences between two clusters
  if (comp){
    if (is.na(k1) || is.na(k)){print('k1 and k2 must be integers, representing the clusters you want to compare')}
    Melt = melt(t(model$phi[,,k1]-model$phi[,,k2]))
    gDiff = ggplot(data = Melt, aes(x=Var1, y=Var2, fill=value)) +  geom_tile() + 
      scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0,  space = "Lab") +
      ggtitle(paste("Difference between regression matrices in cluster",k1, "and", k2))
    print(gDiff)
    
  }
  
  ### Covariance matrices
  matCov = matrix(NA, nrow = dim(model$rho[,,1])[1], ncol = K)
  for (r in 1:K){
    matCov[,r] = diag(model$rho[,,r])
  }
  MeltCov =  melt(matCov)
  gCov = ggplot(data =MeltCov, aes(x=Var1, y=Var2, fill=value)) +  geom_tile() + 
    scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0,  space = "Lab") +
    ggtitle("Covariance matrices")
  print(gCov )
  
  ### Proportions
  gam2 = matrix(NA, ncol = K, nrow = n)
  for (i in 1:n){
    gam2[i, ] = c(model$proba[i, model$affec[i]], model$affec[i])
  }
  
  bp <- ggplot(data.frame(gam2), aes(x=X2, y=X1, color=X2, group = X2)) +
    geom_boxplot() + theme(legend.position = "none")+ background_grid(major = "xy", minor = "none")
  print(bp)
  
  ### Mean in each cluster
  XY = cbind(X,Y)
  XY_class= list()
  meanPerClass= matrix(0, ncol = K, nrow = dim(XY)[2])
  for (r in 1:K){
    XY_class[[r]] = XY[model$affec == r, ]
    if (sum(model$affec==r) == 1){
      meanPerClass[,r] = XY_class[[r]]
    } else {
      meanPerClass[,r] = apply(XY_class[[r]], 2, mean)
    }
  }
  data = data.frame(mean = as.vector(meanPerClass), cluster = as.character(rep(1:K, each = dim(XY)[2])), time = rep(1:dim(XY)[2],K))
  g = ggplot(data, aes(x=time, y = mean, group = cluster, color = cluster))
  print(g + geom_line(aes(linetype=cluster, color=cluster))+  geom_point(aes(color=cluster)) + ggtitle('Mean per cluster'))
  
}