#' @title Select features for a tensor generated from two matrices that

 #'  share samples.
 #'
 #' @param HOSVD  HOSVD 
 #' @param cond list of conditions
 #' @param de initial values for optimization of standard deviation
 #' @param p0 threshold value for the significance

 #' @param breaks number of bins of the histogram of P-values

 #' @param input_all The selected singular value vectors attributed to samples.
 #' if NULL, interactive mode
 #'
 #' @return list of logical vector that represent if the individual features
 #' are selected and P-values. 
 #' @export 
 #'
 #' @examples

 #' library(TDbasedUFE)

 #' set.seed(0)
 #' matrix1 <- matrix(runif(1000),20) #row features, column samples
 #' matrix2 <- matrix(runif(2000),40) #row features, column samples

 #' Z <- prepareTensorfromMatrix(t(matrix1),t(matrix2))

 #' Z <- prepareTensorRect(sample=as.character(seq_len(50)),

 #' feature=list(as.character(seq_len(20)),as.character(seq_len(40))),

 #' sampleData=list(rep(seq_len(2),each=25)),value=Z)

 #' HOSVD <- computeHosvd(Z)
 #' cond <- list(attr(Z,"sampleData")[[1]],NULL,NULL)

 #'index_all <- selectFeatureTransRect(HOSVD,cond,de=c(0.1,0.1),
 #'input_all=2,p0=1e-10)

 selectFeatureTransRect <- function(HOSVD, cond, de = rep(1e-4, 2), p0 = 0.01,

                                    breaks = 100L, input_all = NULL) {{

   # Augument check
   stopifnot("`HOSVD` must be a list." = is.list(HOSVD))
   stopifnot("`cond` must be a list." = is.list(cond))
   stopifnot("`de` must be a numeric." = is.numeric(de))
   stopifnot("`p0` must be a numeric." = is.numeric(p0))
   stopifnot("`breaks` must be a integer." = is.integer(breaks))
   stopifnot("`input_all` must be a vector." = is.vector(input_all) |
     is.null(input_all))
   #
   interact <- FALSE
   if (is.null(input_all)) {
     interact <- TRUE
     j <- 1
     ui <- fluidPage(
       sidebarLayout(
         sidebarPanel(

           h3("Select one with prefarable dependence"),

           actionButton(inputId = "action", label = "Next"),
           actionButton(inputId = "prev", label = "Prev"),
           actionButton(inputId = "select", label = "Select")
         ),
         mainPanel(
           plotOutput("plot")
         )
       )
     )
     server <- function(input, output) {
       observeEvent(input$action, {
         if (j < dim(HOSVD$U[[1]])[2]) j <<- j + 1
       })
       observeEvent(input$prev, {
         if (j != 1) {
           j <<- j - 1

         }

       })
       observeEvent(input$select, {
         input_all <<- j
         stopApp()
       })
       output$plot <- renderPlot({
         input$action
         input$prev

         for (i in seq_along(cond))

         {

           boxplot(HOSVD$U[[1]][, j] ~ cond[[1]], main = j)
           abline(0, 0, col = 2, lty = 2)

         }

       })
     }
     app <- shinyApp(ui, server)
     runApp(app)
     input_all <- j
   } else {

     for (i in seq_along(cond))

     {
       boxplot(HOSVD$U[[1]][, input_all] ~ cond[[1]], main = input_all)
       abline(0, 0, col = 2, lty = 2)
     }
   }
   th <- function(sd, breaks, p0) {
     P2 <- pchisq((u / sd)^2, 1, lower.tail = FALSE)
     hc <- hist(1 - P2, breaks = breaks, plot = FALSE)
     return(sd(hc$count[seq_len(sum(hc$breaks
     < 1 - min(P2[p.adjust(P2, "BH") > p0])))]))
   }
   index_all <- rep(list(NA))
   for (i in seq_len(2))
   {
     u <- HOSVD$U[[i + 1]][, input_all]
     sd <- optim(de[i], function(x) {
       th(x, breaks, p0)
     },
     control = list(warn.1d.NelderMead = FALSE)
     )$par
     sd1 <- seq(0.1 * sd, 2 * sd, by = 0.1 * sd)
     th0 <- apply(matrix(sd1, ncol = 1), 1, function(x) {
       th(x, breaks, p0)
     })
     P2 <- pchisq((u / sd)^2, 1, lower.tail = FALSE)
     ui <- fluidPage(
       sidebarLayout(
         sidebarPanel(
           actionButton(inputId = "action", label = "Next")
         ),
         mainPanel(
           plotOutput("plot")
         )
       )
     )
     server <- function(input, output) {
       observeEvent(input$action, {
         stopApp()
       })
       output$plot <- renderPlot({
         input$action
         par(mfrow = c(1, 2))
         plot(sd1, th0, type = "o")
         arrows(sd, max(th0), sd, min(th0), col = 2)
         hist(1 - P2, breaks = breaks)
         par(mfrow = c(1, 1))
       })
     }
     app <- shinyApp(ui, server)
     if (interact) {
       runApp(app)
     } else {
       par(mfrow = c(1, 2))
       plot(sd1, th0, type = "o")
       arrows(sd, max(th0), sd, min(th0), col = 2)
       hist(1 - P2, breaks = breaks)
       par(mfrow = c(1, 1))

     }

 
     index <- p.adjust(P2, "BH") < p0
     index_all[[i]] <- list(index = index, p.value = P2)
   }
   return(index_all)
 }}