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app.R

@@ -1,51 +1,1334 @@
+#Implementation of a RNN for forex analysis
+#Nacho Garcia 2018
+#Based on the rnn library (https://github.com/bquast/rnn)
+
+
 library(shiny)
-library(bslib)
-library(dplyr)
 library(ggplot2)
+library(httr)
+library(sigmoid)
+
+css <- HTML("
+  .row .nudge-right {
+     padding-right:0;
+  }
+
+  .row .nudge-left {
+     padding-left:0;
+  }
+")
 
-df <- readr::read_csv("penguins.csv")
-# Find subset of columns that are suitable for scatter plot
-df_num <- df |> select(where(is.numeric), -Year)
-
-ui <- page_fillable(theme = bs_theme(bootswatch = "minty"),
-  layout_sidebar(fillable = TRUE,
-    sidebar(
-      varSelectInput("xvar", "X variable", df_num, selected = "Bill Length (mm)"),
-      varSelectInput("yvar", "Y variable", df_num, selected = "Bill Depth (mm)"),
-      checkboxGroupInput("species", "Filter by species",
-        choices = unique(df$Species), selected = unique(df$Species)
+
+
+# Define UI for application that draws a histogram
+ui <- fluidPage(
+   
+   # Application title
+   titlePanel("AI Predicting Currency Exchange Rate"),
+   
+   # 1. Open AUD/USD
+   # 5. Open EUR/USD
+   # 9. Open GBP/USD
+   # 13.Open NZD/USD
+   # 17.Open USD/CAD
+   # 21.Open USD/CHF
+   # 24.Open USD/JPY 
+   
+   # Sidebars
+   sidebarLayout(
+      sidebarPanel(
+        width = 3,
+        selectInput("predX", "Pair to predict:",
+                   choices =  c("AUD/USD" = 1,
+                                   "EUR/USD" = 5,
+                                   "GBP/USD" = 9,
+                                   "NZD/USD"=13,
+                                   "USD/CAD"=17,
+                                   "USD/CHF"=21,
+                                   "USD/JPY"=24), selected = 1),
+        
+        sliderInput("epoch", "Iterations:", 100,5000,1000),
+        sliderInput("L", "Events Used for Training:", 500,3000,2000),
+        sliderInput("nn", "Neurons in the RNN:", 4,128,12),
+        sliderInput("lr", "Learning Rate:", 0.00001,0.01,0.0001),
+        h6(""),
+        actionButton("do", "Predict", align = "center"),
+        h6("By G2C", align = "left")
       ),
-      hr(), # Add a horizontal rule
-      checkboxInput("by_species", "Show species", TRUE),
-      checkboxInput("show_margins", "Show marginal plots", TRUE),
-      checkboxInput("smooth", "Add smoother"),
-    ),
-    plotOutput("scatter")
-  )
-)
-
-server <- function(input, output, session) {
-  subsetted <- reactive({
-    req(input$species)
-    df |> filter(Species %in% input$species)
+      
+      # Show a plot of the generated distribution
+      mainPanel(tabsetPanel(id='conditioned',
+                            tabPanel("Info", htmlOutput("help")),
+                            tabPanel("Plots", plotOutput("Plot"), plotOutput("Plot2") ),
+                            tabPanel("Values", tableOutput("summary"))
+                            
+                            
+                            
+      ))
+      
+      
+      
+      
+      )
+   )
+
+
+# Define server logic required to draw a histogram
+server <- function(input, output) {
+  
+  
+
+  
+  observeEvent(input$do, {
+    
+    Pred<-as.numeric(input$predX)
+    epochD<-input$epoch
+    L<-input$L
+    lr<-input$lr
+    nn<-input$nn
+    
+    GAP<-1
+    
+    
+     #Pred<-5
+    # epochD<-300
+    # L<-3000
+    # lr<-0.0001
+    # nn<-12
+    # 
+    
+    
+    
+    withProgress(message = 'Predicting', value = 0, {
+      incProgress(1, detail = paste("Loading Pairs"))
+      
+  
+      
+      response <- GET(url="https://www.dropbox.com/s/v3ztdtxcbpdx9mn/dfBrute.RData?dl=1")
+      load(rawConnection(response$content))
+      rm(response)
+      
+      Values<-dfBrute[[Pred]]
+      
+      for (h in 1:length(dfBrute)) {
+        dfBrute[[h]]$Open<-(dfBrute[[h]]$Open-min(dfBrute[[h]]$Open)) / (max(dfBrute[[h]]$Open)-min(dfBrute[[h]]$Open))
+        dfBrute[[h]]$High<-(dfBrute[[h]]$High-min(dfBrute[[h]]$High)) / (max(dfBrute[[h]]$High)-min(dfBrute[[h]]$High))
+        dfBrute[[h]]$Low<-(dfBrute[[h]]$Low-min(dfBrute[[h]]$Low)) / (max(dfBrute[[h]]$Low)-min(dfBrute[[h]]$Low))
+        dfBrute[[h]]$Volume<-(dfBrute[[h]]$Volume-min(dfBrute[[h]]$Volume)) / (max(dfBrute[[h]]$Volume)-min(dfBrute[[h]]$Volume))
+      }
+      
+      
+    
+    df<-array(data = NA, dim = c(1,nrow(dfBrute[[1]]),28))
+    dummy<-0
+    for (i in 1:length(dfBrute)) {
+      
+      df[1,,i+dummy]<-dfBrute[[i]]$Open
+      df[1,,i+1+dummy]<-dfBrute[[i]]$High
+      df[1,,i+2+dummy]<-dfBrute[[i]]$Low
+      df[1,,i+3+dummy]<-dfBrute[[i]]$Volume
+      dummy<-dummy+3
+      
+    }
+    
+    })
+    
+    
+    #Training data
+    Xt <- df[,1:L,]
+    X.train <- array(Xt,dim=c(1,L,28))
+    
+    Yt <- df[,1:L+GAP,Pred]
+    y.train <- matrix(Yt, ncol=L)
+    
+    ####RNN functions from rnn library
+    
+    init_r = function(model){
+      if(model$network_type == "rnn"){
+        init_rnn(model)
+      } else if (model$network_type == "lstm"){
+        init_lstm(model)
+      }else if (model$network_type == "gru"){
+        init_gru(model)
+      }
+    }
+    
+    #' @name init_rnn
+    #' @title init_rnn
+    #' @description Initialize the weight parameter for a rnn
+    #' @param model the output model object
+    #' @return the updated model
+    
+    init_rnn = function(model){
+      
+      # Storing layers states, filled with 0 for the moment
+      model$store <- list()
+      for(i in seq(length(model$synapse_dim) - 1)){
+        model$store[[i]] <- array(0,dim = c(dim(model$last_layer_error)[1:2],model$synapse_dim[i+1]))
+      }
+      
+      model$time_synapse            = list()
+      model$recurrent_synapse       = list()
+      model$bias_synapse            = list()
+      
+      #initialize neural network weights, stored in several lists
+      for(i in seq(length(model$synapse_dim) - 1)){
+        model$time_synapse[[i]] <- matrix(runif(n = model$synapse_dim[i]*model$synapse_dim[i+1], min=-1, max=1), nrow=model$synapse_dim[i])
+      }
+      for(i in seq(length(model$hidden_dim))){
+        model$recurrent_synapse[[i]] <- matrix(runif(n = model$hidden_dim[i]*model$hidden_dim[i], min=-1, max=1), nrow=model$hidden_dim[i])
+      }
+      for(i in seq(length(model$synapse_dim) - 1)){
+        model$bias_synapse[[i]] <- runif(model$synapse_dim[i+1],min=-0.1,max=0.1)
+      }
+      
+      # add the update to the model list
+      model$time_synapse_update = lapply(model$time_synapse,function(x){x*0})
+      model$bias_synapse_update = lapply(model$bias_synapse,function(x){x*0})
+      model$recurrent_synapse_update = lapply(model$recurrent_synapse,function(x){x*0})
+      
+      return(model)
+    }
+    
+    #' @name init_lstm
+    #' @title init_lstm
+    #' @description Initialize the weight parameter for a lstm
+    #' @param model the output model object
+    #' @return the updated model
+    
+    init_lstm = function(model){
+      # if(length(model$hidden_dim) != 1){stop("only one layer LSTM supported yet")}
+      
+      # Storing layers states, filled with 0 for the moment
+      model$store <- list()
+      model$time_synapse            = list()
+      model$recurrent_synapse       = list()
+      model$bias_synapse            = list()
+      for(i in seq(length(model$hidden_dim))){
+        # hidden output / cells / forget / input / gate / output
+        model$store[[i]] = array(0,dim = c(dim(model$last_layer_error)[1:2],model$hidden_dim[1],6)) # 4D arrays !!! with dim()[4] = 6
+        model$time_synapse[[i]] = array(runif(n = model$synapse_dim[i] * model$synapse_dim[i+1] * 4, min=-1, max=1),dim = c(model$synapse_dim[i], model$synapse_dim[i+1], 4))# 3D arrays with dim()[3] = 4
+        model$recurrent_synapse[[i]] = array(runif(n = model$synapse_dim[i+1] * model$synapse_dim[i+1] * 4, min=-1, max=1),dim = c(model$synapse_dim[i+1], model$synapse_dim[i+1], 4))# 3D arrays with dim()[3] = 4
+        model$bias_synapse[[i]] = array(runif(n = model$synapse_dim[i+1] * 4, min=-1, max=1),dim = c(model$synapse_dim[i+1], 4))#2D arrays with dim()[2] = 4
+      }
+      
+      model$store[[length(model$store) + 1]] = array(0,dim = c(dim(model$last_layer_error)[1:2],model$output_dim)) # final output layer
+      model$time_synapse[[length(model$time_synapse) + 1]] = array(runif(n = model$hidden_dim[length(model$hidden_dim)] * model$output_dim, min=-1, max=1),dim = c(model$hidden_dim[length(model$hidden_dim)], model$output_dim)) # 4D arrays !!!
+      model$bias_synapse[[length(model$bias_synapse) + 1]] = runif(model$output_dim,min=-0.1,max=0.1)
+      
+      # add the update to the model list
+      model$time_synapse_update = lapply(model$time_synapse,function(x){x*0})
+      model$bias_synapse_update = lapply(model$bias_synapse,function(x){x*0})
+      model$recurrent_synapse_update = lapply(model$recurrent_synapse,function(x){x*0})
+      
+      return(model)
+    }
+    
+    #' @name init_gru
+    #' @title init_gru
+    #' @description Initialize the weight parameter for a gru
+    #' @param model the output model object
+    #' @return the updated model
+    
+    init_gru = function(model){
+      
+      # Storing layers states, filled with 0 for the moment
+      model$store <- list()
+      model$time_synapse            = list()
+      model$recurrent_synapse       = list()
+      model$bias_synapse            = list()
+      for(i in seq(length(model$hidden_dim))){
+        # hidden output / z / r / h
+        model$store[[i]] = array(0,dim = c(dim(model$last_layer_error)[1:2],model$hidden_dim[1],4)) # 4D arrays !!! with dim()[4] = 4
+        model$time_synapse[[i]] = array(runif(n = model$synapse_dim[i] * model$synapse_dim[i+1] * 3, min=-1, max=1),dim = c(model$synapse_dim[i], model$synapse_dim[i+1], 3))# 3D arrays with dim()[3] = 3
+        model$recurrent_synapse[[i]] = array(runif(n = model$synapse_dim[i+1] * model$synapse_dim[i+1] * 3, min=-1, max=1),dim = c(model$synapse_dim[i+1], model$synapse_dim[i+1], 3))# 3D arrays with dim()[3] = 3
+        model$bias_synapse[[i]] = array(runif(n = model$synapse_dim[i+1] * 3, min=-1, max=1),dim = c(model$synapse_dim[i+1], 3))#2D arrays with dim()[2] = 3
+      }
+      
+      model$store[[length(model$store) + 1]] = array(0,dim = c(dim(model$last_layer_error)[1:2],model$output_dim)) # final output layer
+      model$time_synapse[[length(model$time_synapse) + 1]] = array(runif(n = model$hidden_dim[length(model$hidden_dim)] * model$output_dim, min=-1, max=1),dim = c(model$hidden_dim[length(model$hidden_dim)], model$output_dim)) # 4D arrays !!!
+      model$bias_synapse[[length(model$bias_synapse) + 1]] = runif(model$output_dim,min=-0.1,max=0.1)
+      
+      # add the update to the model list
+      model$time_synapse_update = lapply(model$time_synapse,function(x){x*0})
+      model$bias_synapse_update = lapply(model$bias_synapse,function(x){x*0})
+      model$recurrent_synapse_update = lapply(model$recurrent_synapse,function(x){x*0})
+      
+      return(model)
+    }
+    
+    #' @name backprop_r
+    #' @title backprop_r
+    #' @description backpropagate the error in a model object
+    #' @param model the output model object
+    #' @param a the input of this learning batch
+    #' @param c the output of this learning batch
+    #' @param j the indexes of the sample in the current batch
+    #' @param ... argument to be passed to method
+    #' @return the updated model
+    
+    backprop_r = function(model,a,c,j,...){
+      if(model$network_type == "rnn"){
+        backprop_rnn(model,a,c,j,...)
+      } else if (model$network_type == "lstm"){
+        backprop_lstm(model,a,c,j,...)
+      } else if (model$network_type == "gru"){
+        backprop_gru(model,a,c,j,...)
+      }else{
+        stop("network_type_unknown for the backprop")
+      }
+    }
+    
+    #' @name backprop_rnn
+    #' @title backprop_rnn
+    #' @description backpropagate the error in a model object of type rnn
+    #' @param model the output model object
+    #' @param a the input of this learning batch
+    #' @param c the output of this learning batch
+    #' @param j the indexes of the sample in the current batch
+    #' @param ... argument to be passed to method
+    #' @return the updated model
+    
+    backprop_rnn = function(model,a,c,j,...){
+      
+      # store errors
+      model$last_layer_error[j,,] = c - model$store[[length(model$store)]][j,,,drop=F]
+      model$last_layer_delta[j,,] = model$last_layer_error[j,,,drop = F] * sigmoid_output_to_derivative(model$store[[length(model$store)]][j,,,drop=F])
+      
+      if(model$seq_to_seq_unsync){
+        model$last_layer_error[j,1:(model$time_dim_input - 1),] = 0
+        model$last_layer_delta[j,1:(model$time_dim_input - 1),] = 0
+      }
+      
+      
+      model$error[j,model$current_epoch] <- apply(model$last_layer_error[j,,,drop=F],1,function(x){sum(abs(x))})
+      
+      # init futur layer delta, here because there is no layer delta at time_dim+1
+      future_layer_delta  = list()
+      for(i in seq(length(model$hidden_dim))){
+        future_layer_delta[[i]] <- matrix(0,nrow=length(j), ncol = model$hidden_dim[i])
+      }
+      
+      # Weight iteration,
+      for (position in model$time_dim:1) {
+        
+        # input states
+        x            = array(a[,position,],dim=c(length(j),model$input_dim))
+        # error at output layer
+        layer_up_delta = array(model$last_layer_delta[j,position,],dim=c(length(j),model$output_dim))
+        
+        for(i in (length(model$store)):1){
+          if(i != 1){ # need update for time and recurrent synapse
+            layer_current      = array(model$store[[i-1]][j,position,],dim=c(length(j),model$hidden_dim[i-1]))
+            if(position != 1){
+              prev_layer_current = array(model$store[[i-1]][j,position - 1,],dim=c(length(j),model$hidden_dim[i-1]))
+            }else{
+              prev_layer_current = array(0,dim=c(length(j),model$hidden_dim[i-1]))
+            }
+            # error at hidden layers
+            layer_current_delta = (future_layer_delta[[i-1]] %*% t(model$recurrent_synapse[[i-1]]) + layer_up_delta %*% t(model$time_synapse[[i]])) *
+              sigmoid_output_to_derivative(layer_current)
+            model$time_synapse_update[[i]] = model$time_synapse_update[[i]] + t(layer_current) %*% layer_up_delta
+            model$bias_synapse_update[[i]] = model$bias_synapse_update[[i]] + colMeans(layer_up_delta)
+            model$recurrent_synapse_update[[i-1]] = model$recurrent_synapse_update[[i-1]] + t(prev_layer_current) %*% layer_current_delta
+            layer_up_delta = layer_current_delta
+            future_layer_delta[[i-1]] = layer_current_delta
+          }else{ # need only update for time synapse
+            model$time_synapse_update[[i]] = model$time_synapse_update[[i]] + t(x) %*% layer_up_delta
+          }
+        }
+      } # end position back prop loop
+      return(model)
+    }
+    
+    #' @name backprop_lstm
+    #' @title backprop_lstm
+    #' @description backpropagate the error in a model object of type rlstm
+    #' @importFrom sigmoid tanh_output_to_derivative
+    #' @param model the output model object
+    #' @param a the input of this learning batch
+    #' @param c the output of this learning batch
+    #' @param j the indexes of the sample in the current batch
+    #' @param ... argument to be passed to method
+    #' @return the updated model
+    
+    backprop_lstm = function(model,a,c,j,...){
+      
+      # store errors
+      model$last_layer_error[j,,] = c - model$store[[length(model$store)]][j,,,drop=F]
+      model$last_layer_delta[j,,] = model$last_layer_error[j,,,drop = F] * sigmoid_output_to_derivative(model$store[[length(model$store)]][j,,,drop=F])
+      
+      if(model$seq_to_seq_unsync){
+        model$last_layer_error[j,1:(model$time_dim_input - 1),] = 0
+        model$last_layer_delta[j,1:(model$time_dim_input - 1),] = 0
+      }
+      model$error[j,model$current_epoch] <- apply(model$last_layer_error[j,,,drop=F],1,function(x){sum(abs(x))})
+      
+      future_layer_cell_delta = list()
+      future_layer_hidden_delta = list()
+      for(i in seq(length(model$hidden_dim))){
+        future_layer_cell_delta[[i]] = matrix(0, nrow = length(j), ncol = model$hidden_dim[i]) # 4 to actualize
+        future_layer_hidden_delta[[i]] = matrix(0, nrow = length(j), ncol = model$hidden_dim[i]) # 2, to actualize
+      }
+      
+      
+      for (position in model$time_dim:1) {
+        # error at output layer
+        layer_up_delta = array(model$last_layer_delta[j,position,],dim=c(length(j),model$output_dim))
+        
+        # first the last layer to update the layer_up_delta
+        i = length(model$hidden_dim)
+        layer_hidden = array(model$store[[i]][j,position,,1],dim=c(length(j),model$hidden_dim[i]))
+        # output layer update
+        model$time_synapse_update[[i+1]]   = model$time_synapse_update[[i+1]]   + (t(layer_hidden) %*% layer_up_delta)
+        model$bias_synapse_update[[i+1]]   = model$bias_synapse_update[[i+1]]   + colMeans(layer_up_delta)
+        # lstm hidden delta
+        layer_up_delta = (layer_up_delta %*% t(model$time_synapse_update[[i+1]])) * sigmoid_output_to_derivative(layer_hidden) + future_layer_hidden_delta[[i]] # 1 and 3
+        
+        for(i in length(model$hidden_dim):1){
+          # x: input of the layer
+          if(i == 1){
+            x = array(a[,position,],dim=c(length(j),model$input_dim))
+          }else{
+            x = array(model$store[[i - 1]][j,position,,1],dim=c(length(j),model$synapse_dim[i]))
+          }
+          layer_hidden = array(model$store[[i]][j,position,,1],dim=c(length(j),model$hidden_dim[i]))
+          layer_cell = array(model$store[[i]][j,position,,2],dim=c(length(j), model$hidden_dim[i]))
+          if(position != 1){
+            prev_layer_hidden =array(model$store[[i]][j,position-1,,1],dim=c(length(j),model$hidden_dim[i]))
+            preview_layer_cell = array(model$store[[i]][j,position-1,,2],dim=c(length(j), model$hidden_dim[i]))
+          }else{
+            prev_layer_hidden =array(0,dim=c(length(j),model$hidden_dim[i]))
+            preview_layer_cell = array(0,dim=c(length(j), model$hidden_dim[i]))
+          }
+          
+          layer_f = array(model$store[[i]][j,position,,3],dim=c(length(j), model$hidden_dim[i]))
+          layer_i = array(model$store[[i]][j,position,,4],dim=c(length(j), model$hidden_dim[i]))
+          layer_c = array(model$store[[i]][j,position,,5],dim=c(length(j), model$hidden_dim[i]))
+          layer_o = array(model$store[[i]][j,position,,6],dim=c(length(j), model$hidden_dim[i]))
+          
+          # lstm cell delta
+          # layer_cell_delta = (layer_hidden_delta * layer_o) + future_layer_cell_delta    # 5 then 8 (skip 7 as no tanh)
+          # layer_o_delta_post_activation = layer_hidden_delta *  layer_cell # 6 (skip 7 as no tanh)
+          layer_cell_delta = (layer_up_delta * layer_o)* tanh_output_to_derivative(layer_cell) + future_layer_cell_delta[[i]]    # 5, 7 then 8
+          layer_o_delta_post_activation = layer_up_delta *  tanh(layer_cell) # 6 
+          
+          layer_c_delta_post_activation = layer_cell_delta * layer_i    # 9
+          layer_i_delta_post_activation = layer_cell_delta * layer_c    # 10
+          
+          layer_f_delta_post_activation = layer_cell_delta * preview_layer_cell # 12
+          future_layer_cell_delta[[i]] = layer_cell_delta * layer_f # 11
+          
+          layer_o_delta_pre_activation = layer_o_delta_post_activation * sigmoid_output_to_derivative(layer_o) # 13
+          layer_c_delta_pre_activation = layer_c_delta_post_activation * tanh_output_to_derivative(layer_c) # 14
+          layer_i_delta_pre_activation = layer_i_delta_post_activation * sigmoid_output_to_derivative(layer_i) # 15
+          layer_f_delta_pre_activation = layer_f_delta_post_activation * sigmoid_output_to_derivative(layer_f) # 16
+          # 
+          
+          
+          # let's update all our weights so we can try again
+          model$recurrent_synapse_update[[i]][,,1] = model$recurrent_synapse_update[[i]][,,1] + t(prev_layer_hidden) %*% layer_f_delta_post_activation
+          model$recurrent_synapse_update[[i]][,,2] = model$recurrent_synapse_update[[i]][,,2] + t(prev_layer_hidden) %*% layer_i_delta_post_activation
+          model$recurrent_synapse_update[[i]][,,3] = model$recurrent_synapse_update[[i]][,,3] + t(prev_layer_hidden) %*% layer_c_delta_post_activation
+          model$recurrent_synapse_update[[i]][,,4] = model$recurrent_synapse_update[[i]][,,4] + t(prev_layer_hidden) %*% layer_o_delta_post_activation
+          model$time_synapse_update[[i]][,,1] = model$time_synapse_update[[i]][,,1] + t(x) %*% layer_f_delta_post_activation
+          model$time_synapse_update[[i]][,,2] = model$time_synapse_update[[i]][,,2] + t(x) %*% layer_i_delta_post_activation
+          model$time_synapse_update[[i]][,,3] = model$time_synapse_update[[i]][,,3] + t(x) %*% layer_c_delta_post_activation
+          model$time_synapse_update[[i]][,,4] = model$time_synapse_update[[i]][,,4] + t(x) %*% layer_o_delta_post_activation
+          model$bias_synapse_update[[i]][,1] = model$bias_synapse_update[[i]][,1] + colMeans(layer_f_delta_post_activation)
+          model$bias_synapse_update[[i]][,2] = model$bias_synapse_update[[i]][,2] + colMeans(layer_i_delta_post_activation)
+          model$bias_synapse_update[[i]][,3] = model$bias_synapse_update[[i]][,3] + colMeans(layer_c_delta_post_activation)
+          model$bias_synapse_update[[i]][,4] = model$bias_synapse_update[[i]][,4] + colMeans(layer_o_delta_post_activation)
+          
+          layer_f_delta_pre_weight = layer_f_delta_pre_activation %*% t(array(model$recurrent_synapse[[i]][,,1],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) # 20
+          layer_i_delta_pre_weight = layer_i_delta_pre_activation %*% t(array(model$recurrent_synapse[[i]][,,2],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) # 19
+          layer_c_delta_pre_weight = layer_c_delta_pre_activation %*% t(array(model$recurrent_synapse[[i]][,,3],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) # 18
+          layer_o_delta_pre_weight = layer_o_delta_pre_activation %*% t(array(model$recurrent_synapse[[i]][,,4],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) # 17
+          future_layer_hidden_delta[[i]] = layer_o_delta_pre_weight + layer_c_delta_pre_weight + layer_i_delta_pre_weight + layer_f_delta_pre_weight # 21
+          
+          layer_f_delta_pre_weight = layer_f_delta_pre_activation %*% t(array(model$time_synapse[[i]][,,1],dim=c(dim(model$time_synapse[[i]])[1:2]))) # 20
+          layer_i_delta_pre_weight = layer_i_delta_pre_activation %*% t(array(model$time_synapse[[i]][,,2],dim=c(dim(model$time_synapse[[i]])[1:2]))) # 19
+          layer_c_delta_pre_weight = layer_c_delta_pre_activation %*% t(array(model$time_synapse[[i]][,,3],dim=c(dim(model$time_synapse[[i]])[1:2]))) # 18
+          layer_o_delta_pre_weight = layer_o_delta_pre_activation %*% t(array(model$time_synapse[[i]][,,4],dim=c(dim(model$time_synapse[[i]])[1:2]))) # 17
+          layer_up_delta = layer_o_delta_pre_weight + layer_c_delta_pre_weight + layer_i_delta_pre_weight + layer_f_delta_pre_weight # 21
+        }
+      }
+      
+      # future_layers_delta = list()
+      # for(i in seq(length(model$hidden_dim))){
+      #   future_layers_delta[[i]] = array(0,dim=c(length(j),model$hidden_dim[i],4))
+      # }
+      # 
+      # for (position in model$time_dim:1) {
+      #   
+      #   # input states
+      #   x            = array(a[,position,],dim=c(length(j),model$input_dim))
+      #   # error at output layer
+      #   layer_up_delta = array(model$last_layer_delta[j,position,],dim=c(length(j),model$output_dim))
+      #   
+      #   for(i in (length(model$store)):1){
+      #     if(i != 1){ # need update for time and recurrent synapse
+      #       layer_current      = array(model$store[[i-1]][j,position,],dim=c(length(j),model$hidden_dim[i-1]))
+      #       if(position != 1){
+      #         prev_layer_current = array(model$store[[i-1]][j,position - 1,],dim=c(length(j),model$hidden_dim[i-1]))
+      #       }else{
+      #         prev_layer_current = array(0,dim=c(length(j),model$hidden_dim[i-1]))
+      #       }
+      #     }
+      #     if(i == length(model$store)){
+      #       # error at hidden layer
+      #       future_layers_delta[[i-1]][,,1] = (future_layers_delta[[i-1]][,,1] %*% t(model$recurrent_synapse[[i-1]][,,1]) + layer_up_delta %*% t(model$time_synapse_ouput)) *
+      #         sigmoid_output_to_derivative(layer_current)
+      #       future_layers_delta[[i-1]][,,2] = (future_layers_delta[[i-1]][,,2] %*% t(model$recurrent_synapse[[i-1]][,,2]) + layer_up_delta %*% t(model$time_synapse_ouput)) *
+      #         sigmoid_output_to_derivative(layer_current)
+      #       future_layers_delta[[i-1]][,,3] = (future_layers_delta[[i-1]][,,3] %*% t(model$recurrent_synapse[[i-1]][,,3]) + layer_up_delta %*% t(model$time_synapse_ouput)) *
+      #         sigmoid_output_to_derivative(layer_current)
+      #       future_layers_delta[[i-1]][,,4] = (future_layers_delta[[i-1]][,,4] %*% t(model$recurrent_synapse[[i-1]][,,4]) + layer_up_delta %*% t(model$time_synapse_ouput)) *
+      #         sigmoid_output_to_derivative(layer_current)
+      #       
+      #       # let's update all our weights so we can try again
+      #       model$time_synapse_ouput_update   = model$time_synapse_ouput_update   + t(layer_current)      %*% layer_up_delta
+      #       model$recurrent_synapse_update[[i-1]][,,1]  = model$recurrent_synapse_update[[i-1]][,,1] + t(prev_layer_current) %*% future_layers_delta[[i-1]][,,1]
+      #       model$recurrent_synapse_update[[i-1]][,,2]  = model$recurrent_synapse_update[[i-1]][,,2] + t(prev_layer_current) %*% future_layers_delta[[i-1]][,,2]
+      #       model$recurrent_synapse_update[[i-1]][,,3]  = model$recurrent_synapse_update[[i-1]][,,3] + t(prev_layer_current) %*% future_layers_delta[[i-1]][,,3]
+      #       model$recurrent_synapse_update[[i-1]][,,4]  = model$recurrent_synapse_update[[i-1]][,,4] + t(prev_layer_current) %*% future_layers_delta[[i-1]][,,4]
+      #       
+      #       model$bias_synapse_ouput_update = model$bias_synapse_ouput_update + colMeans(layer_up_delta)
+      # 
+      #       model$bias_synapse_update[[i-1]] = model$bias_synapse_update[[i-1]] + apply(future_layers_delta[[i-1]],2:3,mean)
+      #       
+      #     } else if(i == 1){
+      #       model$time_synapse_update[[i]][,,1] = model$time_synapse_update[[i]][,,1] + t(x) %*% future_layers_delta[[i]][,,1]
+      #       model$time_synapse_update[[i]][,,2] = model$time_synapse_update[[i]][,,2] + t(x) %*% future_layers_delta[[i]][,,2]
+      #       model$time_synapse_update[[i]][,,3] = model$time_synapse_update[[i]][,,3] + t(x) %*% future_layers_delta[[i]][,,3]
+      #       model$time_synapse_update[[i]][,,4] = model$time_synapse_update[[i]][,,4] + t(x) %*% future_layers_delta[[i]][,,4]
+      #     }
+      #   }
+      # }
+      return(model)
+    }
+    
+    #' @name backprop_gru
+    #' @title backprop_gru
+    #' @description backpropagate the error in a model object of type gru
+    #' @importFrom sigmoid tanh_output_to_derivative
+    #' @param model the output model object
+    #' @param a the input of this learning batch
+    #' @param c the output of this learning batch
+    #' @param j the indexes of the sample in the current batch
+    #' @param ... argument to be passed to method
+    #' @return the updated model
+    
+    backprop_gru = function(model,a,c,j,...){
+      
+      # store errors
+      model$last_layer_error[j,,] = c - model$store[[length(model$store)]][j,,,drop=F]
+      model$last_layer_delta[j,,] = model$last_layer_error[j,,,drop = F] * sigmoid_output_to_derivative(model$store[[length(model$store)]][j,,,drop=F])
+      
+      # many_to_one
+      if(model$seq_to_seq_unsync){
+        model$last_layer_error[j,1:(model$time_dim_input - 1),] = 0
+        model$last_layer_delta[j,1:(model$time_dim_input - 1),] = 0
+      }
+      model$error[j,model$current_epoch] <- apply(model$last_layer_error[j,,,drop=F],1,function(x){sum(abs(x))})
+      
+      future_layer_hidden_delta = list()
+      for(i in seq(length(model$hidden_dim))){
+        future_layer_hidden_delta[[i]] = matrix(0, nrow = length(j), ncol = model$hidden_dim[i]) # 2, to actualize
+      }
+      
+      
+      for (position in model$time_dim:1) {
+        # error at output layer
+        layer_up_delta = array(model$last_layer_delta[j,position,],dim=c(length(j),model$output_dim))
+        
+        # first the last layer to update the layer_up_delta
+        i = length(model$hidden_dim)
+        layer_hidden = array(model$store[[i]][j,position,,1],dim=c(length(j),model$hidden_dim[i]))
+        # output layer update
+        model$time_synapse_update[[i+1]]   = model$time_synapse_update[[i+1]]   + (t(layer_hidden) %*% layer_up_delta)
+        model$bias_synapse_update[[i+1]]   = model$bias_synapse_update[[i+1]]   + colMeans(layer_up_delta)
+        # lstm hidden delta
+        layer_up_delta = (layer_up_delta %*% t(model$time_synapse_update[[i+1]])) * sigmoid_output_to_derivative(layer_hidden) + future_layer_hidden_delta[[i]] # 1 and 3
+        
+        for(i in length(model$hidden_dim):1){
+          # x: input of the layer
+          if(i == 1){
+            x = array(a[,position,],dim=c(length(j),model$input_dim))
+          }else{
+            x = array(model$store[[i - 1]][j,position,,1],dim=c(length(j),model$synapse_dim[i]))
+          }
+          layer_hidden = array(model$store[[i]][j,position,,1],dim=c(length(j),model$hidden_dim[i]))
+          if(position != 1){
+            prev_layer_hidden =array(model$store[[i]][j,position-1,,1],dim=c(length(j),model$hidden_dim[i]))
+          }else{
+            prev_layer_hidden =array(0,dim=c(length(j),model$hidden_dim[i]))
+          }
+          
+          layer_z = array(model$store[[i]][j,position,,2],dim=c(length(j), model$hidden_dim[i]))
+          layer_r = array(model$store[[i]][j,position,,3],dim=c(length(j), model$hidden_dim[i]))
+          layer_h = array(model$store[[i]][j,position,,4],dim=c(length(j), model$hidden_dim[i]))
+          
+          layer_hidden_delta = layer_up_delta + future_layer_hidden_delta[[i]] #3
+          layer_h_delta_post_activation = layer_hidden_delta *  layer_z # 6 
+          layer_h_delta_pre_activation = layer_h_delta_post_activation * tanh_output_to_derivative(layer_h) # 6 bis
+          layer_z_delta_post_split = layer_hidden_delta *  layer_h # 7 
+          
+          layer_z_delta_post_1_minus = layer_hidden_delta *  prev_layer_hidden # 9 
+          layer_hidden_delta = layer_hidden_delta * (1 - layer_z) # 8
+          
+          layer_z_delta_post_activation = (1 - layer_z_delta_post_1_minus) # 10
+          layer_z_delta_pre_activation = layer_z_delta_post_activation*  sigmoid_output_to_derivative(layer_z) # 10 bis
+          layer_z_delta_pre_weight_h = (layer_z_delta_pre_activation %*% t(model$recurrent_synapse[[i]][,,1]) ) # 14 
+          layer_z_delta_pre_weight_x = (layer_z_delta_pre_activation %*% array(t(model$time_synapse[[i]][,,1]),dim = dim(model$time_synapse[[i]])[2:1])) # 14 
+          # let's update all our weights so we can try again
+          model$recurrent_synapse_update[[i]][,,1] = model$recurrent_synapse_update[[i]][,,1] + t(prev_layer_hidden) %*% layer_z_delta_post_activation
+          model$time_synapse_update[[i]][,,1] = model$time_synapse_update[[i]][,,1] + t(x) %*% layer_z_delta_post_activation
+          model$bias_synapse_update[[i]][,1] = model$bias_synapse_update[[i]][,1] + colMeans(layer_z_delta_post_activation)
+          
+          layer_h_delta_pre_weight_h = (layer_h_delta_pre_activation %*% t(model$recurrent_synapse[[i]][,,3]))# 13 
+          layer_h_delta_pre_weight_x = ( layer_h_delta_pre_activation %*% array(t(model$time_synapse[[i]][,,3]),dim = dim(model$time_synapse[[i]])[2:1])) # 13 
+          # let's update all our weights so we can try again
+          model$recurrent_synapse_update[[i]][,,3] = model$recurrent_synapse_update[[i]][,,3] + t(prev_layer_hidden * layer_r) %*% layer_h_delta_post_activation
+          model$time_synapse_update[[i]][,,3] = model$time_synapse_update[[i]][,,3] + t(x) %*% layer_h_delta_post_activation
+          model$bias_synapse_update[[i]][,3] = model$bias_synapse_update[[i]][,3] + colMeans(layer_h_delta_post_activation)
+          
+          layer_r_delta_post_activation = prev_layer_hidden * layer_h_delta_pre_weight_h # 15
+          layer_r_delta_pre_activation = layer_r_delta_post_activation * sigmoid_output_to_derivative(layer_r) # 15 bis
+          layer_hidden_delta = layer_hidden_delta + layer_r * layer_h_delta_pre_weight_h # 12
+          
+          layer_r_delta_pre_weight_h = (layer_r_delta_pre_activation %*% t(model$recurrent_synapse[[i]][,,2])) # 17 
+          layer_r_delta_pre_weight_x = (layer_r_delta_post_activation %*% array(t(model$time_synapse[[i]][,,2]),dim = dim(model$time_synapse[[i]])[2:1])) # 17 
+          # let's update all our weights so we can try again
+          model$recurrent_synapse_update[[i]][,,2] = model$recurrent_synapse_update[[i]][,,2] + t(prev_layer_hidden) %*% layer_r_delta_post_activation
+          model$time_synapse_update[[i]][,,2] = model$time_synapse_update[[i]][,,2] + t(x) %*% layer_r_delta_post_activation
+          model$bias_synapse_update[[i]][,2] = model$bias_synapse_update[[i]][,2] + colMeans(layer_r_delta_post_activation)
+          
+          layer_r_and_z_delta_pre_weight_h = layer_r_delta_pre_weight_h + layer_z_delta_pre_weight_h # 19
+          layer_r_and_z_delta_pre_weight_x = layer_r_delta_pre_weight_x + layer_z_delta_pre_weight_x # 19
+          
+          future_layer_hidden_delta[[i]] = layer_hidden_delta + layer_r_and_z_delta_pre_weight_h # 23
+          
+          layer_up_delta = layer_r_and_z_delta_pre_weight_x + layer_h_delta_pre_weight_x # 22
+        }
+      }
+      return(model)
+    }
+    
+    
+    update_r = function(model){
+      if(model$update_rule == "sgd"){
+        update_sgd(model)
+      }else if(model$update_rule == "adagrad"){
+        update_adagrad(model)
+      }else{
+        stop("update_rule unknown")
+      }
+    }
+    
+    
+    #' @name update_sgd
+    #' @title update_sgd
+    #' @description Apply the update with stochastic gradient descent
+    #' @param model the output model object
+    #' @return the updated model
+    
+    update_sgd = function(model){
+      
+      if(!is.null(model$clipping)){ # should we clippe the update or the weight, the update will make more sens as the weight lead to killed units
+        clipping = function(x){
+          x[is.nan(x)] = runif(sum(is.nan(x)),-1,1)
+          x[x > model$clipping] = model$clipping
+          x[x < -model$clipping] = - model$clipping
+          return(x)
+        }
+        model$recurrent_synapse_update  = lapply(model$recurrent_synapse_update,clipping)
+        model$time_synapse_update       = lapply(model$time_synapse_update,clipping)
+        model$bias_synapse_update       = lapply(model$bias_synapse_update, clipping)
+      }
+      
+      for(i in seq(length(model$time_synapse))){
+        model$time_synapse[[i]] <- model$time_synapse[[i]] + model$time_synapse_update[[i]]
+        model$bias_synapse[[i]] <- model$bias_synapse[[i]] + model$bias_synapse_update[[i]]
+      }
+      for(i in seq(length(model$recurrent_synapse))){
+        model$recurrent_synapse[[i]] <- model$recurrent_synapse[[i]] + model$recurrent_synapse_update[[i]]
+      }
+      
+      # Initializing the update with the momentum
+      model$time_synapse_update = lapply(model$time_synapse_update,function(x){x* model$momentum})
+      model$bias_synapse_update = lapply(model$bias_synapse_update,function(x){x* model$momentum})
+      model$recurrent_synapse_update = lapply(model$recurrent_synapse_update,function(x){x* model$momentum})
+      
+      return(model)
+    }
+    
+    
+    #' @name update_adagrad
+    #' @title update_adagrad
+    #' @description Apply the update with adagrad, not working yet
+    #' @param model the output model object
+    #' @return the updated model
+    
+    update_adagrad = function(model){
+      ## not working yet, inspiration here:
+      ## https://www.quora.com/What-are-differences-between-update-rules-like-AdaDelta-RMSProp-AdaGrad-and-AdaM
+      if(!is.null(model$clipping)){ # should we clippe the update or the weight, the update will make more sens as the weight lead to killed units
+        clipping = function(x){
+          x[is.nan(x)] = runif(sum(is.nan(x)),-1,1)
+          x[x > model$clipping] = model$clipping
+          x[x < -model$clipping] = - model$clipping
+          return(x)
+        }
+        model$recurrent_synapse_update  = lapply(model$recurrent_synapse_update,clipping)
+        model$time_synapse_update       = lapply(model$time_synapse_update,clipping)
+        model$bias_synapse_update       = lapply(model$bias_synapse_update, clipping)
+      }
+      
+      if(is.null(model$recurrent_synapse_update_old)){ # not really the old update but just a store of the old
+        model$recurrent_synapse_update_old = lapply(model$recurrent_synapse_update,function(x){x*0})
+        model$time_synapse_update_old = lapply(model$time_synapse_update,function(x){x*0})
+        # model$bias_synapse_update_old = lapply(model$bias_synapse_update,function(x){x*0}) # the bias stay the same, we only apply it on the weight
+      }
+      
+      for(i in seq(length(model$time_synapse))){
+        model$time_synapse_update_old[[i]] <- model$time_synapse_update_old[[i]] + model$time_synapse_update[[i]]
+        # model$bias_synapse_old[[i]] <- model$bias_synapse[[i]] + model$bias_synapse_update[[i]]
+      }
+      for(i in seq(length(model$recurrent_synapse))){
+        model$recurrent_synapse_update_old[[i]] <- model$recurrent_synapse_update_old[[i]] + model$recurrent_synapse_update[[i]]
+      }
+      
+      for(i in seq(length(model$time_synapse))){
+        model$time_synapse[[i]] <- model$time_synapse[[i]] + model$learningrate * model$time_synapse_update[[i]] / (model$time_synapse_update_old[[i]] + 0.000000001)
+        model$bias_synapse[[i]] <- model$bias_synapse[[i]] + model$bias_synapse_update[[i]]
+      }
+      for(i in seq(length(model$recurrent_synapse))){
+        model$recurrent_synapse[[i]] <- model$recurrent_synapse[[i]] + model$learningrate * model$recurrent_synapse_update[[i]] / (model$recurrent_synapse_update_old[[i]] + 0.000000001)
+      }
+      
+      return(model)
+    }
+    
+    #' @name epoch_print
+    #' @export
+    #' @title epoch printing for trainr
+    #' @description Print the error adn learning rate at each epoch of the trainr learning, called in epoch_function
+    #' @param model the output model object
+    #' @return nothing
+    
+    epoch_print = function(model){
+      message(paste0("Trained epoch: ",model$current_epoch," - Learning rate: ",model$learningrate))
+      message(paste0("Epoch error: ",colMeans(model$error)[model$current_epoch]))
+      return(model)
+    }
+    
+    #' @name epoch_annealing
+    #' @export
+    #' @title epoch annealing
+    #' @description Apply the learning rate decay to the learning rate, called in epoch_model_function
+    #' @param model the output model object
+    #' @return the updated model
+    
+    epoch_annealing = function(model){
+      model$learningrate = model$learningrate * model$learningrate_decay
+      return(model)
+    }
+    
+    #' @name loss_L1
+    #' @export
+    #' @title L1 loss
+    #' @description Apply the learning rate to the weight update, vocabulary to verify !!
+    #' @param model the output model object
+    #' @return the updated model
+    
+    loss_L1 = function(model){
+      if(model$network_type == "rnn"){
+        model$time_synapse_update = lapply(model$time_synapse_update,function(x){x* model$learningrate})
+        model$bias_synapse_update = lapply(model$bias_synapse_update,function(x){x* model$learningrate})
+        model$recurrent_synapse_update = lapply(model$recurrent_synapse_update,function(x){x* model$learningrate})
+      } else if(model$network_type == "lstm"){
+        model$recurrent_synapse_update  = lapply(model$recurrent_synapse_update,function(x){x * model$learningrate})
+        model$time_synapse_update       = lapply(model$time_synapse_update,function(x){x * model$learningrate})
+        model$bias_synapse_update       = lapply(model$bias_synapse_update, function(x){x * model$learningrate})
+      } else if(model$network_type == "gru"){
+        model$recurrent_synapse_update  = lapply(model$recurrent_synapse_update,function(x){x * model$learningrate})
+        model$time_synapse_update       = lapply(model$time_synapse_update,function(x){x * model$learningrate})
+        model$bias_synapse_update       = lapply(model$bias_synapse_update, function(x){x * model$learningrate})
+      }
+      return(model)
+    }
+    
+    
+    #' @name predictr
+    #' @export
+    #' @importFrom stats runif
+    #' @importFrom sigmoid sigmoid
+    #' @title Recurrent Neural Network
+    #' @description predict the output of a RNN model
+    #' @param model output of the trainr function
+    #' @param X array of input values, dim 1: samples, dim 2: time, dim 3: variables (could be 1 or more, if a matrix, will be coerce to array)
+    #' @param hidden should the function output the hidden units states
+    #' @param real_output option used when the function in called inside trainr, do not drop factor for 2 dimension array output and other actions. Let it to TRUE, the default, to let the function take care of the data.
+    #' @param ... arguments to pass on to sigmoid function
+    #' @return array or matrix of predicted values
+    #' @examples
+    #' \dontrun{ 
+    #' # create training numbers
+    #' X1 = sample(0:127, 10000, replace=TRUE)
+    #' X2 = sample(0:127, 10000, replace=TRUE)
+    #' 
+    #' # create training response numbers
+    #' Y <- X1 + X2
+    #' 
+    #' # convert to binary
+    #' X1 <- int2bin(X1)
+    #' X2 <- int2bin(X2)
+    #' Y  <- int2bin(Y)
+    #' 
+    #' # Create 3d array: dim 1: samples; dim 2: time; dim 3: variables.
+    #' X <- array( c(X1,X2), dim=c(dim(X1),2) )
+    #' 
+    #' # train the model
+    #' model <- trainr(Y=Y[,dim(Y)[2]:1],
+    #'                 X=X[,dim(X)[2]:1,],
+    #'                 learningrate   =  1,
+    #'                 hidden_dim     = 16 )
+    #'              
+    #' # create test inputs
+    #' A1 = int2bin( sample(0:127, 7000, replace=TRUE) )
+    #' A2 = int2bin( sample(0:127, 7000, replace=TRUE) )
+    #' 
+    #' # create 3d array: dim 1: samples; dim 2: time; dim 3: variables
+    #' A <- array( c(A1,A2), dim=c(dim(A1),2) )
+    #'     
+    #' # predict
+    #' B  <- predictr(model,
+    #'                A[,dim(A)[2]:1,]     )
+    #' B = B[,dim(B)[2]:1]
+    #' # convert back to integers
+    #' A1 <- bin2int(A1)
+    #' A2 <- bin2int(A2)
+    #' B  <- bin2int(B)
+    #'  
+    #' # inspect the differences              
+    #' table( B-(A1+A2) )
+    #' 
+    #' # plot the difference
+    #' hist(  B-(A1+A2) )
+    #' }
+    #' 
+    predictr = function(model, X, hidden = FALSE, real_output = T,...){
+      
+      # coerce to array if matrix
+      if(length(dim(X)) == 2){
+        X <- array(X,dim=c(dim(X),1))
+      }
+      
+      if(real_output && model$seq_to_seq_unsync){ ## here we modify the X in case of seq_2_seq & real_output to have the good dimensions
+        time_dim_input = dim(X)[2]
+        store = array(0, dim = c(dim(X)[1],model$time_dim,dim(X)[3]))
+        store[,1:dim(X)[2],] = X
+        X = store
+        rm(store)
+      }
+      
+      if(model$network_type == "rnn"){
+        store = predict_rnn(model, X, hidden, real_output,...)
+      } else if (model$network_type == "lstm"){
+        store = predict_lstm(model, X, hidden, real_output,...)
+      } else if (model$network_type == "gru"){
+        store = predict_gru(model, X, hidden, real_output,...)
+      }else{
+        stop("network_type_unknown for the prediction")
+      }
+      
+      if(real_output && model$seq_to_seq_unsync){
+        if(length(dim(store)) == 2){
+          store = store[,model$time_dim_input:model$time_dim,drop=F]
+        }else{
+          store = store[,model$time_dim_input:model$time_dim,,drop=F]
+        }
+      }
+      
+      return(store)
+    }
+    
+    #' @name predict_rnn
+    #' @importFrom stats runif
+    #' @importFrom sigmoid sigmoid
+    #' @title Recurrent Neural Network
+    #' @description predict the output of a RNN model
+    #' @param model output of the trainr function
+    #' @param X array of input values, dim 1: samples, dim 2: time, dim 3: variables (could be 1 or more, if a matrix, will be coerce to array)
+    #' @param hidden should the function output the hidden units states
+    #' @param real_output option used when the function in called inside trainr, do not drop factor for 2 dimension array output
+    #' @param ... arguments to pass on to sigmoid function
+    #' @return array or matrix of predicted values
+    
+    predict_rnn <- function(model, X, hidden = FALSE, real_output = T,...) {
+      
+      store <- list()
+      for(i in seq(length(model$synapse_dim) - 1)){
+        store[[i]] <- array(0,dim = c(dim(X)[1:2],model$synapse_dim[i+1]))
+      }
+      
+      # store the hidden layers values for each time step, needed in parallel of store because we need the t(-1) hidden states. otherwise, we could take the values from the store list
+      layers_values  = list()
+      for(i in seq(length(model$synapse_dim) - 2)){
+        layers_values[[i]] <- matrix(0,nrow=dim(X)[1], ncol = model$synapse_dim[i+1])
+      }
+      
+      for (position in 1:dim(X)[2]) {
+        
+        # generate input 
+        x = array(X[,position,],dim=dim(X)[c(1,3)])
+        
+        for(i in seq(length(model$synapse_dim) - 1)){
+          if (i == 1) { # first hidden layer, need to take x as input
+            store[[i]][,position,] <- (x %*% model$time_synapse[[i]]) + (layers_values[[i]] %*% model$recurrent_synapse[[i]])
+          } else if (i != length(model$synapse_dim) - 1 & i != 1){ #hidden layers not linked to input layer, depends of the last time step
+            store[[i]][,position,] <- (store[[i-1]][,position,] %*% model$time_synapse[[i]]) + (layers_values[[i]] %*% model$recurrent_synapse[[i]])
+          } else { # output layer depend only of the hidden layer of bellow
+            store[[i]][,position,] <- store[[i-1]][,position,] %*% model$time_synapse[[i]]
+          }
+          if(model$use_bias){ # apply the bias if applicable
+            store[[i]][,position,] <- store[[i]][,position,] + model$bias_synapse[[i]]
+          }
+          # apply the activation function
+          store[[i]][,position,] <- sigmoid(store[[i]][,position,], method=model$sigmoid)
+          
+          if(i != length(model$synapse_dim) - 1){ # for all hidden layers, we need the previous state, looks like we duplicate the values here, it is also in the store list
+            # store hidden layers so we can print it out. Needed for error calculation and weight iteration
+            layers_values[[i]] = store[[i]][,position,]
+          }
+        }
+      }
+      
+      # convert output to matrix if 2 dimensional, real_output argument added if used inside trainr
+      if(real_output){
+        if(dim(store[[length(store)]])[3]==1) {
+          store[[length(store)]] <- matrix(store[[length(store)]],
+                                           nrow = dim(store[[length(store)]])[1],
+                                           ncol = dim(store[[length(store)]])[2])
+        }
+      }
+      
+      # return output
+      if(hidden == FALSE){ # return only the last element of the list, i.e. the output
+        return(store[[length(store)]])
+      }else{ # return everything
+        return(store)
+      }
+    }
+    
+    #' @name predict_lstm
+    #' @importFrom stats runif
+    #' @importFrom sigmoid sigmoid
+    #' @title gru prediction function
+    #' @description predict the output of a lstm model
+    #' @param model output of the trainr function
+    #' @param X array of input values, dim 1: samples, dim 2: time, dim 3: variables (could be 1 or more, if a matrix, will be coerce to array)
+    #' @param hidden should the function output the hidden units states
+    #' @param real_output option used when the function in called inside trainr, do not drop factor for 2 dimension array output
+    #' @param ... arguments to pass on to sigmoid function
+    #' @return array or matrix of predicted values
+    
+    predict_lstm <- function(model, X, hidden = FALSE, real_output = T,...) {
+      
+      store <- list()
+      prev_layer_values = list()
+      c_t = list()
+      for(i in seq(length(model$hidden_dim))){
+        store[[i]] = array(0,dim = c(dim(X)[1:2],model$hidden_dim[i],6)) # 4d arrays !!!, hidden, cell, f, i, g, o
+        prev_layer_values[[i]]  = matrix(0,nrow=dim(X)[1], ncol = model$hidden_dim[i]) # we need this object because of t-1 which do not exist in store
+        c_t[[i]]         = matrix(0,nrow=dim(X)[1], ncol = model$hidden_dim[i]) # we need this object because of t-1 which do not exist in store
+      }
+      store[[length(store)+1]] <- array(0,dim = c(dim(X)[1:2],model$output_dim))
+      
+      for (position in 1:dim(X)[2]) {
+        
+        # generate input
+        x = array(X[,position,],dim=dim(X)[c(1,3)])
+        
+        for(i in seq(length(model$hidden_dim))){
+          # hidden layer (input ~+ prev_hidden)
+          f_t     = (x %*% array(model$time_synapse[[i]][,,1],dim=c(dim(model$time_synapse[[i]])[1:2]))) + (prev_layer_values[[i]] %*% array(model$recurrent_synapse[[i]][,,1],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) 
+          i_t     = (x %*% array(model$time_synapse[[i]][,,2],dim=c(dim(model$time_synapse[[i]])[1:2]))) + (prev_layer_values[[i]] %*% array(model$recurrent_synapse[[i]][,,2],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) 
+          c_in_t  = (x %*% array(model$time_synapse[[i]][,,3],dim=c(dim(model$time_synapse[[i]])[1:2]))) + (prev_layer_values[[i]] %*% array(model$recurrent_synapse[[i]][,,3],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) 
+          o_t     = (x %*% array(model$time_synapse[[i]][,,4],dim=c(dim(model$time_synapse[[i]])[1:2]))) + (prev_layer_values[[i]] %*% array(model$recurrent_synapse[[i]][,,4],dim=c(dim(model$recurrent_synapse[[i]])[1:2])))
+          if(model$use_bias){
+            f_t = f_t + model$bias_synapse[[i]][,1]
+            i_t = i_t + model$bias_synapse[[i]][,2]
+            c_in_t = c_in_t + model$bias_synapse[[i]][,3]
+            o_t = o_t + model$bias_synapse[[i]][,4]
+          }
+          f_t = sigmoid(f_t)
+          i_t = sigmoid(i_t)
+          c_in_t = tanh(c_in_t)
+          o_t = sigmoid(o_t)
+          
+          c_t[[i]]     = f_t * c_t[[i]] + (i_t * c_in_t)
+          store[[i]][,position,,1] = o_t * tanh(c_t[[i]])
+          store[[i]][,position,,2] = c_t[[i]]
+          store[[i]][,position,,3] = f_t
+          store[[i]][,position,,4] = i_t
+          store[[i]][,position,,5] = c_in_t
+          store[[i]][,position,,6] = o_t
+          
+          # replace the x in case of multi layer
+          prev_layer_values[[i]] = x = o_t * tanh(c_t[[i]])# the top of this layer at this position is the past of the top layer at the next position
+        }
+        
+        
+        # output layer (new binary representation)
+        store[[length(store)]][,position,] = store[[length(store) - 1]][,position,,1] %*% model$time_synapse[[length(model$time_synapse)]]
+        if(model$use_bias){
+          store[[length(store)]][,position,] = store[[length(store)]][,position,] + model$bias_synapse[[length(model$bias_synapse)]]
+        }
+        store[[length(store)]][,position,] = sigmoid(store[[length(store)]][,position,])
+      } # end time loop
+      
+      # convert output to matrix if 2 dimensional, real_output argument added if used inside trainr
+      if(real_output){
+        if(dim(store[[length(store)]])[3]==1) {
+          store[[length(store)]] <- matrix(store[[length(store)]],
+                                           nrow = dim(store[[length(store)]])[1],
+                                           ncol = dim(store[[length(store)]])[2])
+        }
+      }
+      
+      # return output
+      if(hidden == FALSE){ # return only the last element of the list, i.e. the output
+        return(store[[length(store)]])
+      }else{ # return everything
+        return(store)
+      }
+    }
+    
+    
+    
+    #' @name predict_gru
+    #' @importFrom stats runif
+    #' @importFrom sigmoid sigmoid
+    #' @title gru prediction function
+    #' @description predict the output of a gru model
+    #' @param model output of the trainr function
+    #' @param X array of input values, dim 1: samples, dim 2: time, dim 3: variables (could be 1 or more, if a matrix, will be coerce to array)
+    #' @param hidden should the function output the hidden units states
+    #' @param real_output option used when the function in called inside trainr, do not drop factor for 2 dimension array output
+    #' @param ... arguments to pass on to sigmoid function
+    #' @return array or matrix of predicted values
+    
+    predict_gru <- function(model, X, hidden = FALSE, real_output = T,...) {
+      
+      store <- list()
+      h_t = list()
+      for(i in seq(length(model$hidden_dim))){
+        store[[i]] = array(0,dim = c(dim(X)[1:2],model$hidden_dim[i],4)) # 4d arrays !!!, hidden, z, r, h
+        h_t[[i]]         = matrix(0,nrow=dim(X)[1], ncol = model$hidden_dim[i]) # we need this object because of t-1 which do not exist in store
+      }
+      store[[length(store)+1]] <- array(0,dim = c(dim(X)[1:2],model$output_dim))
+      
+      for (position in 1:dim(X)[2]) {
+        
+        # generate input
+        x = array(X[,position,],dim=dim(X)[c(1,3)])
+        
+        for(i in seq(length(model$hidden_dim))){
+          # hidden layer (input ~+ prev_hidden)
+          z_t     = (x %*% array(model$time_synapse[[i]][,,1],dim=c(dim(model$time_synapse[[i]])[1:2]))) + (h_t[[i]]  %*% array(model$recurrent_synapse[[i]][,,1],dim=c(dim(model$recurrent_synapse[[i]])[1:2]))) 
+          r_t     = (x %*% array(model$time_synapse[[i]][,,2],dim=c(dim(model$time_synapse[[i]])[1:2]))) + (h_t[[i]]  %*% array(model$recurrent_synapse[[i]][,,2],dim=c(dim(model$recurrent_synapse[[i]])[1:2])))
+          if(model$use_bias){
+            z_t = z_t + model$bias_synapse[[i]][,1]
+            r_t = r_t + model$bias_synapse[[i]][,2]
+          }
+          z_t = sigmoid(z_t)
+          r_t = sigmoid(r_t)
+          
+          h_in_t  = (x %*% array(model$time_synapse[[i]][,,3],dim=c(dim(model$time_synapse[[i]])[1:2]))) + ((h_t[[i]]  * r_t) %*% array(model$recurrent_synapse[[i]][,,3],dim=c(dim(model$recurrent_synapse[[i]])[1:2])))
+          if(model$use_bias){
+            h_in_t = h_in_t + model$bias_synapse[[i]][,3]
+          }
+          h_in_t = tanh(h_in_t)
+          
+          h_t[[i]]     = (1 - z_t) * h_t[[i]] + (z_t * h_in_t)
+          store[[i]][,position,,1] = h_t[[i]]
+          store[[i]][,position,,2] = z_t
+          store[[i]][,position,,3] = r_t
+          store[[i]][,position,,4] = h_in_t
+          
+          # replace the x in case of multi layer
+          x = h_t[[i]]  # the top of this layer at this position is the past of the top layer at the next position
+        }
+        
+        
+        # output layer (new binary representation)
+        store[[length(store)]][,position,] = store[[length(store) - 1]][,position,,1] %*% model$time_synapse[[length(model$time_synapse)]]
+        if(model$use_bias){
+          store[[length(store)]][,position,] = store[[length(store)]][,position,] + model$bias_synapse[[length(model$bias_synapse)]]
+        }
+        store[[length(store)]][,position,] = sigmoid(store[[length(store)]][,position,])
+      } # end time loop
+      
+      # convert output to matrix if 2 dimensional, real_output argument added if used inside trainr
+      if(real_output){
+        if(dim(store[[length(store)]])[3]==1) {
+          store[[length(store)]] <- matrix(store[[length(store)]],
+                                           nrow = dim(store[[length(store)]])[1],
+                                           ncol = dim(store[[length(store)]])[2])
+        }
+      }
+      
+      # return output
+      if(hidden == FALSE){ # return only the last element of the list, i.e. the output
+        return(store[[length(store)]])
+      }else{ # return everything
+        return(store)
+      }
+    }
+    
+    
+    
+    ####
+    
+    error<-as.data.frame(c(1:epochD))
+    colnames(error)<-"Iteration"
+    
+   rnn<- function (Y, X, model = NULL, learningrate, learningrate_decay = 1, 
+              momentum = 0, hidden_dim = c(10), network_type = "rnn", numepochs = 1, 
+              sigmoid = c("logistic", "Gompertz", "tanh"), use_bias = F, 
+              batch_size = 1, seq_to_seq_unsync = F, update_rule = "sgd", 
+              epoch_function = c(epoch_print, epoch_annealing), loss_function = loss_L1, 
+              ...) 
+    
+    {
+      sigmoid <- match.arg(sigmoid)
+      if (length(dim(X)) == 2) {
+        X <- array(X, dim = c(dim(X), 1))
+      }
+      if (length(dim(Y)) == 2) {
+        Y <- array(Y, dim = c(dim(Y), 1))
+      }
+      if (seq_to_seq_unsync) {
+        time_dim_input = dim(X)[2]
+        store = array(0, dim = c(dim(X)[1], dim(X)[2] + dim(Y)[2] - 
+                                   1, dim(X)[3]))
+        store[, 1:dim(X)[2], ] = X
+        X = store
+        store = array(0, dim = c(dim(X)[1], time_dim_input + 
+                                   dim(Y)[2] - 1, dim(Y)[3]))
+        store[, time_dim_input:dim(store)[2], ] = Y
+        Y = store
+      }
+      if (dim(X)[2] != dim(Y)[2] && !seq_to_seq_unsync) {
+        stop("The time dimension of X is different from the time dimension of Y. seq_to_seq_unsync is set to FALSE")
+      }
+      if (dim(X)[1] != dim(Y)[1]) {
+        stop("The sample dimension of X is different from the sample dimension of Y.")
+      }
+      if (is.null(model)) {
+        model = list(...)
+        model$input_dim = dim(X)[3]
+        model$hidden_dim = hidden_dim
+        model$output_dim = dim(Y)[3]
+        model$synapse_dim = c(model$input_dim, model$hidden_dim, 
+                              model$output_dim)
+        model$time_dim = dim(X)[2]
+        model$sigmoid = sigmoid
+        model$network_type = network_type
+        model$numepochs = numepochs
+        model$batch_size = batch_size
+        model$learningrate = learningrate
+        model$learningrate_decay = learningrate_decay
+        model$momentum = momentum
+        model$update_rule = update_rule
+        model$use_bias = use_bias
+        model$seq_to_seq_unsync = seq_to_seq_unsync
+        model$epoch_function = epoch_function
+        model$loss_function = loss_function
+        model$last_layer_error = Y * 0
+        model$last_layer_delta = Y * 0
+        if ("epoch_model_function" %in% names(model)) {
+          stop("epoch_model_function is not used anymore, use epoch_function and return the model inside.")
+        }
+        if (seq_to_seq_unsync) {
+          model$time_dim_input = time_dim_input
+        }
+        if (model$update_rule == "adagrad") {
+          message("adagrad update, loss function not used and momentum set to 0")
+          model$momentum = 0
+        }
+        model <- init_r(model)
+        model$error <- array(0, dim = c(dim(Y)[1], model$numepochs))
+      }
+      else {
+        message("retraining, all options except X, Y and the model itself are ignored, error are reseted")
+        if (model$input_dim != dim(X)[3]) {
+          stop("input dim changed")
+        }
+        if (model$time_dim != dim(X)[2]) {
+          stop("time dim changed")
+        }
+        if (model$output_dim != dim(Y)[3]) {
+          stop("output dim changed")
+        }
+        if (seq_to_seq_unsync && model$time_dim_input != time_dim_input) {
+          stop("time input dim changed")
+        }
+        model$error <- array(0, dim = c(dim(Y)[1], model$numepochs))
+      }
+      for (epoch in seq(model$numepochs)) {
+        error$error[epoch]<-colMeans(model$error)[model$current_epoch]
+ 
+        incProgress(1/model$numepochs, detail = paste("Learning Rate:",
+                                      lr, "Neurons in Recursive Neural Network:",nn, "Iteration:", model$current_epoch,
+                                      "Error:", colMeans(model$error)[model$current_epoch] ))
+        
+        
+        model$current_epoch = epoch
+        index = sample(seq(round(dim(Y)[1]/model$batch_size)), 
+                       dim(Y)[1], replace = T)
+        lj = list()
+        for (i in seq(round(dim(Y)[1]/model$batch_size))) {
+          lj[[i]] = seq(dim(Y)[1])[index == i]
+        }
+        lj[unlist(lapply(lj, length)) < 1] = NULL
+        for (j in lj) {
+          a = X[j, , , drop = F]
+          c = Y[j, , , drop = F]
+          store = predictr(model, a, hidden = T, real_output = F)
+          if (model$network_type == "rnn") {
+            for (i in seq(length(model$synapse_dim) - 1)) {
+              model$store[[i]][j, , ] = store[[i]]
+            }
+          }
+          else if (model$network_type == "lstm" | model$network_type == 
+                   "gru") {
+            for (i in seq(length(model$hidden_dim))) {
+              model$store[[i]][j, , , ] = store[[i]]
+            }
+            model$store[[length(model$hidden_dim) + 1]][j, 
+                                                        , ] = store[[length(model$hidden_dim) + 1]]
+          }
+          model = backprop_r(model, a, c, j)
+          if (model$update_rule == "sgd") {
+            model = model$loss_function(model)
+          }
+          model = update_r(model)
+        }
+        for (i in model$epoch_function) {
+          model <- i(model)
+          if (!is.list(model)) {
+            stop("one epoch function didn't return the model.")
+          }
+        }
+      
+        
+        
+      }
+      if (colMeans(model$error)[epoch] <= min(colMeans(model$error)[1:epoch])) {
+        model$store_best <- model$store
+      }
+      attr(model, "error") <- colMeans(model$error)
+     
+      
+      return(model)
+    }
+    
+   withProgress(message = 'Training Model:', value = 0, {
+     
+     
+     
+   model <- rnn(X = X.train,
+                   Y = y.train,
+                   learningrate = lr,
+                  
+                   sigmoid = c("Gompertz"),
+                   numepochs = epochD,
+                   hidden_dim = nn)
+   
+   })
+
+   
+   xtest <- df[,1:ncol(df),]
+   xtest<- array(xtest, dim=c(1,ncol(df),28))
+   predicted<-predictr(model, xtest)
+   
+   forplot<-as.data.frame(t(predicted))
+   colnames(forplot)<-"predicted"
+   
+   forplot$real<-df[1,1:ncol(df),Pred]
+   
+   forplot$time<-c(1:nrow(forplot))
+   forplot$date<-Values$Local.time
+   
+   Values$Predicted<-(t(predicted)*(max(Values$Open)-min(Values$Open)))+min(Values$Open)
+      
+   error$error<-model$error[1,]
+   output$Plot <- renderPlot({
+
+     P<-ggplot(forplot)+
+  geom_line(aes(y=predicted, x=time ), colour="red")+
+  geom_line(aes(y=real, x=time ), colour="blue")+
+       xlim(L,ncol(forplot))+
+       xlab("Time (10M)")+
+       ylab("Relative Price (0-1)")+
+       theme_minimal(base_size = 20)+
+       ggtitle("Predicted Prices")+
+       ylim(0,1)
+       
+
+print(P)
+     
+   })
+   
+   output$Plot2 <- renderPlot({
+     
+     Q<-ggplot(error)+
+       geom_line(aes(y=error, x=Iteration ), colour="red")+
+
+       
+       xlab("Epoch")+
+       ylab("Error")+
+       theme_minimal(base_size = 20)+
+       ggtitle("Error/Iteration")
+     
+     
+     print(Q)
+     
+   })
+   
+   
+   
+   output$summary <- renderTable({
+     Values
+   })
+      
+
+  })
+   
+  output$help <- renderUI({
+    
+    HTML(paste(
+      "","This application explores the possibilities of using a recursive neural network (RNN) to predict pseudo-stochastic time series.",
+      "Forex (Foreign Exchange) is a highly dynamic and stochastic market which can be used to benchmark RNN", 
+      "The application loads the price series and volumes from 7 different markets and use the interrelations among them to predict the price of currency 10 minutes after the last observation.",
+      "Since the time-frame is 10 minutes the algorithm must analyze the last 3000 time points and find a pattern to predict the forthcoming values.",
+      "","The application uses four parameters:","",
+      "<b>Iterations:</b> Number of times that the dataset is presented to the algorithm. The higher the better but the slower. How new iterations improve the performance can be observed in the Error/Iteration plot",
+      "","<b>Events Used for Training:</b> The number previous events are used to predict the coming events, the higher the better","",
+      "<b>Neurons in the RNN:</b> RNN are special types of Neural Networks so it is possible to adjust the number of neurons in the deep layer, the effect of this number in the performance depends on the dataset","",
+      "<b>Learning Rate:</b> This represents the size of the steps used to optimize the model. Low values are better but slower","",
+      sep = "</br>"
+      
+    ))
+    
   })
   
-  output$scatter <- renderPlot({
-    p <- ggplot(subsetted(), aes(!!input$xvar, !!input$yvar)) + list(
-      theme(legend.position = "bottom"),
-      if (input$by_species) aes(color=Species),
-      geom_point(),
-      if (input$smooth) geom_smooth()
-    )
-
-    if (input$show_margins) {
-      margin_type <- if (input$by_species) "density" else "histogram"
-      p <- p |> ggExtra::ggMarginal(type = margin_type, margins = "both",
-        size = 8, groupColour = input$by_species, groupFill = input$by_species)
-    }
-    
-    p
-  }, res = 100)
+
 }
 
-shinyApp(ui, server)
+# Run the application 
+shinyApp(ui = ui, server = server)
+