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+#' @description
+#' A short description...
+#' Plot the fundamental diagram and its envelope
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param date_range Date vector. example: c('2021-01-01','2022-01-01'). Full period if NULL (default).
+#' @param segments Character vector. Selected road segment, all if NULL (default).
+#' @param weekday_choice weekday Character vector. Weekday choosen. Default to the all week.
+#' @param hour_choice Integer vector. Hours choosen, default to the all day.
+#' @param vacation_choice Character vector. Selected vacation. Full period by default (NULL).
+#' @param holiday_choise Boolean. Selected holiday.  Full period by default (NULL).
+#' @param direction_choice Character Direction choosen. Default to NULL.
+#' @param NumberOfSlope Integer. Number of slope tested. Default to 50.
+#' @param NumberOfOrdinate Integer. Number of ordinate tested. Default to 45.
+#' 
+#' 
+#' @return 
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#' @import ggplot2
+#'
+#' @examples
+#' plot_diagram_envelop(traffic)
+#' plot_diagram_envelop(traffic,
+#'   date_range = c('2022-07-01','2022-09-01'),
+#'   weekday_choice= c('monday','friday','sunday),
+#'   hour_choice= c(1,5,10,14,21),
+#'   vacation_choice=NULL,
+#'   holiday_choice=TRUE,
+#'   segments = 'RteVitre-06',
+#'   NumberOfSlope=60,
+#'   NumberOfOrdinate=65,
+#'   direction_choice='lft)
+
+
+plot_diagram_envelop <- function (enriched_data,
+                                     date_range = NULL,
+                                     weekday_choice = NULL,
+                                     hour_choice = NULL,
+                                     vacation_choice=NULL,
+                                     holiday_choice=NULL,
+                                     segments = NULL,
+                                     direction_choice=NULL,
+                                     NumberOfSlope=50,
+                                     NumberOfOrdinate=45)
+{
+  enriched_data<-filter_demand_user(enriched_data,segments,date_range,weekday_choice,hour_choice,
+                                    vacation_choice,holiday_choice)
+  
+  id_seg<-unique(enriched_data$segment_id)
+  
+  #Plot the fundamental diagram for each sensor
+  for (id in id_seg)
+  {
+    df<-enriched_data[enriched_data$segment_id==id,]
+    
+    df<-create_necessary_column(df)
+    list_charac<-calculate_characteristic(df ,direction_choice)
+    df<-calculate_data_dimensionless(df,direction_choice,list_charac)
+    
+    list_final_1<-calculate_necessary_data(df,NumberOfSlope,NumberOfOrdinate,
+                                           slope=c(-2,-0.1),ordinate=c(1,1.5),direction_choice)
+    
+    list_final_2<-calculate_necessary_data(df,NumberOfSlope,NumberOfOrdinate,
+                                           slope=c(-6,list_final_1$a),
+                                           ordinate=c(list_final_1$b,4*list_final_1$b),
+                                           direction_choice)
+    
+    # Repasser en données dimensionnées 
+    list_final_1$a<-list_charac$speed*list_final_1$a/list_charac$density
+    list_final_1$b<-list_charac$speed*list_final_1$b
+    
+    list_final_2$a<-list_charac$speed*list_final_2$a/list_charac$density
+    list_final_2$b<-list_charac$speed*list_final_2$b
+    
+    # Affiche le diagramme et les droites
+    plot(plot_lines(df,list_final_1,list_final_2,direction_choice))
+  }
+}
+
+#' @description
+#' A short description...
+#' Filter the dataframe from user's demand
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param date_range Date vector. example: c('2021-01-01','2022-01-01'). Full period if NULL (default).
+#' @param segments Character vector. Selected road segment, all if NULL (default).
+#' @param weekday_choice weekday Character vector. Weekday choosen. Default to the all week.
+#' @param hour_choice Integer vector. Hours choosen, default to the all day.
+#' @param vacation_choice Character vector. Selected vacation. Full period by default (NULL).
+#' @param holiday_choise Boolean. Selected holiday.  Full period by default (NULL).
+#'  
+#' @return enriched_data 
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' filter_demand_user(traffic)
+#' filter_demand_user(traffic,
+#'  date_range = c('2022-07-01','2022-09-01'),
+#'  weekday_choice= c('monday','friday','sunday),
+#'  hour_choice= c(1,5,10,14,21),
+#'  vacation_choice=NULL,
+#'  holiday_choice=TRUE,
+#'  segments = 'RteVitre-06')
+
+filter_demand_user<-function (enriched_data,
+                              segments=NULL,
+                              date_range=NULL,
+                              weekday_choice=NULL,
+                              hour_choice=NULL,
+                              vacation_choice=NULL,
+                              holiday_choice=NULL)
+{
+  if(!is.null(segments))
+  {enriched_data<-enriched_data %>% filter(segment_name %in% segments)}
+  
+  if(!is.null(date_range))
+  {enriched_data<-enriched_data[enriched_data$day>=date[1] & enriched_data$day<= date[2],]}
+  
+  enriched_data$weekday<-tolower(enriched_data$weekday)
+  tolower(weekday_choice)
+  
+  if(!is.null(weekday_choice))
+  { enriched_data<-enriched_data %>% filter(weekday %in% weekday_choice)}
+  
+  if(!is.null(hour_choice))
+  {enriched_data<-enriched_data %>% filter(hour %in% hour_choice)}
+  
+  if(!is.null(vacation_choice))
+  {
+    if(vacation_choice==FALSE)
+      {enriched_data<-enriched_data[enriched_data$vacation!='no vacation',]}
+    
+    else
+    {enriched_data<-enriched_data[enriched_data$vacation=='no vacation',]}
+  }
+  
+  if(!is.null(holiday_choice))
+  {enriched_data<-enriched_data %>% filter(holiday %in% holiday_choice)}
+  
+  enriched_data$weekend<-ifelse(enriched_data$weekday %in% c('saturday','sunday'), "Weekend", "Week")
+  return(enriched_data)
+}
+
+#' @description
+#' A short description...
+#' Create the necessary columns to have the final envelope of the fundamental diagram.
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' 
+#' @return enriched_data
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' create_necessary_column(traffic)
+
+create_necessary_column <- function (enriched_data)
+{
+  if("speed_hist_car_lft" %in% colnames(enriched_data))
+  {enriched_data<-restore_v85(enriched_data)}
+  
+  enriched_data<-retrieve_missing_data(enriched_data)
+  
+  enriched_data<-calculate_axes(enriched_data)
+  
+  return(enriched_data)
+}
+
+#' Restore the v85 by direction from speed_hist_car
+#'
+#' Add two colums in the dataframe : v85_lft and v85_rgt
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#'
+#' @return enriched_data 
+#' @export
+#'
+#' @examples
+#' restore_v85(enriched_data)
+
+
+restore_v85<-function(enriched_data)
+{
+  
+  speed<-seq(5,125,by=5)
+  
+  
+  enriched_data$v85_lft<-0
+  enriched_data$v85_rgt<-0
+  
+  for (i in 1:length(enriched_data$car))
+  {
+    #Left
+    vec<-enriched_data$speed_hist_car_lft[i]
+    elements <- strsplit(vec, ",")[[1]]
+    elements[1]<- gsub("\\[", "", elements[1])
+    elements[25]<- gsub("\\]", "", elements[25])
+    vector <- as.numeric(elements)
+    per_vec <- sum(vector)
+    per_85 <- 0.85*per_vec
+    j<-1
+    sum<-0
+    
+    while (sum<per_85 & j<length(vector))
+    {
+      sum<-sum+vector[j]
+      j<-j+1
+    }
+    enriched_data$v85_lft[i]<-speed[j]
+    
+    #Right
+    vec<-enriched_data$speed_hist_car_rgt[i]
+    elements <- strsplit(vec, ",")[[1]]
+    elements[1]<- gsub("\\[", "", elements[1])
+    elements[25]<- gsub("\\]", "", elements[25])
+    vector <- as.numeric(elements)
+    per_vec <- sum(vector)
+    per_85 <- 0.85*per_vec    
+    j<-1
+    sum<-0
+    
+    while (sum<per_85 & j<length(vector))
+    {
+      sum<-sum+vector[j]
+      j<-j+1
+    }
+    enriched_data$v85_rgt[i]<-speed[j]
+  }
+  return(enriched_data)
+}
+
+#' @description
+#' A short description...
+#' Calculate necessary data to trace the axes of the fundamental diagram
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#'  
+#' @return enriched_data 
+#' @export
+#'
+#'
+#' @examples
+#' calculate_axes(traffic)
+
+calculate_axes<-function(enriched_data)
+{
+  enriched_data$veh_h<-enriched_data$car
+  enriched_data$km_h<-enriched_data$v85
+  enriched_data$veh_km<-0
+  for(i in 1:length(enriched_data$veh_km))
+  {enriched_data$veh_km[i]<-enriched_data$veh_h[i]/enriched_data$km_h[i]}
+  
+  
+  if("speed_hist_car_lft" %in% colnames(enriched_data))   
+  {
+    enriched_data$veh_h_lft<-enriched_data$car_lft*4
+    enriched_data$km_h_lft<-enriched_data$v85_lft
+    enriched_data$veh_km_lft<-0
+    
+    enriched_data$veh_h_rgt<-enriched_data$car_rgt*4
+    enriched_data$km_h_rgt<-enriched_data$v85_rgt
+    enriched_data$veh_km_rgt<-0
+    
+    for(i in 1:length(enriched_data$car))
+    {
+      enriched_data$veh_km_lft[i]<-enriched_data$veh_h_lft[i]/enriched_data$km_h_lft[i]
+      enriched_data$veh_km_rgt[i]<-enriched_data$veh_h_rgt[i]/enriched_data$km_h_rgt[i]
+    }
+  }
+  return(enriched_data)
+}
+
+#' @description
+#' A short description...
+#' Calculate characteristics values of the fundamental diagram. 
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param direction_choice Character. Direction choosen. Default to NULL.
+#' 
+#' @return list(flow,speed,density)
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' calculate_characteristic(traffic)
+#' calculate_characteristic(traffic,
+#'   direction_choice='lft')
+
+calculate_characteristic<- function (enriched_data,
+                                     direction_choice=NULL)
+{
+  if(is.null(direction_choice) || !("speed_hist_car_lft" %in% colnames(enriched_data)))
+  {
+    density <- sum(enriched_data$veh_km,na.rm = TRUE)/length(enriched_data$veh_km)
+    speed<- sum(enriched_data$km_h,na.rm = TRUE)/length(enriched_data$km_h)
+    flow<- sum(enriched_data$veh_h,na.rm = TRUE)/length(enriched_data$veh_h)
+  }
+  
+  
+  else if (direction_choice=='lft')
+  {
+    density<-sum(enriched_data$veh_km_lft,na.rm = TRUE)/length(enriched_data$veh_km_lft)
+    speed<-sum(enriched_data$km_h_lft,na.rm = TRUE)/length(enriched_data$km_h_lft)
+    flow<- sum(enriched_data$veh_h_lft,na.rm = TRUE)/length(enriched_data$veh_h_lft)
+  }
+  
+  else
+  {
+    density<-sum(enriched_data$veh_km_rgt,na.rm = TRUE)/length(enriched_data$veh_km_rgt)
+    speed<-sum(enriched_data$km_h_rgt,na.rm = TRUE)/length(enriched_data$km_h_rgt)
+    flow<- sum(enriched_data$veh_h_rgt,na.rm = TRUE)/length(enriched_data$veh_h_rgt)
+  }
+  
+  
+  return(list(flow=flow,speed=speed,density=density)) 
+  
+}
+
+#' @description
+#' A short description...
+#' Create news columns to have dimensionless data.
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param direction_choice Character Direction choosen. Default to NULL.
+#' @param list_charac List of Reals. Characteristics values.
+#' 
+#' @return enriched_data
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' calculate_data_dimensionless(traffic,
+#'   direction_choice='lft,
+#'   list_charac=calculate_characteristic(traffic))
+
+
+calculate_data_dimensionless<- function (enriched_data,
+                                         direction_choice=NULL,
+                                         list_charac)
+{
+  if(!("speed_hist_car_lft" %in% colnames(enriched_data)) || is.null(direction_choice))
+  {
+    enriched_data <- enriched_data %>% 
+      mutate (
+        veh_km_adim=veh_km/list_charac$density,
+        km_h_adim=km_h/list_charac$speed,
+        veh_h_adim= veh_h/list_charac$flow)
+  }
+  
+  else if (direction_choice=='lft')
+  {
+    enriched_data <- enriched_data %>% 
+      mutate (
+        veh_km_lft_adim=veh_km_lft/list_charac$density,
+        km_h_lft_adim=km_h_lft/list_charac$speed,
+        veh_h_lft_adim=veh_h_lft/list_charac$flow)
+  }
+  
+  else
+  {
+    enriched_data <- enriched_data %>% 
+      mutate (
+        veh_km_rgt_adim=veh_km_rgt/list_charac$density,
+        km_h_rgt_adim=km_h_rgt/list_charac$speed,
+        veh_h_rgt_adim=veh_h_rgt/list_charac$flow)
+  }
+  
+  return(enriched_data)
+  
+}
+
+#' @description
+#' A short description...
+#' Calculate a and b from the equation y=ax+b
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param NumberOfSlope Integer. Number of slope tested. Default to 50.
+#' @param NumberOfOrdinate Integer. Number of ordinate tested. Default to 45.
+#' @param slope Real vector. vector of 2 reals.
+#' @param ordinate Real vector. vector of 2 reals.
+#' @param direction_choice Character. Direction choosen.default to NULL.
+#' 
+#' @return list(a,b)
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' calculate_necessary_data (traffic,
+#'   NumberOfSlope=60,
+#'   NumberOfOrdinate=65,
+#'   slope=c(-2,-0.1),
+#'   ordinate=c(1,1.5),
+#'   direction_choice=NULL)
+
+calculate_necessary_data <- function (enriched_data,
+                                      NumberOfSlope=50,
+                                      NumberOfOrdinate=45,
+                                      slope,
+                                      ordinate,
+                                      direction_choice=NULL)
+{
+  percent<-95
+  
+  for(i in 1:2)
+  {
+  # Create vectors to have the values we want to test
+  slope_line<-seq(from=slope[1],to=slope[2],length.out=NumberOfSlope)
+  ordinate_line<-seq(from=ordinate[1],to=ordinate[2],length.out=NumberOfOrdinate)
+  
+  # Percent of the point under the line
+  mat_inter<-count_point(enriched_data,slope_line,ordinate_line,direction_choice,
+                         NumberOfSlope,NumberOfOrdinate,percent)
+  
+  # Calculate the alpha slope
+  alpha<-calculate_interpolation_line(ordinate_line,mat_inter,
+                                      NumberOfSlope,NumberOfOrdinate)
+  
+  # Calculate the final line
+  final_slope<-slope_line[which(alpha==max(alpha))]
+  final_ordinate<-ordinate_line[mat_inter[which(alpha==max(alpha)),NumberOfOrdinate+1]]
+  
+  # Update data for the following loop
+  percent<- 98
+  slope<-c(final_slope,final_slope)
+  ordinate<-c(final_ordinate,4*final_ordinate)
+  
+  }
+  final_slope<-final_slope[1]
+  final_ordinate<-final_ordinate[1]
+  
+  return(list(a=final_slope,b=final_ordinate))
+}
+
+#' @description
+#' A short description...
+#' Calculate the percent of point under the line tested.
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param slope_line Real vector. Slope tested.Length vector = NumberOfSlope.
+#' @param ordinate_line Real vector. Ordinate tested.Length vector = NumberOfOrdinate.
+#' @param direction_choice Character. Direction choosen.
+#' @param NumberOfSlope Integer. Number of slope tested. Default to 50.
+#' @param NumberOfOrdinate Integer. Number of ordinate tested. Default to 45.
+#' @param percent Real. Percent of point under which we want the number of points.
+#' 
+#' @return mat_inter
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' count_point(traffic,
+#'   slope_line=seq(from=-2,to=-0.1,length.out=50),
+#'   ordinate_line=seq(from=1,to=1.5,length.out=45),
+#'   direction_choice='lft',
+#'   NumberOfSlope=50,
+#'   NumberofOrdinate=45,
+#'   percent=95)
+
+
+count_point<-function(enriched_data,
+                      slope_line,
+                      ordinate_line,
+                      direction_choice=NULL,
+                      NumberOfSlope=50,
+                      NumberOfordiante=45,
+                      percent)
+  
+{
+  if(is.null(direction_choice) || !("speed_hist_car_lft" %in% colnames(enriched_data)) )
+  {
+    abcissa_point<-enriched_data$veh_km_adim
+    ordinate_point<-enriched_data$km_h_adim
+  }
+  
+  else if (direction_choice=='lft')
+  {
+    abcissa_point<-enriched_data$veh_km_lft_adim
+    ordinate_point<-enriched_data$km_h_lft_adim
+  }
+  
+  else
+  {
+    abcissa_point<-enriched_data$veh_km_rgt_adim
+    ordinate_point<-enriched_data$km_h_rgt_adim
+  }
+  
+  
+  mat_inter<-matrix(0,nrow=NumberOfSlope,ncol=NumberOfordiante+1)
+    
+  for(a in 1:NumberOfSlope)
+  {
+    test_slope<-slope_line[a]
+      
+    for(b in 1:NumberOfordiante)
+    {
+      test_ordinate<-ordinate_line[b]
+      length_vector<-0  
+      
+      NumberOfPoint<-0
+      for(i in 1:length(abcissa_point))
+      {
+        if(!is.na(abcissa_point[i]))
+        {
+          length_vector<-length_vector+1
+          test_equation<-test_slope*abcissa_point[i]+test_ordinate
+          if(ordinate_point[i]<test_equation){NumberOfPoint<-NumberOfPoint+1}
+        }
+        
+      }
+      mat_inter[a,b]<-100*NumberOfPoint/length_vector
+      if( mat_inter[a,b]>=percent & mat_inter[a,NumberOfordiante+1]==0)
+        {mat_inter[a,NumberOfordiante+1]=b}
+    }
+    if(mat_inter[a,NumberOfordiante+1]==0)
+      {mat_inter[a,NumberOfordiante+1]=1}
+  }
+  
+ return(mat_inter)
+}
+
+#' @description
+#' A short description...
+#' Calculate the slope of the interpolation line for each slope tested.
+#'
+#'
+#' @param ordinate_line Real vector. Ordinate test.Length vector = NumberOfOrdinate.
+#' @param mat_inter Real matrix. Percent of point under the tested line. Matrix result of the function 'count_point'
+#' @param NumberOfSlope Integer. Number of slope tested. Default to 50.
+#' @param NumberOfOrdinate Integer. Number of ordinate tested. Default to 45.
+#' 
+#' @return alpha
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#'
+#' @examples
+#' calculate_interpolation_line(ordinate_line,
+#'   mat_inter,
+#'   NumberOfSlope=60,
+#'   NumberOfOrdinate=65)
+
+calculate_interpolation_line<-function (ordinate_line,
+                                        mat_inter,
+                                        NumberOfSlope=50,
+                                        NumberOfOrdinate=45)
+{
+  alpha<-rep(0,NumberOfSlope)
+  
+  for (i in 1:NumberOfSlope) 
+  {
+    if(mat_inter[i,NumberOfOrdinate+1] > 1)
+    {
+    xout <- seq(ordinate_line[mat_inter[i,NumberOfOrdinate+1]-1],
+                ordinate_line[mat_inter[i,NumberOfOrdinate+1]], 
+                by = ordinate_line[mat_inter[i,NumberOfOrdinate+1]]-ordinate_line[mat_inter[i,NumberOfOrdinate+1]-1])
+    interpolated <- approx(ordinate_line,mat_inter[i,1:NumberOfOrdinate], xout = xout,method = 'linear')
+    x_interp <- interpolated$x
+    y_interp <- interpolated$y
+    alpha[i]<- (y_interp[2]-y_interp[1])/(x_interp[2]-x_interp[1])
+    }
+  }
+  
+  return(alpha)
+}
+
+#' @description
+#' A short description...
+#' Plot the fundamental diagram and its envelope.
+#'
+#'
+#' @param enriched_data enriched data.frame containing all the data for all your sensors
+#' @param list_final_1 List of reals. Values of the line's equation.
+#' @param list_final_2 List of reals. Values of the line's equation.
+#' @param direction_choice Character Direction choosen. Default to NULL.
+#' 
+#' @return 
+#' @export
+#'
+#' @import dplyr
+#' @import lubridate
+#' @import ggplot2
+#'
+#' @examples
+#' plot_lines(traffic,
+#'   list_final_1=c(-0.1,70),
+#'   list_final_2=c(-5,80),
+#'   direction_choice=NULL)
+
+plot_lines <- function (enriched_data,
+                        list_final_1,
+                        list_final_2,
+                        direction_choice=NULL)
+{
+  #Define the axes of the diagram
+  if(!("speed_hist_car_lft" %in% colnames(enriched_data)) || is.null(direction_choice))
+  {
+    abscissa<-enriched_data$veh_km
+    ordinate<-enriched_data$km_h
+  }
+  
+  else if(direction_choice=='lft')
+  {
+    abscissa<-enriched_data$veh_km_lft
+    ordinate<-enriched_data$km_h_lft
+  }
+  
+  else
+  {
+    abscissa<-enriched_data$veh_km_rgt
+    ordinate<-enriched_data$km_h_rgt
+  }
+  
+  # Calculate the intersection between the lines
+  x_inter<-(list_final_2$b - list_final_1$b)/(list_final_1$a - list_final_2$a)
+  y_inter <- list_final_1$a * x_inter + list_final_1$b
+  
+  #Calculate the ordinate of the lines
+  y1<-list_final_1$a*abscissa+list_final_1$b
+  y2<-list_final_2$a*abscissa+list_final_2$b
+  
+  #Plot the fundamental diagram and its envelope
+  graph<-ggplot(data = enriched_data, mapping = aes(x = abscissa, y = ordinate, color = 'red')) +
+    geom_point(pch = 20) +
+    labs(x = 'Density', y = 'Speed', title = paste('Segment :', enriched_data$segment_fullname[1]))
+  
+  
+  graph+
+    geom_line(mapping=aes(x=abscissa,y=y1),color='black')+
+    geom_line(mapping=aes(x=abscissa,y=y2),color='black')+
+    geom_point(aes(x = x_inter, y = y_inter), color = "green", size = 2) +
+    coord_cartesian(xlim =c(0, max(abscissa)), ylim = c(0, max(ordinate)))
+}