## Function to calculate a new point given an initial point, a distance to travel, and a bearing 
calc_new_coords <- function(dist, init_lat, init_long,  bearing) {
  # Convert  to radians
  bearing <- bearing * pi / 180
  init_lat <-init_lat * pi / 180  
  init_long <- init_long * pi / 180  
  
  
  # Calculate latitude of the second point
  new_lat <- asin(sin(init_lat) * cos(dist / 6371) + cos(init_lat) * sin(dist / 6371) * cos(bearing))
  
  # Calculate the difference in longitude
  delta_lambda <- atan2(sin(bearing) * sin(dist / 6371) * cos(init_lat),
                        cos(dist / 6371) - sin(init_lat) * sin(new_lat))
  
  # Calculate longitude of the second point
  new_long <- init_long + delta_lambda
  
  # Convert the calculated latitudes and longitudes back to degrees
  lat_j_deg <- new_lat * 180 / pi
  long_j_deg <- new_long * 180 / pi
  
  # Return the coordinates of the second point
  return(c(latitude=new_lat * 180 / pi, longitude=new_long * 180 / pi))
}


## Function to calculate spatial distances between coordinates
calc_spatial_dist <- function(data_file){
  pairs <- t(combn(data_file[,"id"], 2))
  ind_i_coords <- data_file[match(pairs[, 1],  data_file[,"id"]),c("longitude","latitude")] * pi/180
  ind_j_coords <- data_file[match(pairs[, 2],  data_file[,"id"]),c("longitude","latitude")] * pi/180
  
  # Sets locations to 0 when they are the same, this solves a issues where acos can return nan
  # When coordinates are the same due to floating point errors
  same_loc <- abs(ind_i_coords[,1]-ind_j_coords[,1]) < 1e-10 & 
    abs(ind_i_coords[,2]-ind_j_coords[,2]) < 1e-10
  ind_i_coords[same_loc & !is.na(same_loc),] <- 0
  ind_j_coords[same_loc & !is.na(same_loc),] <- 0
  
  #ifelse(ind_i_coords[,1]==ind_j_coords[,1] & ind_i_coords[,2]==ind_j_coords[,2], 0,
  spatial_dists <- acos(sin(ind_i_coords[,2])*sin(ind_j_coords[,2])+cos(ind_i_coords[,2])*cos(ind_j_coords[,2])*
                          cos(ind_j_coords[,1]-ind_i_coords[,1]))*6371
  
  return(data.frame(id1 = pairs[,1], id2=pairs[,2], dist=spatial_dists))
}


## Function to rescale vector to specified range
rescale <- function(x, new_min = 0, new_max = 100){
  (new_max - new_min) / (max(x) - min(x)) * (x - min(x)) + new_min
}


## Inverse Logit Function
inverse_logit <- function(x) {
  return(1 / (1 + exp(-x)))
}


## Function to make colours transparent
col_trans <- function (org_col,alpha_lev){
  sapply(org_col, function (x){
    col_rbg<-col2rgb(x)
    rgb(col_rbg[1],col_rbg[2],col_rbg[3],max=255,alpha=alpha_lev*255)
  })
}


## Function to reverse standardization
reverse_standardization_pred <- function(col, prediction) {
  
  # calculate the mean
  mean_val <- mean(col)
  
  # calculate the standard deviation
  std_val <- sd(col)
  
  # apply it to the prediction
  real_val <- prediction * std_val + mean_val
  
  return(real_val)
}


## Function to get x-coordinate given a slope, y-coordinate and y-intercept
get_x <- function(slope, yint, y){
  return((y-yint)/slope)
}