Make a loop to find the distance between stations in R
There are two issues here:

Your input data frame might not look the way you expect it to - the latitude and longitude columns are recycled so you have multiple different coordinates for the same station. Try adding rep() in the lat and long columns as well as station.

In your code lat1 <- df$latitude[df$station == stations[i]] returns a vector, because there are multiple matches. I think you're expecting a single value. Use only the first matching element (since they are now all the same elements in the vector after adding rep() as above):


df <- data.frame(
  station = rep(c("A", "B", "C", "D"), each = 20),
  temperature = rnorm(80),
  latitude = rep(c(40.7128, 34.0522, 41.8781, 39.9526), each = 20),
  longitude = rep(c(-74.0060, -118.2437, -87.6298, -75.1652), each = 20)
)
stations <- unique(df$station)

my_points <- matrix(NA, nrow = length(unique(df$station)), ncol = length(unique(df$station)))

# Loop through each station combination
for (i in 1:length(stations)) {
  for (j in 1:length(stations)) {
    # Get temperatures for the two stations
    lat1 <- df$latitude[df$station == stations[i]][1]
    lon1 <- df$longitude[df$station == stations[i]][1]
    lat2 <- df$latitude[df$station == stations[j]][1]
    lon2 <- df$longitude[df$station == stations[j]][1]
    my_points[i, j] <- as.vector(dist(matrix(c(lon1,lon2,lat1,lat2),
                                             nrow = 2)))  
    
  }
}

distance_df <- as.data.frame(my_points)


This gives:
         V1       V2       V3        V4
1  0.000000 44.73631 13.67355  1.386235
2 44.736313  0.00000 31.59835 43.480707
3 13.673546 31.59835  0.00000 12.612446
4  1.386235 43.48071 12.61245  0.000000

A slightly better way of finding unique stations:
unique(df[, c("station", "latitude", "longitude")])

You can then loop over those instead:
# Loop through each station combination
for (i in 1:length(stations)) {
  for (j in 1:length(stations)) {
    # Get temperatures for the two stations
    lat1 <- unique_df$latitude[unique_df$station == stations[i]]
    lon1 <- unique_df$longitude[unique_df$station == stations[i]]
    lat2 <- unique_df$latitude[unique_df$station == stations[j]]
    lon2 <- unique_df$longitude[unique_df$station == stations[j]]
    my_points[i, j] <- as.vector(dist(matrix(c(lon1,lon2,lat1,lat2),
                                             nrow = 2)))  
    
  }
}



I have made this code to find the distance between stations but in the output, there is only one value. Can you find the error?
df <- data.frame(
  station = rep(c("A", "B", "C", "D"), each = 20),
  temperature = rnorm(80),
  latitude = c(40.7128, 34.0522, 41.8781, 39.9526),
  longitude = c(-74.0060, -118.2437, -87.6298, -75.1652)
)
stations <- unique(df$station)

my_points <- matrix(NA, nrow = length(unique(df$station)), ncol = length(unique(df$station)))

# Loop through each station combination
for (i in 1:length(stations)) {
  for (j in 1:length(stations)) {
    # Get temperatures for the two stations
    lat1 <- df$latitude[df$station == stations[i]]
    lon1 <- df$longitude[df$station == stations[i]]
    lat2 <- df$latitude[df$station == stations[j]]
    lon2 <- df$longitude[df$station == stations[j]]
    my_points[i, j] <- as.vector(dist(matrix(c(lon1,lon2,lat1,lat2),
                                             nrow = 2)))  
    
  }
}

distance_df <- as.data.frame(my_points)

