Expand list of coordinates to get all combinations within a group in R

问题

I have a DF with about 1 million records. Each record includes latitude and longitude, and the records are grouped as in the example data (except with much larger groups)

data.frame(Latitude=c(-30.25,-30.89,-30.48,-30.10), 
           Longitude=c(116.321,116.98,116.78,116.38), 
           grp=c('a','a','b','b'))

Within each group I need to find the maximum distance between any two sets of coordinates. Once I have all combinations of coordinates in a DF with I can calculate distances no problems, but can not efficiently get each combination into a DF that looks something like this

data.frame(Latitude1=c(-30.25,-30.25,-30.89,-30.89,-30.48,-30.48,-30.10,-30.10), 
           Longitude1=c(116.321,116.32,116.98,116.98,116.78,116.78,116.38,116.38), 
           Latitude2=c(-30.25,-30.89,-30.25,-30.89,-30.48,-30.10,-30.48,-30.10), 
           Longitude2=c(116.321,116.98,116.98,116.321,116.78,116.38,116.38,116.78), 
           grp=c('a','a','a','a','b','b','b','b'))

I've written a nested loop to do this, but it is very slow and I'm, sure there is a better way. I looked at duplicating the columns and using expand.grid, but can find how to use it with multiple factors Any help would be appreciated. Thanks

回答1:

If you're comfortable using development / non-released packages, I've written spatialdatatable to do efficient geo* calculations on data.table objects.

Here's a solution working on 100,000 rows of data. The steps are

Join the data to itself to give you the giant point-to-point data set
Calculate the distances between each pair of points (using haversine distance)
Select the greatest distance within each group.

library(data.table)
# devtools::install_github("SymbolixAU/spatialdatatable")
library(spatialdatatable)


## generate random data
lons <- sample(0:180, 1e5, replace = T)
lats <- sample(-90:1, 1e5, replace = T)
grp <- sample(letters, 1e5, replace = T)
df <- data.frame(lon = lons, lat = lats, grp = grp)

## set as a data.table object, and assign an 'id' to each point
setDT(df)
df[, id := .I]

## 1. join the df to itself to give all points to all other points
df <- df[
    df
    , on = "grp"
    , nomatch = 0
    , allow.cartesian = T
    ][id != i.id]   ## remove points joined with themselves

## 2. calculate distances
df[, dist := spatialdatatable::dtHaversine(lat, lon, i.lat, i.lon)]

## 3. select greatest distance per group
df[ df[, .I[which.max(dist)], by = grp]$V1 ][order(grp)]

#     lon lat grp    id i.lon i.lat  i.id     dist
#  1:   1   0   a 27726   180     0 10996 19903920
#  2:   1   1   b 63425   180    -3 57218 19766508
#  3:   1   1   c 18255   177    -2    56 19556799
#  4:   0  -1   d 43560   179     0  8518 19857865
#  5: 178  -2   e 37485     0     0 34482 19700640
#  6:   1  -2   f 79879   180     1 70765 19857889
#  7: 178   1   g 84268     1    -3 44148 19614379
#  8: 178  -5   h 49310     1     1  1306 19459455
#  9:   0   1   i 92786   179    -2 55584 19857889
# 10: 180   0   j 92704     0     0 36757 20015115
# 11:   0  -1   k 75760   180     0 71050 19903920
# 12:   0  -1   l 42202   180     0 10839 19903920
# 13:   0   1   m 73069   177    -2  2708 19663598
# 14:   0   1   n 10830   180    -1  1236 20015115
# 15:   3  -2   o 43380   180     1  3829 19663598
# 16: 179   1   p 95740     0    -1  3061 19903937
# 17:   0  -1   q 49476   180     0 18257 19903920
# 18: 180   0   r 96154     1     0 42435 19903920
# 19: 180  -1   s 82115     1     0 47784 19857865
# 20: 178  -2   t 42861     0     0 22020 19700640
# 21: 180   0   u 22965     0    -1 12158 19903920
# 22: 178   0   v 18557     0    -2 17457 19700640
# 23: 178  -2   w 58321     1    -1 13906 19543390
# 24:   0  -1   x 93181   177    -3 67084 19459211
# 25:   0  -1   y 46491   178     1  5548 19792759
# 26:   3   1   z 43109   180    -3   769 19614379

compared to library(geosphere)

回答2:

How about something like this to get you started. We make use of geosphere::distm to calculate distances (here geodesic distances):

Split data.frame into groups based on grp:
```
lst <- split(df, df$grp)
```

Calculate geodesic distances

library(geosphere);
dist <- lapply(lst, function(x) distm(x[, c("Longitude", "Latitude")]));

The result is a list of symmetric distance matrices, where rows/columns correspond to records.

dist;
#$a
#         [,1]     [,2]
#[1,]     0.00 95029.27
#[2,] 95029.27     0.00
#
#$b
#         [,1]     [,2]
#[1,]     0.00 57056.28
#[2,] 57056.28     0.00

You can then go and filter records based on the minimum distance per group. You only give 2 points per group, so extracting the maximum distance is trivial because there is only one.

来源：https://stackoverflow.com/questions/49662535/expand-list-of-coordinates-to-get-all-combinations-within-a-group-in-r

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coordinates

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