I want to perform coordinate descent iteration on a set of points whose latitudes and longitudes are given in arrays . The iteration should help me estimate nearest locations for the set of latitude and longitude points. I have an array 'a' and 'b' of lat/long values. Both the arrays denote the same set of locations.
Longitude Latitude
1. 100.1130 17.5406
2. 99.8961 20.0577
3. 99.8829 20.0466
4. 101.2457 16.8041
5. 102.1314 19.8881
You could use the dist() function for this:
mat2 <- dist(mat,method = "euclidean")
1. 2. 3. 4.
2. 2.52642792
3. 2.51654168 0.01724674
4. 1.35108902 3.52240445 3.51724752
5. 3.09591583 2.24172484 2.25407952 3.20866335
The five closest points have the distances
> head(sort(mat2),5)
#[1] 0.01724674 1.35108902 2.24172484 2.25407952 2.51654168
The pairs of points in the distance matrix can be deduced quite easily from their index:
> head(order(mat2),5)
#[1] 5 3 7 9 2
The index is the entry counting columnwise starting from the upper left, so mat2[5]=0.01724674 is the distance between point 2 and point 3, mat2[3]=1.351089 is the distance between point 1 and point 4, etc.
We can define a function that extracts these pairs:
dist_pairs <- function(x,y){
idx1 = ceiling(x / (y - 1))
idx2 = x %% (y - 1) + idx1
return(c(idx1, idx2))
}
where the second argument is the number of rows in the original matrix; 5 in this case. As an example, the result of
> dist_pairs(9, nrow(mat))
#[1] 3 4
means that the entry number 9 in the distance matrix contains the distance between points 3 and 4.
Edit
By looking at the answer by @Jaap and re-reading the OP, I realized that you are interested in finding the point that is closest to each data point, and not necessarily in ranking those pairs in your set which have the smallest distance between each other.
To obtain this information, the code can be adapted in a similar way as suggested by @Jaap:
mat3 <- as.matrix(mat2)
diag(mat3) <- NA
mat <- as.data.frame(mat)
mat$closest <- apply(mat3,1,which.min)
> mat
# Longitude Latitude closest
#1 100.1130 17.5406 4
#2 99.8961 20.0577 3
#3 99.8829 20.0466 2
#4 101.2457 16.8041 1
#5 102.1314 19.8881 2
data
mat <- as.matrix(read.table(text=" Longitude Latitude
100.1130 17.5406
99.8961 20.0577
99.8829 20.0466
101.2457 16.8041
102.1314 19.8881", header=T))
When you want to calculate the distance between points with latitude/longitude coordinates, the distm function from the geosphere package gives you several methods: distCosine, distHaversine, distVincentySphere & distVincentyEllipsoid. Of these, the distVincentyEllipsoid is considered the most accurate one. In these answers I showed how to calculate the distance between two different lists of points:
However, your case is a bit different as you want to compare within a list of points with coordinates. By slightly changing the method I showed in these answers, you can achieve the same. An illustration on how to do that with the data you provided:
The data:
points <- structure(list(p = structure(1:5, .Label = c("A", "B", "C", "D", "E"), class = "factor"),
lon = c(100.113, 99.8961, 99.8829, 101.2457, 102.1314),
lat = c(17.5406, 20.0577, 20.0466, 16.8041, 19.8881)),
.Names = c("p", "lon", "lat"), class = "data.frame", row.names = c(NA, -5L))
Note that I added a variable p with names for the points.
Original method:
First you create a distance matrix with:
distmat <- distm(points[,c('lon','lat')], points[,c('lon','lat')], fun=distVincentyEllipsoid)
which gives:
> distmat
[,1] [,2] [,3] [,4] [,5]
[1,] 0.0 279553.803 278446.927 145482.3 335897.8
[2,] 279553.8 0.000 1848.474 387314.3 234708.0
[3,] 278446.9 1848.474 0.000 386690.7 235998.8
[4,] 145482.3 387314.334 386690.666 0.0 353951.5
[5,] 335897.8 234707.958 235998.784 353951.5 0.0
When you now assign the nearest point to each point with:
points$nearest <- points$p[apply(distmat, 1, which.min)]
each point will be assigned to itself as nearest point:
> points
p lon lat nearest
1 A 100.1130 17.5406 A
2 B 99.8961 20.0577 B
3 C 99.8829 20.0466 C
4 D 101.2457 16.8041 D
5 E 102.1314 19.8881 E
Adaptation:
You can prevent that behavior by replacing the the 0 values in the distance matrix distmat with:
distmat[distmat==0] <- NA
When you now assign the nearest point to each point with:
points$nearest <- points$p[apply(distmat, 1, which.min)]
you get the correct values:
> points
p lon lat nearest
1 A 100.1130 17.5406 D
2 B 99.8961 20.0577 C
3 C 99.8829 20.0466 B
4 D 101.2457 16.8041 A
5 E 102.1314 19.8881 B
