Fast and Flexible Distance Computations

A fast and flexible replacement for dist, to compute euclidean distances.

Usage

fdist(x, v = NULL, ..., method = "euclidean", nthreads = .op[["nthreads"]])

Arguments

x

a numeric vector or matrix. Data frames/lists can be passed but will be converted to matrix using qM. Non-numeric (double) inputs will be coerced.

v

an (optional) numeric (double) vector such that length(v) == NCOL(x), to compute distances with (the rows of) x. Other vector types will be coerced.

...

not used. A placeholder for possible future arguments.

method

an integer or character string indicating the method of computing distances.

Int.	String	Description
1	`"euclidean"`	euclidean distance
2	`"euclidean_squared"`	squared euclidean distance (more efficient)

nthreads

integer. The number of threads to use. If v = NULL (full distance matrix), multithreading is along the distance matrix columns (decreasing thread loads as matrix is lower triangular). If v is supplied, multithreading is at the sub-column level (across elements).

Value

If v = NULL, a full lower-triangular distance matrix between the rows of x is computed and returned as a 'dist' object (all methods apply, see dist). Otherwise, a numeric vector of distances of each row of x with v is returned. See Examples.

Note

fdist does not check for missing values, so NA's will result in NA distances.

kit::topn is a suitable complimentary function to find nearest neighbors. It is very efficient and skips missing values by default.

Examples

# Distance matrix
m = as.matrix(mtcars)
str(fdist(m)) # Same as dist(m)
#>  'dist' num [1:496] 0.615 54.909 98.113 210.337 65.472 ...
#>  - attr(*, "Size")= int 32
#>  - attr(*, "Labels")= chr [1:32] "Mazda RX4" "Mazda RX4 Wag" "Datsun 710" "Hornet 4 Drive" ...
#>  - attr(*, "Diag")= logi FALSE
#>  - attr(*, "Upper")= logi FALSE
#>  - attr(*, "method")= chr "euclidean"

# Distance with vector
d = fdist(m, fmean(m))
kit::topn(d, 5)  # Index of 5 nearest neighbours
#> [1] 15 16 17 31 19

# Mahalanobis distance
m_mahal = t(forwardsolve(t(chol(cov(m))), t(m)))
fdist(m_mahal, fmean(m_mahal))
#>  [1] 2.991099 2.878877 2.989507 2.469155 2.330035 2.979523 3.022627 3.167072
#>  [9] 4.753222 3.520384 3.325489 3.078332 2.365275 2.454885 3.346836 2.944842
#> [17] 3.501088 3.013076 3.867089 3.208810 3.665023 2.495443 2.405554 3.417825
#> [25] 2.591927 1.909395 4.284409 3.741747 4.644675 3.339588 4.380911 3.144643
sqrt(unattrib(mahalanobis(m, fmean(m), cov(m))))
#>  [1] 2.991099 2.878877 2.989507 2.469155 2.330035 2.979523 3.022627 3.167072
#>  [9] 4.753222 3.520384 3.325489 3.078332 2.365275 2.454885 3.346836 2.944842
#> [17] 3.501088 3.013076 3.867089 3.208810 3.665023 2.495443 2.405554 3.417825
#> [25] 2.591927 1.909395 4.284409 3.741747 4.644675 3.339588 4.380911 3.144643
# \donttest{
# Distance of two vectors
x <- rnorm(1e6)
y <- rnorm(1e6)
microbenchmark::microbenchmark(
  fdist(x, y),
  fdist(x, y, nthreads = 2),
  sqrt(sum((x-y)^2))
)
#> Unit: microseconds
#>                       expr      min        lq     mean   median       uq
#>                fdist(x, y)  928.158  964.3200 1115.312 1006.140 1024.200
#>  fdist(x, y, nthreads = 2)  926.764  940.9295 1132.001  998.965 1013.807
#>       sqrt(sum((x - y)^2)) 2656.882 2894.6820 4991.064 3101.957 3368.970
#>       max neval
#>  11186.44   100
#>  15499.07   100
#>  95558.00   100
# }