distmat: Distance Matrix

In pracma: Practical Numerical Math Functions

Distance Matrix

Description

Computes the Euclidean distance between rows of two matrices.

Usage

distmat(X, Y)
pdist(X)
pdist2(X, Y)

Arguments

X	matrix of some size m x k; vector will be taken as row matrix.
Y	matrix of some size n x k; vector will be taken as row matrix.

Details

Computes Euclidean distance between two vectors A and B as:

||A-B|| = sqrt ( ||A||^2 + ||B||^2 - 2*A.B )

and vectorizes to rows of two matrices (or vectors).

pdist2 is an alias for distmat, while pdist(X) is the same as distmat(X, X).

Value

matrix of size m x n if x is of size m x k and y is of size n x k.

Note

If a is m x r and b is n x r then

apply(outer(a,t(b),"-"),c(1,4),function(x)sqrt(sum(diag(x*x))))

is the m x n matrix of distances between the m rows of a and n rows of b.

This can be modified as necessary, if one wants to apply distances other than the euclidean.

BUT: The code shown here is 10-100 times faster, utilizing the similarity between Euclidean distance and matrix operations.

References

Copyright (c) 1999 Roland Bunschoten for a Matlab version on MatlabCentral under the name distance.m. Translated to R by Hans W Borchers.

See Also

dist

Examples

A <- c(0.0, 0.0)
B <- matrix(c(
        0,0, 1,0, 0,1, 1,1), nrow=4, ncol = 2, byrow = TRUE)
distmat(A, B)  #=> 0 1 1 sqrt(2)

X <- matrix(rep(0.5, 5), nrow=1, ncol=5)
Y <- matrix(runif(50), nrow=10, ncol=5)
distmat(X, Y)

# A more vectorized form of distmat:
distmat2 <- function(x, y) {
    sqrt(outer(rowSums(x^2), rowSums(y^2), '+') - tcrossprod(x, 2 * y))
}

pracma documentation built on Nov. 10, 2023, 1:14 a.m.