Compute Schur products (element-wise) of all pairwise combinations of columns in matrix

Fast computation of all pairwise element-wise column products of a matrix.

pairwise_Schur_product(x, self = FALSE)

Arguments

x

A matrix with dimensions r*c.

self

A logical that determines whether a column should also be multiplied by itself.

Value

A matrix with the same number of rows as x and a number of columns corresponding to c choose 2 (+ c if self is TRUE), where c is the number of columns of x.

Details

Note that the output order of columns corresponds to the order of the columns in x. First column 1 is multiplied with each of the other columns, then column 2 with the remaining columns etc.

Author

Claus Ekstrom <claus@rprimer.dk>

Examples

X <- cbind(rep(1, 4), 1:4, 4:1)
pairwise_Schur_product(X)
#>      [,1] [,2] [,3]
#> [1,]    1    4    4
#> [2,]    2    3    6
#> [3,]    3    2    6
#> [4,]    4    1    4
pairwise_Schur_product(X, self=TRUE)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    1    1    4    1    4   16
#> [2,]    1    2    3    4    6    9
#> [3,]    1    3    2    9    6    4
#> [4,]    1    4    1   16    4    1