Numerical and Symbolic Outer Product

Computes the outer product of two numeric or character arrays.

x %outer% y

Arguments

x

numeric or character array.

y

numeric or character array.

Value

array.

Details

The outer product between two arrays A and B is computed as: $$C_{i_1\dots i_mj_1\dots j_n} = A_{i_1\dots i_m}B_{j_1\dots j_n}$$

References

Guidotti, E. (2020). "calculus: High dimensional numerical and symbolic calculus in R". https://arxiv.org/abs/2101.00086

See also

Other basic arithmetic: %diff%(), %div%(), %dot%(), %inner%(), %kronecker%(), %prod%(), %sum%()

Examples

### numeric outer product 
c(1,2) %outer% c(2,3)
#>      [,1] [,2]
#> [1,]    2    3
#> [2,]    4    6

### symbolic outer product 
c("a","b") %outer% c("c","d")
#>      [,1]        [,2]       
#> [1,] "(a) * (c)" "(a) * (d)"
#> [2,] "(b) * (c)" "(b) * (d)"