# outer

0th

Percentile

##### Outer Product of Arrays

The outer product of the arrays X and Y is the array A with dimension c(dim(X), dim(Y)) where element A[c(arrayindex.x, arrayindex.y)] = FUN(X[arrayindex.x], Y[arrayindex.y], …).

Keywords
array
##### Usage
outer(X, Y, FUN = "*", …)
X %o% Y
##### Arguments
X, Y

First and second arguments for function FUN. Typically a vector or array.

FUN

a function to use on the outer products, found via match.fun (except for the special case "*").

optional arguments to be passed to FUN.

##### Details

X and Y must be suitable arguments for FUN. Each will be extended by rep to length the products of the lengths of X and Y before FUN is called.

FUN is called with these two extended vectors as arguments (plus any arguments in …). It must be a vectorized function (or the name of one) expecting at least two arguments and returning a value with the same length as the first (and the second).

Where they exist, the [dim]names of X and Y will be copied to the answer, and a dimension assigned which is the concatenation of the dimensions of X and Y (or lengths if dimensions do not exist).

FUN = "*" is handled as a special case via as.vector(X) %*% t(as.vector(Y)), and is intended only for numeric vectors and arrays.

%o% is binary operator providing a wrapper for outer(x, y, "*").

##### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

%*% for usual (inner) matrix vector multiplication; kronecker which is based on outer; Vectorize for vectorizing a non-vectorized function.
library(base) # NOT RUN { x <- 1:9; names(x) <- x # Multiplication & Power Tables x %o% x y <- 2:8; names(y) <- paste(y,":", sep = "") outer(y, x, "^") outer(month.abb, 1999:2003, FUN = "paste") ## three way multiplication table: x %o% x %o% y[1:3] # }