If x_varand y_varare atomic vectors or arrays, and the function returns an atomic vector of known length, you can use the basic function R outer:
outer(x_var, y_var, FUN = f)
This will return an array with dimensions c(dim(x_var), dim(y_var)). Dimension names are similarly combined. For instance:
x_var <- setNames(1:3, c("a", "b", "c"))
y_var <- setNames(4:5, c("d", "e"))
outer(x_var, y_var, '+')
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