Consider computing the addition of these arrays x and y:

(x <- array(1:15, c(3, 5)))
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    4    7   10   13
#> [2,]    2    5    8   11   14
#> [3,]    3    6    9   12   15
(y <- array(1:5 * 100, c(1, 5)))
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  100  200  300  400  500

This cannot be done efficiently in base ‘R’; it can be done fast and memory-efficiently with the ‘broadcast’ package:

x + y
Error in x + y : non-conformable arrays

# You *could* do the following....
x + y[rep(1L, nrow(x)), ]
# ... but if x or y is very large: 
Error: cannot allocate vector of size

broadcaster(x) <- TRUE
broadcaster(y) <- TRUE
x + y
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  101  204  307  410  513
#> [2,]  102  205  308  411  514
#> [3,]  103  206  309  412  515
#> broadcaster

‘broadcast’ supports a wide range of infix operators, including arithmetic-, relational-, Boolean- string- and bit-wise operators.

Using broadcasting, bind_array() from the ‘broadcast’ package can bind arrays together in ways that cannot efficiently be done with rbind(), cbind(), or abind::abind(). Consider, for example, column-binding these arrays x and y:

(x <- array(1:12, c(3, 4)))
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    4    7   10
#> [2,]    2    5    8   11
#> [3,]    3    6    9   12
(y <- array(1:4 * 100, c(1, 4)))
#>      [,1] [,2] [,3] [,4]
#> [1,]  100  200  300  400

This cannot be done efficiently in base ‘R’; it can be done fast and memory-efficiently with the ‘broadcast’ package:

cbind(x, y)
Error in cbind(x, y) :
  number of rows of matrices must match

# You *could* do the following....
cbind(x, y[rep(1L, nrow(x)), ])
# ... but if x or y is very large:
Error: cannot allocate vector of size

bind_array(list(x, y), along = 2L)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,]    1    4    7   10  100  200  300  400
#> [2,]    2    5    8   11  100  200  300  400
#> [3,]    3    6    9   12  100  200  300  400

bind_array() is also considerably faster and more memory efficient than abind(). See the benchmarks.

The idea of broadcasted infix operations and broadcasted array binding has been generalized to also include bcapply() (a broadcasted apply-like function), bc_ifelse() (broadcasted version of ifelse()), bc_strrep() (broadcasted version of strrep()).

Broadcast provides casting functions, that cast subset-groups of an array to a new dimension, cast nested lists to dimensional lists, and vice-versa.
These functions are useful for facilitating complex broadcasted operations, though they also have much merit beside broadcasting.

For example, you cannot broadcast through hierarchies of a list, but you can broadcast along dimensions. So suppose you have the following list:

x <- list(
  student1 = list(
    homework1 = sample(0:100, 5),
    homework2 = sample(0:100, 5),
    homework3 = sample(0:100, 5)
  ),
  student2 = list(
    homework1 = sample(0:100, 5),
    homework2 = sample(0:100, 5),
    homework3 = sample(0:100, 5)
  ),
  student3 = list(
    homework1 = sample(0:100, 5),
    homework2 = sample(0:100, 5),
    homework3 = sample(0:100, 5)
  )
)

Since all values in the list are numbers, you might want to turn this into a numeric array, to make mathematical computations and analyses on it easier.

This can be done with the ‘broadcast’ package with the following steps. First, turn the nested list into a shallow (i.e. non-nested), dimensional list using cast_hier2dim():

x2 <- cast_hier2dim(x, in2out = FALSE, direction.names = 1L)
print(x2)
#>          homework1 homework2 homework3
#> student1 integer,5 integer,5 integer,5
#> student2 integer,5 integer,5 integer,5
#> student3 integer,5 integer,5 integer,5

Second, turn the shallow (i.e. non-nested), dimensional list into an atomic array using cast_shallow2atomic():

x3 <- cast_shallow2atomic(x2, 1L)
print(x3)
#> , , homework1
#> 
#>      student1 student2 student3
#> [1,]       67        6       73
#> [2,]       38       72       41
#> [3,]        0       78       37
#> [4,]       33       84       19
#> [5,]       86       36       27
#> 
#> , , homework2
#> 
#>      student1 student2 student3
#> [1,]       42       88       19
#> [2,]       13       36       43
#> [3,]       81       33       86
#> [4,]       58      100       69
#> [5,]       50       43       39
#> 
#> , , homework3
#> 
#>      student1 student2 student3
#> [1,]       96       78       43
#> [2,]       84       32       24
#> [3,]       20       83       69
#> [4,]       53       34       38
#> [5,]       73       69       50

‘broadcast’ comes with a few linear algebra functions for statistics. For example, the sd_lc() function to compute the standard deviation of a linear combination of variables - regardless of what the distribution of the variables is.