Broadcast Arrays to a Common Shape

Broadcasts arrays to a common shape, aligning their axes from the first one, so that a vector meets a matrix as a column.

Usage

nv_broadcast_arrays(...)

Arguments

...

(arrayish)
Arrays to broadcast.

Value

(list() of arrayish)
The inputs, each with its own data type and the common shape.

Broadcasting Rules

1. If the arrays have different numbers of axes, append size-1 axes to the shorter shape, so axis 1 meets axis 1. A length-n vector therefore lines up with the rows of an n by m matrix and is replicated across its columns. NumPy prepends instead.

2. For each axis: if the sizes match, keep them; if one is 1, expand it to the other's size; otherwise raise an error.

Relation to base R

Base R has no broadcasting between arrays – matrix(1, 3, 3) + matrix(1, 1, 3) is a "non-conformable arrays" error. It does recycle a vector over a matrix, though, and for a vector as long as the first axis that lands on exactly this broadcast, which is why a vector meets a matrix as a column in both. The two part ways once the lengths stop lining up: matrix(1, 2, 3) + c(1, 2, 3) recycles on regardless, where the matching broadcast is an error.

The deviation from NumPy's broadcasting rules is still motivated by keeping anvl's behaviour similar to base R in spirit, see the examples for more.

See also

nv_broadcast_scalars(), nv_broadcast_to()

Examples

# interpreting vectors as columns
# base R:
x1 <- c(1, 2)
m1 <- array(1, dim = c(2, 2))
x1 + m1
#>      [,1] [,2]
#> [1,]    2    2
#> [2,]    3    3
# anvl:
args <- nv_broadcast_arrays(nv_array(x1), nv_array(m1))
print(args)
#> [[1]]
#> AnvlArray
#>  1 1
#>  2 2
#> [ CPUf32{2,2} ] 
#> 
#> [[2]]
#> AnvlArray
#>  1 1
#>  1 1
#> [ CPUf32{2,2} ] 
#> 
args[[1]] + args[[2]]
#> AnvlArray
#>  2 2
#>  3 3
#> [ CPUf32{2,2} ] 


# axes of size 1 are expanded to the other operand's size
y1 <- nv_array(1:3, shape = c(1, 3))
y2 <- nv_array(1:3, shape = c(3, 1))
nv_broadcast_arrays(y1, y2)
#> [[1]]
#> AnvlArray
#>  1 2 3
#>  1 2 3
#>  1 2 3
#> [ CPUi32{3,3} ] 
#> 
#> [[2]]
#> AnvlArray
#>  1 1 1
#>  2 2 2
#>  3 3 3
#> [ CPUi32{3,3} ] 
#>