‘Numpy’-like Broadcasted Operations for Atomic and Recursive Arrays with Minimal Dependencies in ‘R’

Introduction

🗺️Overview

‘broadcast’ is a relatively small package that, as the name suggests, performs “broadcasting” (similar to broadcasting in the ‘Numpy’ module for ‘Python’).

In the context of operations involving 2 (or more) arrays, “broadcasting” refers to recycling array dimensions without allocating additional memory, which is considerably faster and more memory-efficient than R’s regular dimensions replication mechanism.

Please read the Broadcasting explained page for a more complete explanation of what “broadcasting” is.

At its core, the ‘broadcast’ package provides 3 functionalities, all 3 related to “broadcasting”:

Functions for broadcasted element-wise operations between any 2 arrays. They support a large set of relational-, arithmetic-, Boolean-, and string operations.
The bind_array() function for binding arrays along any arbitrary dimension. Similar to the fantastic abind::abind() function, but with a few key differences:
- bind_array() is faster and more memory efficient;
- bind_array() supports broadcasting;
- bind_array() supports both atomic and recursive arrays (abind() only supports atomic arrays).
‘broadcast’ provides several generic functions for broadcasting, namely bcapply() (broadcasted apply-like function) and bc_ifelse() (broadcasted version of ifelse()).

Additionally, ‘broadcast’ includes the acast() function, for casting/pivoting an array into a new dimension. Roughly analogous to data.table::dcast(), but for arrays.

🤷🏽Why use ‘broadcast’

Efficiency

Broadcasting dimensions is faster and more memory efficient than replicating dimensions.
Efficient programs use less energy and resources, and is thus better for the environment.
Benchmarks can be found on the website.

Convenience

Have you ever been bothered by any of the following while programming in :

Receiving the “non-conformable arrays” error message in a simple array operation, when it intuitively should work?
Receiving the “cannot allocate vector of size…” error message because unnecessarily allocated too much memory in array operations?
abind::abind() being too slow, or ruining the structure of recursive arrays?
that there is no built-in way to cast or pivot arrays?
that certain ‘Numpy’ operations have no equivalent operation in ?

If you answered “YES” to any of the above, ‘broadcast’ may be the - package for you.

Minimal Dependencies

Besides linking to ‘Rcpp’, ‘broadcast’ does not depend on, vendor, link to, include, or otherwise use any external libraries; ‘broadcast’ was essentially made from scratch and can be installed out-of-the-box.

Not using external libraries brings a number of advantages:

Avoid dependency hell: Every dependency that is added to a software package increases the likelihood of something breaking (AKA “dependency hell”). ‘broadcast’ thus avoids this.
Avoid wasting resources for translations: Using libraries from other languages, such as ‘xtensor’ (‘C++’) or ‘Numpy’ (‘Python’) means that - at some point - one needs to convert between the structure of to that of the other language, and vice-versa, which wastes precious time, memory, and power. ‘broadcast’ requires no such translations of structures, and is therefore much less wasteful.
Ensure consistent behaviour: Using libraries from other languages also means one cannot always guarantee consistent behaviour for some operations. For example: both ‘Numpy’ and ‘xtensor’ have only limited support for missing values, whereas supports missing values for both atomic and recursive array/vector types (except type of ‘Raw’). Since ‘broadcast’ does not rely on external libraries, it can ensure behaviour that is consistent with the rest of .

Tested

The ‘broadcast’ package is frequently checked using a large suite of unit tests via the tinytest package. These tests have a coverage of over 90%. So the chance of a function from this package breaking completely is relatively low.

‘broadcast’ is still relatively new package, however, so (small) bugs are still very much possible. I encourage users who find bugs to report them promptly to the issues tab on the GitHub page, and I will fix them as soon as time permits.

🚀Quick Example

Consider the matrices x and y:

x <- array(1:20, c(4, 5))
y <- array(1:5 * 100, c(1, 5))
print(x)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    5    9   13   17
#> [2,]    2    6   10   14   18
#> [3,]    3    7   11   15   19
#> [4,]    4    8   12   16   20
print(y)
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  100  200  300  400  500

Suppose one wishes to compute the element-wise addition of these 2 arrays.

This won’t work in base :

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

You could do the following….

x + y[rep(1L, 4L),]
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  101  205  309  413  517
#> [2,]  102  206  310  414  518
#> [3,]  103  207  311  415  519
#> [4,]  104  208  312  416  520

… but this becomes an issue when x and/or y become very large, as the above operation involves replicating/copying y several times - which costs memory, reduces speed, and the code is not easily scalable for arrays with different dimensions.

The ‘broadcast’ package performs “broadcasting”, which can do the above, but faster, without unnecessary copies, and scalable to arrays of any size (up to 16 dimensions).
Like so:

bc.num(x, y, "+")
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  101  205  309  413  517
#> [2,]  102  206  310  414  518
#> [3,]  103  207  311  415  519
#> [4,]  104  208  312  416  520

or like so:

broadcaster(x) <- TRUE
broadcaster(y) <- TRUE
x + y
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]  101  205  309  413  517
#> [2,]  102  206  310  414  518
#> [3,]  103  207  311  415  519
#> [4,]  104  208  312  416  520
#> broadcaster

📊Status

‘broadcast’ is fully functional, but still experimental.

If you have any suggestions or feedback on the package, its documentation, or even the benchmarks, I encourage you to let me know (either as an Issue or a Discussion).
I’m eager to read your input!

📖Documentation

The documentation in the ‘broadcast’ website is divided into 3 main parts:

Guides and Vignettes: contains the topic-oriented guides in the form of a few Vignettes.
Reference Manual: contains the function-oriented reference manual.
About: Contains the Acknowledgements, Change logs and License file. Here you’ll also find some information regarding the relationship between ‘broadcast’ and other packages/modules.