r - What are the differences between vector, matrix and array data types?

Question

R comes with three types to store lists of homogenous objects: vector, matrix and array.

As far as I can tell:

• vector is special cases for 1 dimension arrays
• matrix is a special case for 2 dimensions arrays
• array can also have any dimension level (including 1 and 2).

What is the difference between using 1D arrays over vectors and 2D arrays over matrices? Do we need to cast between those, or will it happen automagically?

Answer 1

There is no difference between a matrix and a 2D array:

> x <- matrix(1:10, 2)
> y <- array(1:10, c(2, 5))
> identical(x, y)
[1] TRUE
...

matrix is just a more convenient constructor, and there are many functions and methods that only accept 2D arrays (a.k.a. matrices).

Internally, arrays are just vectors with a dimension attribute:

...
> attributes(x)
$dim
[1] 2 5

> dim(x) <- NULL
> x
 [1]  1  2  3  4  5  6  7  8  9 10
> z <- 1:10
> dim(z) <- c(2, 5)
> is.matrix(z)
[1] TRUE

To cite the language definition:

Matrices and arrays are simply vectors with the attribute dim and optionally dimnames attached to the vector.

[...]

The dim attribute is used to implement arrays. The content of the array is stored in a vector in column-major order and the dim attribute is a vector of integers specifying the respective extents of the array. R ensures that the length of the vector is the product of the lengths of the dimensions. The length of one or more dimensions may be zero.

A vector is not the same as a one-dimensional array since the latter has a dim attribute of length one, whereas the former has no dim attribute.