Indexing tensors

In this article we describe the indexing operator for torch tensors and how it compares to the R indexing operator for arrays.

Torch’s indexing semantics are closer to numpy’s semantics than R’s. You will find a lot of similarities between this article and the numpy indexing article available here.

Single element indexing

Single element indexing for a 1-D tensors works mostly as expected. Like R, it is 1-based. Unlike R though, it accepts negative indices for indexing from the end of the array. (In R, negative indices are used to remove elements.)

x <- torch_tensor(1:10)
x[1]
x[-1]

You can also subset matrices and higher dimensions arrays using the same syntax:

x <- x$reshape(shape = c(2,5))
x
x[1,3]
x[1,-1]

Note that if one indexes a multidimensional tensor with fewer indices than dimensions, one gets an error, unlike in R that would flatten the array. For example:

x[1]

Slicing and striding

It is possible to slice and stride arrays to extract sub-arrays of the same number of dimensions, but of different sizes than the original. This is best illustrated by a few examples:

x <- torch_tensor(1:10)
x
x[2:5]
x[1:(-7)]

You can also use the 1:10:2 syntax which means: In the range from 1 to 10, take every second item. For example:

x[1:5:2]

Another special syntax is the N, meaning the size of the specified dimension.

x[5:N]

Getting the complete dimension

Like in R, you can take all elements in a dimension by leaving an index empty.

Consider a matrix:

x <- torch_randn(2, 3)
x

The following syntax will give you the first row:

x[1,]

And this would give you the first 2 columns:

x[,1:2]

Dropping dimensions

By default, when indexing by a single integer, this dimension will be dropped to avoid the singleton dimension:

x <- torch_randn(2, 3)
x[1,]$shape

You can optionally use the drop = FALSE argument to avoid dropping the dimension.

x[1,,drop = FALSE]$shape

Adding a new dimension

It’s possible to add a new dimension to a tensor using index-like syntax:

x <- torch_tensor(c(10))
x$shape
x[, newaxis]$shape
x[, newaxis, newaxis]$shape

You can also use NULL instead of newaxis:

x[,NULL]$shape

Dealing with variable number of indices

Sometimes we don’t know how many dimensions a tensor has, but we do know what to do with the last available dimension, or the first one. To subsume all others, we can use ..:

z <- torch_tensor(1:125)$reshape(c(5,5,5))
z[1,..]
z[..,1]