Indexing tensors

library(torch)

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$reshape(shape = c(2,5)) x x[1,3] x[1,-1] Note that if one indexes a multidimensional tensor with fewer indices than dimensions, one gets an error, unlike in R that would flatten the array. For example: x[1] Slicing and striding It is possible to slice and stride arrays to extract sub-arrays of the same number of dimensions, but of different sizes than the original. This is best illustrated by a few examples: x <- torch_tensor(1:10) x x[2:5] x[1:(-7)] You can also use the 1:10:2 syntax which means: In the range from 1 to 10, take every second item. For example: x[1:5:2] Another special syntax is the N, meaning the size of the specified dimension. x[5:N] Note: the slicing behavior relies on Non Standard Evaluation. It requires that the expression is passed to the [ not exactly the resulting R vector. To allow dynamic dynamic indices, you can create a new slice using the slc function. For example: x[1:5:2] is equivalent to: x[slc(start = 1, end = 5, step = 2)] Getting the complete dimension Like in R, you can take all elements in a dimension by leaving an index empty. Consider a matrix: x <- torch_randn(2, 3) x The following syntax will give you the first row: x[1,] And this would give you the first 2 columns: x[,1:2] Dropping dimensions By default, when indexing by a single integer, this dimension will be dropped to avoid the singleton dimension: x <- torch_randn(2, 3) x[1,]$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]

Indexing with vectors

Vector indexing is also supported but care must be taken regarding performance as, in general its much less performant than slice based indexing.

Note: Starting from version 0.5.0, vector indexing in torch follows R semantics, prior to that the behavior was similar to numpy’s advanced indexing. To use the old behavior, consider using ?torch_index, ?torch_index_put or torch_index_put_.

x <- torch_randn(4,4)
x[c(1,3), c(1,3)]

You can also use boolean vectors, for example:

x[c(TRUE, FALSE, TRUE, FALSE), c(TRUE, FALSE, TRUE, FALSE)]

The above examples also work if the index were long or boolean tensors, instead of R vectors. It’s also possible to index with multi-dimensional boolean tensors:

x <- torch_tensor(rbind(
c(1,2,3),
c(4,5,6)
))
x[x>3]