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]
#> torch_tensor
#> 1
#> [ CPULongType{} ]
x[-1]
#> torch_tensor
#> 10
#> [ CPULongType{} ]

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

x <- x$reshape(shape = c(2,5))
x
#> torch_tensor
#>   1   2   3   4   5
#>   6   7   8   9  10
#> [ CPULongType{2,5} ]
x[1,3]
#> torch_tensor
#> 3
#> [ CPULongType{} ]
x[1,-1]
#> torch_tensor
#> 5
#> [ CPULongType{} ]

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]
#> torch_tensor
#>  1
#>  2
#>  3
#>  4
#>  5
#> [ CPULongType{5} ]

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
#> torch_tensor
#>   1
#>   2
#>   3
#>   4
#>   5
#>   6
#>   7
#>   8
#>   9
#>  10
#> [ CPULongType{10} ]
x[2:5]
#> torch_tensor
#>  2
#>  3
#>  4
#>  5
#> [ CPULongType{4} ]
x[1:(-7)]
#> torch_tensor
#>  1
#>  2
#>  3
#>  4
#> [ CPULongType{4} ]

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]
#> torch_tensor
#>  1
#>  3
#>  5
#> [ CPULongType{3} ]

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

x[5:N]
#> torch_tensor
#>   5
#>   6
#>   7
#>   8
#>   9
#>  10
#> [ CPULongType{6} ]

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
#> torch_tensor
#> -0.6076  0.2493  1.7494
#> -1.2213  0.2575  0.6397
#> [ CPUFloatType{2,3} ]

The following syntax will give you the first row:

x[1,]
#> torch_tensor
#> -0.6076
#>  0.2493
#>  1.7494
#> [ CPUFloatType{3} ]

And this would give you the first 2 columns:

x[,1:2]
#> torch_tensor
#> -0.6076  0.2493
#> -1.2213  0.2575
#> [ CPUFloatType{2,2} ]

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
#> [1] 3

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

x[1,,drop = FALSE]$shape
#> [1] 1 3

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$shape
#> [1] 1
x[, newaxis]$shape
#> [1] 1 1
x[, newaxis, newaxis]$shape
#> [1] 1 1 1

You can also use NULL instead of newaxis:

x[,NULL]$shape
#> [1] 1 1

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,..]
#> torch_tensor
#>   1   2   3   4   5
#>   6   7   8   9  10
#>  11  12  13  14  15
#>  16  17  18  19  20
#>  21  22  23  24  25
#> [ CPULongType{5,5} ]
z[..,1]
#> torch_tensor
#>    1    6   11   16   21
#>   26   31   36   41   46
#>   51   56   61   66   71
#>   76   81   86   91   96
#>  101  106  111  116  121
#> [ CPULongType{5,5} ]