# 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]
#> 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} ] 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] #> torch_tensor #> 1 #> 3 #> 5 #> [ CPULongType{3} ] is equivalent to: x[slc(start = 1, end = 5, step = 2)] #> torch_tensor #> 1 #> 3 #> 5 #> [ CPULongType{3} ] ## 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 #> 1.1082 -0.0210 -1.1702 #> -0.0558 0.7846 -0.4737 #> [ CPUFloatType{2,3} ] The following syntax will give you the first row: x[1,] #> torch_tensor #> 1.1082 #> -0.0210 #> -1.1702 #> [ CPUFloatType{3} ] And this would give you the first 2 columns: x[,1:2] #> torch_tensor #> 1.1082 -0.0210 #> -0.0558 0.7846 #> [ 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} ]

## 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)]
#> torch_tensor
#>  1.0644 -1.1929
#> -0.5789 -0.8773
#> [ CPUFloatType{2,2} ]

You can also use boolean vectors, for example:

x[c(TRUE, FALSE, TRUE, FALSE), c(TRUE, FALSE, TRUE, FALSE)]
#> torch_tensor
#>  1.0644 -1.1929
#> -0.5789 -0.8773
#> [ CPUFloatType{2,2} ]

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]
#> torch_tensor
#>  4
#>  5
#>  6
#> [ CPUFloatType{3} ]