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Indexing tensors

Source: vignettes/indexing.Rmd
indexing.Rmd

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, torch’s behaviour differs from R, which flattens the array. In torch, the missing indices are considered complete slices :.

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
#> -1.1594 -1.9351  1.0987
#> -0.2400  0.9302  0.4572
#> [ CPUFloatType{2,3} ]

The following syntax will give you the first row:

x[1,]
#> torch_tensor
#> -1.1594
#> -1.9351
#>  1.0987
#> [ CPUFloatType{3} ]

And this would give you the first 2 columns:

x[,1:2]
#> torch_tensor
#> -1.1594 -1.9351
#> -0.2400  0.9302
#> [ 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
#>  0.6781 -0.5159
#> -1.0444 -1.0188
#> [ CPUFloatType{2,2} ]

You can also use boolean vectors, for example:

x[c(TRUE, FALSE, TRUE, FALSE), c(TRUE, FALSE, TRUE, FALSE)]
#> torch_tensor
#>  0.6781 -0.5159
#> -1.0444 -1.0188
#> [ 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} ]