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

    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]