# TensorFlow tensors

TensorFlow, as the name indicates, is a framework to define and run computations involving tensors. A tensor is a generalization of vectors and matrices to potentially higher dimensions. Internally, TensorFlow represents tensors as n-dimensional arrays of base datatypes.

When writing a TensorFlow program, the main object you manipulate and pass around is the tf$Tensor. A tf$Tensor object represents a partially defined computation that will eventually produce a value. TensorFlow programs work by first building a graph of tf$Tensor objects, detailing how each tensor is computed based on the other available tensors and then by running parts of this graph to achieve the desired results. A tf$Tensor has the following properties:

• a data type (float32, int32, or string, for example)
• a shape

Each element in the Tensor has the same data type, and the data type is always known. The shape (that is, the number of dimensions it has and the size of each dimension) might be only partially known. Most operations produce tensors of fully-known shapes if the shapes of their inputs are also fully known, but in some cases it’s only possible to find the shape of a tensor at graph execution time.

Some types of tensors are special, and these will be covered in other units of the TensorFlow guide. The main ones are:

• tf$Variable • tf$constant
• tf$SparseTensor With the exception of tf.Variable, the value of a tensor is immutable, which means that in the context of a single execution tensors only have a single value. However, evaluating the same tensor twice can return different values; for example that tensor can be the result of reading data from disk, or generating a random number. ## Rank The rank of a tf$Tensor object is its number of dimensions. Synonyms for rank include order or degree or n-dimension. Note that rank in TensorFlow is not the same as matrix rank in mathematics. As the following table shows, each rank in TensorFlow corresponds to a different mathematical entity:

RankMath entity
0Scalar (magnitude only)
1Vector (magnitude and direction)
2Matrix (table of numbers)
33-Tensor (cube of numbers)
nn-Tensor (you get the idea)

### Rank 0

The following snippet demonstrates creating a few rank 0 variables:

library(tensorflow)
mammal <- tf$Variable("Elephant", tf$string)
ignition <- tf$Variable(451, tf$int16)
floating <- tf$Variable(3.14159265359, tf$float64)
its_complicated <- tf$Variable(12.3 - 4.85i, tf$complex64)

Note: A string is treated as a single object in TensorFlow, not as a sequence of characters. It is possible to have scalar strings, vectors of strings, etc.

### Rank 1

To create a rank 1 tf.Tensor object, you can pass a list of items as the initial value. For example:

mystr <- tf$Variable(c("Hello"), tf$string)
cool_numbers <- tf$Variable(c(3.14159, 2.71828), tf$float32)
first_primes <- tf$Variable(c(2, 3, 5, 7, 11), tf$int32)
its_very_complicated <- tf$Variable(c(12.3 - 4.85i, 7.5 - 6.23i), tf$complex64)

### Higher ranks

A rank 2 tf$Tensor object consists of at least one row and at least one column: mymat <- tf$Variable(list(c(7, 2),c(11, 3)), tf$int16) Higher-rank Tensors, similarly, consist of an n-dimensional array. For example, during image processing, many tensors of rank 4 are used, with dimensions corresponding to example-in-batch, image height, image width, and color channel. my_image <- tf$zeros(shape = shape(10, 299, 299, 3)) # batch x height x width x color

r <- tf$rank(my_image) r ## tf.Tensor(4, shape=(), dtype=int32) ### Referring to tf$Tensor slices

Tensor elements can be extracted either by using functions like tf$gather() and tf$slice(), or by using [ syntax.

Extracting tensor elements with [ in R is similar to extracting elements from standard R arrays, albeit with some minor differences in capabilities. In contrast to most tf$ functions, [ defaults to R style 1-based rather than 0-based indexes. Currently, only numeric indexes in [ are supported (no logical or character indexes) Extracting works identically to R arrays if the slicing index is missing, supplied as a scalar, or as a sequence (e.g, created by : or seq_len()) x[,1] ) # all rows, first column x[1:2,] ) # first two rows, all columns x[,1, drop = FALSE] ) # all rows, first column, but preserving the tensor rank [ also supports slices with a strided step, which can be specified in traditional R style with seq() or with a python-style second colon. If you are unfamiliar with python-style strided step syntax, see here for a quick primer x[, seq(1, 5, by = 2)] # R style x[, 1:5:2] # Equivalent python-style strided step  Missing arguments for python syntax are valid, but they must be supplied as NULL or whole expression must by backticked. x[, ::2] x[, NULL:NULL:2] x[, 2:]  [ also accepts tf$newaxis and all_dims() as arguments

x[,, tf$newaxis] x[all_dims(), 1] # all_dims expands to the shape of the tensor An important difference between extracting R arrays and tensorflow tensors with [ is how negative numbers are interpreted. For tensorflow tensors, negative numbers are interpreted as selecting elements by counting from tail (e.g, they are interpreted python-style). x[-1,] # the last row Tensors are accepted by [ as well, but note that tensors suplied to [ are not translated from R to python. Meaning that tensors are interpreted as 0-based, and if slicing a range with :, then the returned arrays is exclusive of the upper bound. x[, tf$constant(1L)] # second column
x[, tf$constant(0L):tf$constant(2L)] # first two columns

If you are translating existing python code to R, note that you can set an option to have all [ arguments be interpreted pure-python style by setting options(tensorflow.extract.style = "python"). See ?[.tensorflow.tensor for additional options and details.

## Shape

The shape of a tensor is the number of elements in each dimension. TensorFlow automatically infers shapes during graph construction. These inferred shapes might have known or unknown rank. If the rank is known, the sizes of each dimension might be known or unknown.

The TensorFlow documentation uses three notational conventions to describe tensor dimensionality: rank, shape, and dimension number. The following table shows how these relate to one another:

RankShapeDimension numberExample
0[]0-DA 0-D tensor. A scalar.
1[D0]1-DA 1-D tensor with shape [5].
2[D0, D1]2-DA 2-D tensor with shape [3, 4].
3[D0, D1, D2]3-DA 3-D tensor with shape [1, 4, 3].
n[D0, D1, … Dn-1]n-DA tensor with shape [D0, D1, … Dn-1].

Shapes can be represented via lists of ints, or with the tf$TensorShape. ### Getting a tf$Tensor object’s shape

There are two ways of accessing the shape of a tf$Tensor. While building the graph, it is often useful to ask what is already known about a tensor’s shape. This can be done by reading the shape property of a tf$Tensor object. This method returns a TensorShape object, which is a convenient way of representing partially-specified shapes (since, when building the graph, not all shapes will be fully known).

It is also possible to get a tf$Tensor that will represent the fully-defined shape of another tf$Tensor at runtime. This is done by calling the tf$shape operation. This way, you can build a graph that manipulates the shapes of tensors by building other tensors that depend on the dynamic shape of the input tf$Tensor.

For example, here is how to make a vector of zeros with the same size as the number of columns in a given matrix:

zeros <- tf$zeros(my_image$shape[2])

### Changing the shape of a tf$Tensor The number of elements of a tensor is the product of the sizes of all its shapes. The number of elements of a scalar is always 1. Since there are often many different shapes that have the same number of elements, it’s often convenient to be able to change the shape of a tf.Tensor, keeping its elements fixed. This can be done with tf.reshape. The following examples demonstrate how to reshape tensors: rank_three_tensor <- tf$ones(shape(3, 4, 5))
matrix <- tf$reshape(rank_three_tensor, shape(6, 10)) # Reshape existing content into # a 6x10 matrix matrixB <- tf$reshape(matrix, shape(3, -1))  #  Reshape existing content into a 3x20
# matrix. -1 tells reshape to calculate
# the size of this dimension.
matrixAlt <- tf$reshape(matrixB, shape(4, 3, -1)) # Reshape existing content into a #4x3x5 tensor # Note that the number of elements of the reshaped Tensors has to match the # original number of elements. Therefore, the following example generates an # error because no possible value for the last dimension will match the number # of elements. ## Data types In addition to dimensionality, Tensors have a data type. Refer to the tf$DType page for a complete list of the data types.

It is not possible to have a tf$Tensor with more than one data type. It is possible, however, to serialize arbitrary data structures as strings and store those in tf$Tensors.

It is possible to cast tf$Tensors from one datatype to another using tf$cast:

# Cast a constant integer tensor into floating point.
float_tensor <- tf$cast(tf$constant(c(1L, 2L, 3L)), dtype=tf$float32) To inspect a tf$Tensor’s data type use the Tensor.dtype property.

When creating a tf$Tensor from an R object you may optionally specify the datatype. If you don’t, TensorFlow chooses a datatype that can represent your data. TensorFlow converts R integers to tf$int32 and R floating point numbers to tf\$float32. Otherwise TensorFlow uses the same rules numpy uses when converting to arrays.