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# Tensor Transformations

Note: Functions taking Tensor arguments can also take anything accepted by tf.convert_to_tensor.

## Casting

TensorFlow provides several operations that you can use to cast tensor data types in your graph.

### tf.string_to_number(string_tensor, out_type=None, name=None)

Converts each string in the input Tensor to the specified numeric type.

(Note that int32 overflow results in an error while float overflow results in a rounded value.)

##### Args:
• string_tensor: A Tensor of type string.
• out_type: An optional tf.DType from: tf.float32, tf.int32. Defaults to tf.float32. The numeric type to interpret each string in string_tensor as.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type out_type. A Tensor of the same shape as the input string_tensor.

### tf.to_double(x, name='ToDouble')

Casts a tensor to type float64.

##### Args:
• x: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor or SparseTensor with same shape as x with type float64.

##### Raises:
• TypeError: If x cannot be cast to the float64.

• -

### tf.to_float(x, name='ToFloat')

Casts a tensor to type float32.

##### Args:
• x: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor or SparseTensor with same shape as x with type float32.

##### Raises:
• TypeError: If x cannot be cast to the float32.

• -

### tf.to_bfloat16(x, name='ToBFloat16')

Casts a tensor to type bfloat16.

##### Args:
• x: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor or SparseTensor with same shape as x with type bfloat16.

##### Raises:
• TypeError: If x cannot be cast to the bfloat16.

• -

### tf.to_int32(x, name='ToInt32')

Casts a tensor to type int32.

##### Args:
• x: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor or SparseTensor with same shape as x with type int32.

##### Raises:
• TypeError: If x cannot be cast to the int32.

• -

### tf.to_int64(x, name='ToInt64')

Casts a tensor to type int64.

##### Args:
• x: A Tensor or SparseTensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor or SparseTensor with same shape as x with type int64.

##### Raises:
• TypeError: If x cannot be cast to the int64.

• -

### tf.cast(x, dtype, name=None)

Casts a tensor to a new type.

The operation casts x (in case of Tensor) or x.values (in case of SparseTensor) to dtype.

For example:

# tensor a is [1.8, 2.2], dtype=tf.float
tf.cast(a, tf.int32) ==> [1, 2]  # dtype=tf.int32
##### Args:
• x: A Tensor or SparseTensor.
• dtype: The destination type.
• name: A name for the operation (optional).
##### Returns:

A Tensor or SparseTensor with same shape as x.

##### Raises:
• TypeError: If x cannot be cast to the dtype.

## Shapes and Shaping

TensorFlow provides several operations that you can use to determine the shape of a tensor and change the shape of a tensor.

### tf.shape(input, name=None)

Returns the shape of a tensor.

This operation returns a 1-D integer tensor representing the shape of input.

For example:

# 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
shape(t) ==> [2, 2, 3]
##### Args:
• input: A Tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type int32.

### tf.size(input, name=None)

Returns the size of a tensor.

This operation returns an integer representing the number of elements in input.

For example:

# 't' is [[[1, 1,, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]]
size(t) ==> 12
##### Args:
• input: A Tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type int32.

### tf.rank(input, name=None)

Returns the rank of a tensor.

This operation returns an integer representing the rank of input.

For example:

# 't' is [[[1, 1, 1], [2, 2, 2]], [[3, 3, 3], [4, 4, 4]]]
# shape of tensor 't' is [2, 2, 3]
rank(t) ==> 3

Note: The rank of a tensor is not the same as the rank of a matrix. The rank of a tensor is the number of indices required to uniquely select each element of the tensor. Rank is also known as "order", "degree", or "ndims."

##### Args:
• input: A Tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor of type int32.

### tf.reshape(tensor, shape, name=None)

Reshapes a tensor.

Given tensor, this operation returns a tensor that has the same values as tensor with shape shape.

If shape is the special value [-1], then tensor is flattened and the operation outputs a 1-D tensor with all elements of tensor.

If shape is 1-D or higher, then the operation returns a tensor with shape shape filled with the values of tensor. In this case, the number of elements implied by shape must be the same as the number of elements in tensor.

For example:

# tensor 't' is [1, 2, 3, 4, 5, 6, 7, 8, 9]
# tensor 't' has shape [9]
reshape(t, [3, 3]) ==> [[1, 2, 3]
[4, 5, 6]
[7, 8, 9]]

# tensor 't' is [[[1, 1], [2, 2]]
#                [[3, 3], [4, 4]]]
# tensor 't' has shape [2, 2]
reshape(t, [2, 4]) ==> [[1, 1, 2, 2]
[3, 3, 4, 4]]

# tensor 't' is [[[1, 1, 1],
#                 [2, 2, 2]],
#                [[3, 3, 3],
#                 [4, 4, 4]],
#                [[5, 5, 5],
#                 [6, 6, 6]]]
# tensor 't' has shape [3, 2, 3]
# pass '[-1]' to flatten 't'
reshape(t, [-1]) ==> [1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6]
##### Args:
• tensor: A Tensor.
• shape: A Tensor of type int32. Defines the shape of the output tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as tensor.

### tf.squeeze(input, squeeze_dims=None, name=None)

Removes dimensions of size 1 from the shape of a tensor.

Given a tensor input, this operation returns a tensor of the same type with all dimensions of size 1 removed. If you don't want to remove all size 1 dimensions, you can remove specific size 1 dimensions by specifying squeeze_dims.

For example:

# 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
shape(squeeze(t)) ==> [2, 3]

Or, to remove specific size 1 dimensions:

# 't' is a tensor of shape [1, 2, 1, 3, 1, 1]
shape(squeeze(t, [2, 4])) ==> [1, 2, 3, 1]
##### Args:
• input: A Tensor. The input to squeeze.
• squeeze_dims: An optional list of ints. Defaults to []. If specified, only squeezes the dimensions listed. The dimension index starts at 0. It is an error to squeeze a dimension that is not 1.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input. Contains the same data as input, but has one or more dimensions of size 1 removed.

### tf.expand_dims(input, dim, name=None)

Inserts a dimension of 1 into a tensor's shape.

Given a tensor input, this operation inserts a dimension of 1 at the dimension index dim of input's shape. The dimension index dim starts at zero; if you specify a negative number for dim it is counted backward from the end.

This operation is useful if you want to add a batch dimension to a single element. For example, if you have a single image of shape [height, width, channels], you can make it a batch of 1 image with expand_dims(image, 0), which will make the shape [1, height, width, channels].

Other examples:

# 't' is a tensor of shape [2]
shape(expand_dims(t, 0)) ==> [1, 2]
shape(expand_dims(t, 1)) ==> [2, 1]
shape(expand_dims(t, -1)) ==> [2, 1]

# 't2' is a tensor of shape [2, 3, 5]
shape(expand_dims(t2, 0)) ==> [1, 2, 3, 5]
shape(expand_dims(t2, 2)) ==> [2, 3, 1, 5]
shape(expand_dims(t2, 3)) ==> [2, 3, 5, 1]

This operation requires that:

-1-input.dims() <= dim <= input.dims()

This operation is related to squeeze(), which removes dimensions of size 1.

##### Args:
• input: A Tensor.
• dim: A Tensor of type int32. 0-D (scalar). Specifies the dimension index at which to expand the shape of input.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input. Contains the same data as input, but its shape has an additional dimension of size 1 added.

## Slicing and Joining

TensorFlow provides several operations to slice or extract parts of a tensor, or join multiple tensors together.

### tf.slice(input_, begin, size, name=None)

Extracts a slice from a tensor.

This operation extracts a slice of size size from a tensor input starting at the location specified by begin. The slice size is represented as a tensor shape, where size[i] is the number of elements of the 'i'th dimension of input that you want to slice. The starting location (begin) for the slice is represented as an offset in each dimension of input. In other words, begin[i] is the offset into the 'i'th dimension of input that you want to slice from.

begin is zero-based; size is one-based. If size[i] is -1, all remaining elements in dimension i are included in the slice. In other words, this is equivalent to setting:

size[i] = input.dim_size(i) - begin[i]

This operation requires that:

0 <= begin[i] <= begin[i] + size[i] <= Di for i in [0, n]

For example:

# 'input' is [[[1, 1, 1], [2, 2, 2]],
#             [[3, 3, 3], [4, 4, 4]],
#             [[5, 5, 5], [6, 6, 6]]]
tf.slice(input, [1, 0, 0], [1, 1, 3]) ==> [[[3, 3, 3]]]
tf.slice(input, [1, 0, 0], [1, 2, 3]) ==> [[[3, 3, 3],
[4, 4, 4]]]
tf.slice(input, [1, 0, 0], [2, 1, 3]) ==> [[[3, 3, 3]],
[[5, 5, 5]]]
##### Args:
• input_: A Tensor.
• begin: An int32 or int64 Tensor.
• size: An int32 or int64 Tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor the same type as input.

### tf.split(split_dim, num_split, value, name='split')

Splits a tensor into num_split tensors along one dimension.

Splits value along dimension split_dim into num_split smaller tensors. Requires that num_split evenly divide value.shape[split_dim].

For example:

# 'value' is a tensor with shape [5, 30]
# Split 'value' into 3 tensors along dimension 1
split0, split1, split2 = tf.split(1, 3, value)
tf.shape(split0) ==> [5, 10]
##### Args:
• split_dim: A 0-D int32 Tensor. The dimension along which to split. Must be in the range [0, rank(value)).
• num_split: A 0-D int32 Tensor. The number of ways to split.
• value: The Tensor to split.
• name: A name for the operation (optional).
##### Returns:

num_split Tensor objects resulting from splitting value.

### tf.tile(input, multiples, name=None)

Constructs a tensor by tiling a given tensor.

This operation creates a new tensor by replicating input multiples times. The output tensor's i'th dimension has input.dims(i) * multiples[i] elements, and the values of input are replicated multiples[i] times along the 'i'th dimension. For example, tiling [a b c d] by [2] produces [a b c d a b c d].

##### Args:
• input: A Tensor. 1-D or higher.
• multiples: A Tensor of type int32. 1-D. Length must be the same as the number of dimensions in input
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input.

### tf.pad(input, paddings, name=None)

This operation pads a input with zeros according to the paddings you specify. paddings is an integer tensor with shape [Dn, 2], where n is the rank of input. For each dimension D of input, paddings[D, 0] indicates how many zeros to add before the contents of input in that dimension, and paddings[D, 1] indicates how many zeros to add after the contents of input in that dimension.

The padded size of each dimension D of the output is:

paddings(D, 0) + input.dim_size(D) + paddings(D, 1)

For example:

# 't' is [[1, 1], [2, 2]]
# 'paddings' is [[1, 1]], [2, 2]]
# rank of 't' is 2
[0, 0, 0, 0, 0]
[0, 1, 1, 0, 0]
[[0, 2, 2, 0, 0]
[0, 0, 0, 0, 0]]
##### Args:
• input: A Tensor.
• paddings: A Tensor of type int32.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input.

### tf.concat(concat_dim, values, name='concat')

Concatenates tensors along one dimension.

Concatenates the list of tensors values along dimension concat_dim. If values[i].shape = [D0, D1, ... Dconcat_dim(i), ...Dn], the concatenated result has shape

[D0, D1, ... Rconcat_dim, ...Dn]

where

Rconcat_dim = sum(Dconcat_dim(i))

That is, the data from the input tensors is joined along the concat_dim dimension.

The number of dimensions of the input tensors must match, and all dimensions except concat_dim must be equal.

For example:

t1 = [[1, 2, 3], [4, 5, 6]]
t2 = [[7, 8, 9], [10, 11, 12]]
tf.concat(0, [t1, t2]) ==> [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
tf.concat(1, [t1, t2]) ==> [[1, 2, 3, 7, 8, 9], [4, 5, 6, 10, 11, 12]]

# tensor t3 with shape [2, 3]
# tensor t4 with shape [2, 3]
tf.shape(tf.concat(0, [t3, t4])) ==> [4, 3]
tf.shape(tf.concat(1, [t3, t4])) ==> [2, 6]
##### Args:
• concat_dim: 0-D int32 Tensor. Dimension along which to concatenate.
• values: A list of Tensor objects or a single Tensor.
• name: A name for the operation (optional).
##### Returns:

A Tensor resulting from concatenation of the input tensors.

### tf.pack(values, name='pack')

Packs a list of rank-R tensors into one rank-(R+1) tensor.

Packs tensors in values into a tensor with rank one higher than each tensor in values and shape [len(values)] + values[0].shape. The output satisfies output[i, ...] = values[i][...].

This is the opposite of unpack. The numpy equivalent is

tf.pack([x, y, z]) = np.asarray([x, y, z])
##### Args:
• values: A list of Tensor objects with the same shape and type.
• name: A name for this operation (optional).
##### Returns:
• output: A packed Tensor with the same type as values.

• -

### tf.unpack(value, num=None, name='unpack')

Unpacks the outer dimension of a rank-R tensor into rank-(R-1) tensors.

Unpacks num tensors from value along the first dimension. If num is not specified (the default), it is inferred from value's shape. If value.shape[0] is not known, ValueError is raised.

The ith tensor in output is the slice value[i, ...]. Each tensor in output has shape value.shape[1:].

This is the opposite of pack. The numpy equivalent is

tf.unpack(x, n) = list(x)
##### Args:
• value: A rank R > 0 Tensor to be unpacked.
• num: An int. The first dimension of value. Automatically inferred if None (the default).
• name: A name for the operation (optional).
##### Returns:

The list of Tensor objects unpacked from value.

##### Raises:
• ValueError: If num is unspecified and cannot be inferred.

• -

### tf.reverse_sequence(input, seq_lengths, seq_dim, name=None)

Reverses variable length slices in dimension seq_dim.

This op first slices input along the first dimension, and for each slice i, reverses the first seq_lengths[i] elements along the dimension seq_dim.

The elements of seq_lengths must obey seq_lengths[i] < input.dims[seq_dim], and seq_lengths must be a vector of length input.dims(0).

The output slice i along dimension 0 is then given by input slice i, with the first seq_lengths[i] slices along dimension seq_dim reversed.

For example:

# Given this:
seq_dim = 1
input.dims = (4, ...)
seq_lengths = [7, 2, 3, 5]

# then slices of input are reversed on seq_dim, but only up to seq_lengths:
output[0, 0:7, :, ...] = input[0, 7:0:-1, :, ...]
output[1, 0:2, :, ...] = input[1, 2:0:-1, :, ...]
output[2, 0:3, :, ...] = input[2, 3:0:-1, :, ...]
output[3, 0:5, :, ...] = input[3, 5:0:-1, :, ...]

# while entries past seq_lens are copied through:
output[0, 7:, :, ...] = input[0, 7:, :, ...]
output[1, 2:, :, ...] = input[1, 2:, :, ...]
output[2, 3:, :, ...] = input[2, 3:, :, ...]
output[3, 2:, :, ...] = input[3, 2:, :, ...]
##### Args:
• input: A Tensor. The input to reverse.
• seq_lengths: A Tensor of type int64. 1-D with length input.dims(0) and max(seq_lengths) < input.dims(seq_dim)
• seq_dim: An int. The dimension which is partially reversed.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input. The partially reversed input. It has the same shape as input.

### tf.reverse(tensor, dims, name=None)

Reverses specific dimensions of a tensor.

Given a tensor, and a bool tensor dims representing the dimensions of tensor, this operation reverses each dimension i of tensor where dims[i] is True.

tensor can have up to 8 dimensions. The number of dimensions of tensor must equal the number of elements in dims. In other words:

rank(tensor) = size(dims)

For example:

# tensor 't' is [[[[ 0,  1,  2,  3],
#                  [ 4,  5,  6,  7],
#                  [ 8,  9, 10, 11]],
#                 [[12, 13, 14, 15],
#                  [16, 17, 18, 19],
#                  [20, 21, 22, 23]]]]
# tensor 't' shape is [1, 2, 3, 4]

# 'dims' is [False, False, False, True]
reverse(t, dims) ==> [[[[ 3,  2,  1,  0],
[ 7,  6,  5,  4],
[ 11, 10, 9, 8]],
[[15, 14, 13, 12],
[19, 18, 17, 16],
[23, 22, 21, 20]]]]

# 'dims' is [False, True, False, False]
reverse(t, dims) ==> [[[[12, 13, 14, 15],
[16, 17, 18, 19],
[20, 21, 22, 23]
[[ 0,  1,  2,  3],
[ 4,  5,  6,  7],
[ 8,  9, 10, 11]]]]

# 'dims' is [False, False, True, False]
reverse(t, dims) ==> [[[[8, 9, 10, 11],
[4, 5, 6, 7],
[0, 1, 2, 3]]
[[20, 21, 22, 23],
[16, 17, 18, 19],
[12, 13, 14, 15]]]]
##### Args:
• tensor: A Tensor. Must be one of the following types: uint8, int8, int32, bool, float32, float64. Up to 8-D.
• dims: A Tensor of type bool. 1-D. The dimensions to reverse.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as tensor. The same shape as tensor.

### tf.transpose(a, perm=None, name='transpose')

Transposes a. Permutes the dimensions according to perm.

The returned tensor's dimension i will correspond to the input dimension perm[i]. If perm is not given, it is set to (n-1...0), where n is the rank of the input tensor. Hence by default, this operation performs a regular matrix transpose on 2-D input Tensors.

For example:

# 'x' is [[1 2 3]
#         [4 5 6]]
tf.transpose(x) ==> [[1 4]
[2 5]
[3 6]]

# Equivalently
tf.transpose(x perm=[0, 1]) ==> [[1 4]
[2 5]
[3 6]]

# 'perm' is more useful for n-dimensional tensors, for n > 2
# 'x' is   [[[1  2  3]
#            [4  5  6]]
#           [[7  8  9]
#            [10 11 12]]]
# Take the transpose of the matrices in dimension-0
tf.transpose(b, perm=[0, 2, 1]) ==> [[[1  4]
[2  5]
[3  6]]

[[7 10]
[8 11]
[9 12]]]
##### Args:
• a: A Tensor.
• perm: A permutation of the dimensions of a.
• name: A name for the operation (optional).
##### Returns:

A transposed Tensor.

### tf.gather(params, indices, name=None)

Gather slices from params according to indices.

indices must be an integer tensor of any dimension (usually 0-D or 1-D). Produces an output tensor with shape indices.shape + params.shape[1:] where:

# Scalar indices
output[:, ..., :] = params[indices, :, ... :]

# Vector indices
output[i, :, ..., :] = params[indices[i], :, ... :]

# Higher rank indices
output[i, ..., j, :, ... :] = params[indices[i, ..., j], :, ..., :]

If indices is a permutation and len(indices) == params.shape[0] then this operation will permute params accordingly.

##### Args:
• params: A Tensor.
• indices: A Tensor. Must be one of the following types: int32, int64.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as params.

### tf.dynamic_partition(data, partitions, num_partitions, name=None)

Partitions data into num_partitions tensors using indices from partitions.

For each index tuple js of size partitions.ndim, the slice data[js, ...] becomes part of outputs[partitions[js]]. The slices with partitions[js] = i are placed in outputs[i] in lexicographic order of js, and the first dimension of outputs[i] is the number of entries in partitions equal to i. In detail,

outputs[i].shape = [sum(partitions == i)] + data.shape[partitions.ndim:]

outputs[i] = pack([data[js, ...] for js if partitions[js] == i])

data.shape must start with partitions.shape.

For example:

# Scalar partitions
partitions = 1
num_partitions = 2
data = [10, 20]
outputs[0] = []  # Empty with shape [0, 2]
outputs[1] = [[10, 20]]

# Vector partitions
partitions = [0, 0, 1, 1, 0]
num_partitions = 2
data = [10, 20, 30, 40, 50]
outputs[0] = [10, 20, 50]
outputs[1] = [30, 40]
##### Args:
• data: A Tensor.
• partitions: A Tensor of type int32. Any shape. Indices in the range [0, num_partitions).
• num_partitions: An int that is >= 1. The number of partitions to output.
• name: A name for the operation (optional).
##### Returns:

A list of num_partitions Tensor objects of the same type as data.

### tf.dynamic_stitch(indices, data, name=None)

Interleave the values from the data tensors into a single tensor.

Builds a merged tensor such that

merged[indices[m][i, ..., j], ...] = data[m][i, ..., j, ...]

For example, if each indices[m] is scalar or vector, we have

# Scalar indices
merged[indices[m], ...] = data[m][...]

# Vector indices
merged[indices[m][i], ...] = data[m][i, ...]

Each data[i].shape must start with the corresponding indices[i].shape, and the rest of data[i].shape must be constant w.r.t. i. That is, we must have data[i].shape = indices[i].shape + constant. In terms of this constant, the output shape is

merged.shape = [max(indices)] + constant

Values are merged in order, so if an index appears in both indices[m][i] and indices[n][j] for (m,i) < (n,j) the slice data[n][j] will appear in the merged result.

For example:

indices[0] = 6
indices[1] = [4, 1]
indices[2] = [[5, 2], [0, 3]]
data[0] = [61, 62]
data[1] = [[41, 42], [11, 12]]
data[2] = [[[51, 52], [21, 22]], [[1, 2], [31, 32]]]
merged = [[1, 2], [11, 12], [21, 22], [31, 32], [41, 42],
[51, 52], [61, 62]]
##### Args:
• indices: A list of at least 2 Tensor objects of type int32.
• data: A list with the same number of Tensor objects as indices of Tensor objects of the same type.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as data.