# 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.strided_slice(input_, begin, end, strides, begin_mask=0, end_mask=0, ellipsis_mask=0, new_axis_mask=0, shrink_axis_mask=0, name=None)

Extracts a strided slice from a tensor.

To a first order, this operation extracts a slice of size end - begin from a tensor input starting at the location specified by begin. The slice continues by adding stride to the begin index until all dimensions are not less than end. Note that components of stride can be negative, which causes a reverse slice.

This operation can be thought of an encoding of a numpy style sliced range. Given a python slice input[, , ..., ] this function will be called as follows.

begin, end, and strides will be all length n. n is in general not the same dimensionality as input.

For the ith spec, begin_mask, end_mask, ellipsis_mask, new_axis_mask, and shrink_axis_mask will have the ith bit corrsponding to the ith spec.

If the ith bit of begin_mask is non-zero, begin[i] is ignored and the fullest possible range in that dimension is used instead. end_mask works analogously, except with the end range.

foo[5:,:,:3] on a 7x8x9 tensor is equivalent to foo[5:7,0:8,0:3]. foo[::-1] reverses a tensor with shape 8.

If the ith bit of ellipsis_mask, as many unspecified dimensions as needed will be inserted between other dimensions. Only one non-zero bit is allowed in ellipsis_mask.

For example foo[3:5,...,4:5] on a shape 10x3x3x10 tensor is equivalent to foo[3:5,:,:,4:5] and foo[3:5,...] is equivalent to foo[3:5,:,:,:].

If the ith bit of new_axis_mask is one, then a begin, end, and stride are ignored and a new length 1 dimension is added at this point in the output tensor.

For example foo[3:5,4] on a 10x8 tensor produces a shape 2 tensor whereas foo[3:5,4:5] produces a shape 2x1 tensor with shrink_mask being 1<<1 == 2.

If the ith bit of shrink_axis_mask is one, then begin, end[i], and stride[i] are used to do a slice in the appropriate dimension, but the output tensor will be reduced in dimensionality by one. This is only valid if the ith entry of slice[i]==1.

NOTE: begin and end are zero-indexed.strides entries must be non-zero.

# '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], [2, 1, 3], [1, 1, 1]) ==> [[[3, 3, 3]]]
tf.slice(input, [1, 0, 0], [2, 2, 3], [1, 1, 1]) ==> [[[3, 3, 3],
[4, 4, 4]]]
tf.slice(input, [1, 1, 0], [2, -1, 3], [1, -1, 1]) ==>[[[4, 4, 4],
[3, 3, 3]]]

##### Args:
• input_: A Tensor.
• begin: An int32 or int64 Tensor.
• end: An int32 or int64 Tensor.
• strides: An int32 or int64 Tensor.
• begin_mask: An int32 mask.
• end_mask: An int32 mask.
• ellipsis_mask: An int32 mask.
• new_axis_mask: An int32 mask.
• shrink_axis_mask: An int32 mask.
• 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]

num_items = t.get_shape()[axis].value
[tf.squeeze(s, [axis]) for s in tf.split(axis, num_items, t)]


can be rewritten as

tf.unpack(t, axis=axis)

##### 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 Python integer. 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(tensor, paddings, mode='CONSTANT', name=None)

This operation pads a tensor according to the paddings you specify. paddings is an integer tensor with shape [n, 2], where n is the rank of tensor. For each dimension D of input, paddings[D, 0] indicates how many values to add before the contents of tensor in that dimension, and paddings[D, 1] indicates how many values to add after the contents of tensor in that dimension. If mode is "REFLECT" then both paddings[D, 0] and paddings[D, 1] must be no greater than tensor.dim_size(D) - 1. If mode is "SYMMETRIC" then both paddings[D, 0] and paddings[D, 1] must be no greater than tensor.dim_size(D).

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

paddings[D, 0] + tensor.dim_size(D) + paddings[D, 1]

For example:

# 't' is [[1, 2, 3], [4, 5, 6]].
# 'paddings' is [[1, 1,], [2, 2]].
# rank of 't' is 2.
[0, 0, 1, 2, 3, 0, 0],
[0, 0, 4, 5, 6, 0, 0],
[0, 0, 0, 0, 0, 0, 0]]

[3, 2, 1, 2, 3, 2, 1],
[6, 5, 4, 5, 6, 5, 4],
[3, 2, 1, 2, 3, 2, 1]]

[2, 1, 1, 2, 3, 3, 2],
[5, 4, 4, 5, 6, 6, 5],
[5, 4, 4, 5, 6, 6, 5]]

##### Args:
• tensor: A Tensor.
• paddings: A Tensor of type int32.
• mode: One of "CONSTANT", "REFLECT", or "SYMMETRIC".
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as tensor.

##### Raises:
• ValueError: When mode is not one of "CONSTANT", "REFLECT", or "SYMMETRIC".

### 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]

tf.concat(axis, [tf.expand_dims(t, axis) for t in tensors])


can be rewritten as

tf.pack(tensors, axis=axis)

##### 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, axis=0, name='pack')

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

Packs the list of tensors in values into a tensor with rank one higher than each tensor in values, by packing them along the axis dimension. Given a list of length N of tensors of shape (A, B, C);

if axis == 0 then the output tensor will have the shape (N, A, B, C). if axis == 1 then the output tensor will have the shape (A, N, B, C). Etc.

For example:

# 'x' is [1, 4]
# 'y' is [2, 5]
# 'z' is [3, 6]
pack([x, y, z]) => [[1, 4], [2, 5], [3, 6]]  # Pack along first dim.
pack([x, y, z], axis=1) => [[1, 2, 3], [4, 5, 6]]


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.
• axis: An int. The axis to pack along. Defaults to the first dimension. Supports negative indexes.
• name: A name for this operation (optional).
##### Returns:
• output: A packed Tensor with the same type as values.
##### Raises:
• ValueError: If axis is out of the range [-(R+1), R+1).

### tf.unpack(value, num=None, axis=0, name='unpack')

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

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

For example, given a tensor of shape (A, B, C, D);

If axis == 0 then the i'th tensor in output is the slice value[i, :, :, :] and each tensor in output will have shape (B, C, D). (Note that the dimension unpacked along is gone, unlike split).

If axis == 1 then the i'th tensor in output is the slice value[:, i, :, :] and each tensor in output will have shape (A, C, D). Etc.

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 length of the dimension axis. Automatically inferred if None (the default).
• axis: An int. The axis to unpack along. Defaults to the first dimension. Supports negative indexes.
• 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.
• ValueError: If axis is out of the range [-R, R).

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

Reverses variable length slices.

This op first slices input along the dimension batch_dim, 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[batch_dim].

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

For example:

# Given this:
batch_dim = 0
seq_dim = 1
input.dims = (4, 8, ...)
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:, :, ...]


In contrast, if:

# Given this:
batch_dim = 2
seq_dim = 0
input.dims = (8, ?, 4, ...)
seq_lengths = [7, 2, 3, 5]

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

# while entries past seq_lens are copied through:
output[7:, :, 0, :, ...] = input[7:, :, 0, :, ...]
output[2:, :, 1, :, ...] = input[2:, :, 1, :, ...]
output[3:, :, 2, :, ...] = input[3:, :, 2, :, ...]
output[2:, :, 3, :, ...] = input[2:, :, 3, :, ...]

##### Args:
• input: A Tensor. The input to reverse.
• seq_lengths: A Tensor of type int64. 1-D with length input.dims(batch_dim) and max(seq_lengths) < input.dims(seq_dim)
• seq_dim: An int. The dimension which is partially reversed.
• batch_dim: An optional int. Defaults to 0. The dimension along which reversal is performed.
• 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, half, float32, float64, complex64, complex128. 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=[1, 0]) ==> [[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(x, 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.extract_image_patches(images, ksizes, strides, rates, padding, name=None)

Extract patches from images and put them in the "depth" output dimension.

##### Args:
• images: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half. 4-D Tensor with shape [batch, in_rows, in_cols, depth].
• ksizes: A list of ints that has length >= 4. The size of the sliding window for each dimension of images.
• strides: A list of ints that has length >= 4. 1-D of length 4. How far the centers of two consecutive patches are in the images. Must be: [1, stride_rows, stride_cols, 1].
• rates: A list of ints that has length >= 4. 1-D of length 4. Must be: [1, rate_rows, rate_cols, 1]. This is the input stride, specifying how far two consecutive patch samples are in the input. Equivalent to extracting patches with patch_sizes_eff = patch_sizes + (patch_sizes - 1) * (rates - 1), followed by subsampling them spatially by a factor ofrates.
• padding: A string from: "SAME", "VALID". The type of padding algorithm to use.

We specify the size-related attributes as:

  ksizes = [1, ksize_rows, ksize_cols, 1]
strides = [1, strides_rows, strides_cols, 1]
rates = [1, rates_rows, rates_cols, 1]

• name: A name for the operation (optional).

##### Returns:

A Tensor. Has the same type as images. 4-D Tensor with shape [batch, out_rows, out_cols, ksize_rows * ksize_cols * depth] containing image patches with size ksize_rows x ksize_cols x depth vectorized in the "depth" dimension.

### tf.space_to_batch(input, paddings, block_size, name=None)

SpaceToBatch for 4-D tensors of type T.

Zero-pads and then rearranges (permutes) blocks of spatial data into batch. More specifically, this op outputs a copy of the input tensor where values from the height and width dimensions are moved to the batch dimension. After the zero-padding, both height and width of the input must be divisible by the block size.

##### Args:
• input: A Tensor. 4-D with shape [batch, height, width, depth].
• paddings: A Tensor of type int32. 2-D tensor of non-negative integers with shape [2, 2]. It specifies the padding of the input with zeros across the spatial dimensions as follows:

  paddings = [[pad_top, pad_bottom], [pad_left, pad_right]]


The effective spatial dimensions of the zero-padded input tensor will be:

  height_pad = pad_top + height + pad_bottom


The attr block_size must be greater than one. It indicates the block size.

• Non-overlapping blocks of size block_size x block size in the height and width dimensions are rearranged into the batch dimension at each location.
• The batch of the output tensor is batch * block_size * block_size.

The shape of the output will be:

[batch*block_size*block_size, height_pad/block_size, width_pad/block_size,
depth]


Some examples:

(1) For the following input of shape [1, 2, 2, 1] and block_size of 2:

prettyprint x = [[[[1], [2]], [[3], [4]]]]

The output tensor has shape [4, 1, 1, 1] and value:

prettyprint [[[[1]]], [[[2]]], [[[3]]], [[[4]]]]

(2) For the following input of shape [1, 2, 2, 3] and block_size of 2:

prettyprint x = [[[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]]]

The output tensor has shape [4, 1, 1, 3] and value:

prettyprint [[[1, 2, 3]], [[4, 5, 6]], [[7, 8, 9]], [[10, 11, 12]]]

(3) For the following input of shape [1, 4, 4, 1] and block_size of 2:

prettyprint x = [[[[1], [2], [3], [4]], [[5], [6], [7], [8]], [[9], [10], [11], [12]], [[13], [14], [15], [16]]]]

The output tensor has shape [4, 2, 2, 1] and value:

prettyprint x = [[[[1], [3]], [[5], [7]]], [[[2], [4]], [[10], [12]]], [[[5], [7]], [[13], [15]]], [[[6], [8]], [[14], [16]]]]

(4) For the following input of shape [2, 2, 4, 1] and block_size of 2:

prettyprint x = [[[[1], [2], [3], [4]], [[5], [6], [7], [8]]], [[[9], [10], [11], [12]], [[13], [14], [15], [16]]]]

The output tensor has shape [8, 1, 2, 1] and value:

prettyprint x = [[[[1], [3]]], [[[9], [11]]], [[[2], [4]]], [[[10], [12]]], [[[5], [7]]], [[[13], [15]]], [[[6], [8]]], [[[14], [16]]]]

Among others, this operation is useful for reducing atrous convolution into regular convolution.

• block_size: An int that is >= 2.

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

A Tensor. Has the same type as input.

### tf.batch_to_space(input, crops, block_size, name=None)

BatchToSpace for 4-D tensors of type T.

Rearranges (permutes) data from batch into blocks of spatial data, followed by cropping. This is the reverse transformation of SpaceToBatch. More specifically, this op outputs a copy of the input tensor where values from the batch dimension are moved in spatial blocks to the height and width dimensions, followed by cropping along the height and width dimensions.

##### Args:
• input: A Tensor. 4-D tensor with shape [batch*block_size*block_size, height_pad/block_size, width_pad/block_size, depth]. Note that the batch size of the input tensor must be divisible by block_size * block_size.
• crops: A Tensor of type int32. 2-D tensor of non-negative integers with shape [2, 2]. It specifies how many elements to crop from the intermediate result across the spatial dimensions as follows:

crops = [[crop_top, crop_bottom], [crop_left, crop_right]]

• block_size: An int that is >= 2.

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

A Tensor. Has the same type as input. 4-D with shape [batch, height, width, depth], where:

    height = height_pad - crop_top - crop_bottom
width = width_pad - crop_left - crop_right


The attr block_size must be greater than one. It indicates the block size.

Some examples:

(1) For the following input of shape [4, 1, 1, 1] and block_size of 2:

prettyprint [[[[1]]], [[[2]]], [[[3]]], [[[4]]]]

The output tensor has shape [1, 2, 2, 1] and value:

prettyprint x = [[[[1], [2]], [[3], [4]]]]

(2) For the following input of shape [4, 1, 1, 3] and block_size of 2:

prettyprint [[[1, 2, 3]], [[4, 5, 6]], [[7, 8, 9]], [[10, 11, 12]]]

The output tensor has shape [1, 2, 2, 3] and value:

prettyprint x = [[[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]]]

(3) For the following input of shape [4, 2, 2, 1] and block_size of 2:

prettyprint x = [[[[1], [3]], [[5], [7]]], [[[2], [4]], [[10], [12]]], [[[5], [7]], [[13], [15]]], [[[6], [8]], [[14], [16]]]]

The output tensor has shape [1, 4, 4, 1] and value:

prettyprint x = [[[1], [2], [3], [4]], [[5], [6], [7], [8]], [[9], [10], [11], [12]], [[13], [14], [15], [16]]]

(4) For the following input of shape [8, 1, 2, 1] and block_size of 2:

prettyprint x = [[[[1], [3]]], [[[9], [11]]], [[[2], [4]]], [[[10], [12]]], [[[5], [7]]], [[[13], [15]]], [[[6], [8]]], [[[14], [16]]]]

The output tensor has shape [2, 2, 4, 1] and value:

prettyprint x = [[[[1], [3]], [[5], [7]]], [[[2], [4]], [[10], [12]]], [[[5], [7]], [[13], [15]]], [[[6], [8]], [[14], [16]]]]

### tf.space_to_depth(input, block_size, name=None)

SpaceToDepth for tensors of type T.

Rearranges blocks of spatial data, into depth. More specifically, this op outputs a copy of the input tensor where values from the height and width dimensions are moved to the depth dimension. The attr block_size indicates the input block size and how the data is moved.

• Non-overlapping blocks of size block_size x block size are rearranged into depth at each location.
• The depth of the output tensor is input_depth * block_size * block_size.
• The input tensor's height and width must be divisible by block_size.

That is, assuming the input is in the shape: [batch, height, width, depth], the shape of the output will be: [batch, height/block_size, width/block_size, depth*block_size*block_size]

This operation requires that the input tensor be of rank 4, and that block_size be >=1 and a divisor of both the input height and width.

This operation is useful for resizing the activations between convolutions (but keeping all data), e.g. instead of pooling. It is also useful for training purely convolutional models.

For example, given this input of shape [1, 2, 2, 1], and block_size of 2:

x = [[[[1], [2]],
[[3], [4]]]]


This operation will output a tensor of shape [1, 1, 1, 4]:

[[[[1, 2, 3, 4]]]]


Here, the input has a batch of 1 and each batch element has shape [2, 2, 1], the corresponding output will have a single element (i.e. width and height are both 1) and will have a depth of 4 channels (1 * block_size * block_size). The output element shape is [1, 1, 4].

For an input tensor with larger depth, here of shape [1, 2, 2, 3], e.g.

x = [[[[1, 2, 3], [4, 5, 6]],
[[7, 8, 9], [10, 11, 12]]]]


This operation, for block_size of 2, will return the following tensor of shape [1, 1, 1, 12]

[[[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]]]]


Similarly, for the following input of shape [1 4 4 1], and a block size of 2:

x = [[[[1],   [2],  [5],  [6]],
[[3],   [4],  [7],  [8]],
[[9],  [10], [13],  [14]],
[[11], [12], [15],  [16]]]]


the operator will return the following tensor of shape [1 2 2 4]:

x = [[[[1, 2, 3, 4],
[5, 6, 7, 8]],
[[9, 10, 11, 12],
[13, 14, 15, 16]]]]

##### Args:
• input: A Tensor.
• block_size: An int that is >= 2. The size of the spatial block.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input.

### tf.depth_to_space(input, block_size, name=None)

DepthToSpace for tensors of type T.

Rearranges data from depth into blocks of spatial data. This is the reverse transformation of SpaceToDepth. More specifically, this op outputs a copy of the input tensor where values from the depth dimension are moved in spatial blocks to the height and width dimensions. The attr block_size indicates the input block size and how the data is moved.

• Chunks of data of size block_size * block_size from depth are rearranged into non-overlapping blocks of size block_size x block_size
• The width the output tensor is input_depth * block_size, whereas the height is input_height * block_size.
• The depth of the input tensor must be divisible by block_size * block_size.

That is, assuming the input is in the shape: [batch, height, width, depth], the shape of the output will be: [batch, height*block_size, width*block_size, depth/(block_size*block_size)]

This operation requires that the input tensor be of rank 4, and that block_size be >=1 and that block_size * block_size be a divisor of the input depth.

This operation is useful for resizing the activations between convolutions (but keeping all data), e.g. instead of pooling. It is also useful for training purely convolutional models.

For example, given this input of shape [1, 1, 1, 4], and a block size of 2:

x = [[[[1, 2, 3, 4]]]]



This operation will output a tensor of shape [1, 2, 2, 1]:

   [[[[1], [2]],
[[3], [4]]]]


Here, the input has a batch of 1 and each batch element has shape [1, 1, 4], the corresponding output will have 2x2 elements and will have a depth of 1 channel (1 = 4 / (block_size * block_size)). The output element shape is [2, 2, 1].

For an input tensor with larger depth, here of shape [1, 1, 1, 12], e.g.

x = [[[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]]]]


This operation, for block size of 2, will return the following tensor of shape [1, 2, 2, 3]

   [[[[1, 2, 3], [4, 5, 6]],
[[7, 8, 9], [10, 11, 12]]]]



Similarly, for the following input of shape [1 2 2 4], and a block size of 2:

x =  [[[[1, 2, 3, 4],
[5, 6, 7, 8]],
[[9, 10, 11, 12],
[13, 14, 15, 16]]]]


the operator will return the following tensor of shape [1 4 4 1]:

x = [[ [1],   [2],  [5],  [6]],
[ [3],   [4],  [7],  [8]],
[ [9],  [10], [13],  [14]],
[ [11], [12], [15],  [16]]]


##### Args:
• input: A Tensor.
• block_size: An int that is >= 2. The size of the spatial block, same as in Space2Depth.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as input.

### tf.gather(params, indices, validate_indices=None, 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.
• validate_indices: An optional bool. Defaults to True.
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as params.

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

Gather values or slices from params according to indices.

params is a Tensor of rank R and indices is a Tensor of rank M.

indices must be integer tensor, containing indices into params. It must be shape [d_0, ..., d_N, R] where 0 < R <= M.

The innermost dimension of indices (with length R) corresponds to indices into elements (if R = M) or slices (if R < M) along the Nth dimension of params.

Produces an output tensor with shape

[d_0, ..., d_{n-1}, params.shape[R], ..., params.shape[M-1]].


Some examples below.

Simple indexing into a matrix:

indices = [[0, 0], [1, 1]]
params = [['a', 'b'], ['c', 'd']]
output = ['a', 'd']


Slice indexing into a matrix:

indices = [[1], [0]]
params = [['a', 'b'], ['c', 'd']]
output = [['c', 'd'], ['a', 'b']]


Indexing into a 3-tensor:

indices = [[1]]
params = [[['a0', 'b0'], ['c0', 'd0']],
[['a1', 'b1'], ['c1', 'd1']]]
output = [[['a1', 'b1'], ['c1', 'd1']]]

indices = [[0, 1], [1, 0]]
params = [[['a0', 'b0'], ['c0', 'd0']],
[['a1', 'b1'], ['c1', 'd1']]]
output = [['c0', 'd0'], ['a1', 'b1']]

indices = [[0, 0, 1], [1, 0, 1]]
params = [[['a0', 'b0'], ['c0', 'd0']],
[['a1', 'b1'], ['c1', 'd1']]]
output = ['b0', 'b1']


Batched indexing into a matrix:

indices = [[[0, 0]], [[0, 1]]]
params = [['a', 'b'], ['c', 'd']]
output = [['a'], ['b']]


Batched slice indexing into a matrix:

indices = [[[1]], [[0]]]
params = [['a', 'b'], ['c', 'd']]
output = [[['c', 'd']], [['a', 'b']]]


Batched indexing into a 3-tensor:

indices = [[[1]], [[0]]]
params = [[['a0', 'b0'], ['c0', 'd0']],
[['a1', 'b1'], ['c1', 'd1']]]
output = [[[['a1', 'b1'], ['c1', 'd1']]],
[[['a0', 'b0'], ['c0', 'd0']]]]

indices = [[[0, 1], [1, 0]], [[0, 0], [1, 1]]]
params = [[['a0', 'b0'], ['c0', 'd0']],
[['a1', 'b1'], ['c1', 'd1']]]
output = [[['c0', 'd0'], ['a1', 'b1']],
[['a0', 'b0'], ['c1', 'd1']]]

indices = [[[0, 0, 1], [1, 0, 1]], [[0, 1, 1], [1, 1, 0]]]
params = [[['a0', 'b0'], ['c0', 'd0']],
[['a1', 'b1'], ['c1', 'd1']]]
output = [['b0', 'b1'], ['d0', 'c1']]

##### Args:
• params: A Tensor. M-D. The tensor from which to gather values.
• indices: A Tensor. Must be one of the following types: int32, int64. (N+1)-D. Index tensor having shape [d_0, ..., d_N, R].
• name: A name for the operation (optional).
##### Returns:

A Tensor. Has the same type as params. (N+M-R)-D. Values from params gathered from indices given by indices.

### 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.

### tf.boolean_mask(tensor, mask, name='boolean_mask')

Apply boolean mask to tensor. Numpy equivalent is tensor[mask].

# 1-D example
tensor = [0, 1, 2, 3]
mask = [True, False, True, False]


In general, 0 < dim(mask) = K <= dim(tensor), and mask's shape must match the first K dimensions of tensor's shape. We then have: boolean_mask(tensor, mask)[i, j1,...,jd] = tensor[i1,...,iK,j1,...,jd] where (i1,...,iK) is the ith True entry of mask (row-major order).

##### Args:
• tensor: N-D tensor.
• mask: K-D boolean tensor, K <= N and K must be known statically.
• name: A name for this operation (optional).
##### Returns:

Tensor populated by entries in tensor corresponding to True values in mask.

##### Raises:
• ValueError: If shapes do not conform.

• Examples:

# 2-D example
tensor = [[1, 2], [3, 4], [5, 6]]


### tf.one_hot(indices, depth, on_value=None, off_value=None, axis=None, dtype=None, name=None)

Returns a one-hot tensor.

The locations represented by indices in indices take value on_value, while all other locations take value off_value.

on_value and off_value must have matching data types. If dtype is also provided, they must be the same data type as specified by dtype.

If on_value is not provided, it will default to the value 1 with type dtype

If off_value is not provided, it will default to the value 0 with type dtype

If the input indices is rank N, the output will have rank N+1. The new axis is created at dimension axis (default: the new axis is appended at the end).

If indices is a scalar the output shape will be a vector of length depth

If indices is a vector of length features, the output shape will be:

  features x depth if axis == -1
depth x features if axis == 0


If indices is a matrix (batch) with shape [batch, features], the output shape will be:

  batch x features x depth if axis == -1
batch x depth x features if axis == 1
depth x batch x features if axis == 0


If dtype is not provided, it will attempt to assume the data type of on_value or off_value, if one or both are passed in. If none of on_value, off_value, or dtype are provided, dtype will default to the value tf.float32

# Examples

Suppose that

  indices = [0, 2, -1, 1]
depth = 3
on_value = 5.0
off_value = 0.0
axis = -1


Then output is [4 x 3]:

  output =
[5.0 0.0 0.0]  // one_hot(0)
[0.0 0.0 5.0]  // one_hot(2)
[0.0 0.0 0.0]  // one_hot(-1)
[0.0 5.0 0.0]  // one_hot(1)


Suppose that

  indices = [[0, 2], [1, -1]]
depth = 3
on_value = 1.0
off_value = 0.0
axis = -1


Then output is [2 x 2 x 3]:

  output =
[
[1.0, 0.0, 0.0]  // one_hot(0)
[0.0, 0.0, 1.0]  // one_hot(2)
][
[0.0, 1.0, 0.0]  // one_hot(1)
[0.0, 0.0, 0.0]  // one_hot(-1)
]


Using default values for on_value and off_value:

  indices = [0, 1, 2]
depth = 3


The output will be

  output =
[[1., 0., 0.],
[0., 1., 0.],
[0., 0., 1.]]

##### Args:
• indices: A Tensor of indices.
• depth: A scalar defining the depth of the one hot dimension.
• on_value: A scalar defining the value to fill in output when indices[j] = i. (default: 1)
• off_value: A scalar defining the value to fill in output when indices[j] != i. (default: 0)
• axis: The axis to fill (default: -1, a new inner-most axis).
• dtype: The data type of the output tensor.
##### Returns:
• output: The one-hot tensor.
##### Raises:
• TypeError: If dtype of either on_value or off_value don't match dtype
• TypeError: If dtype of on_value and off_value don't match one another