# Gather¶

Versioned name : Gather-8

Category : Data movement

Short description : Gather operation takes slices of data of the first input tensor according to the indices specified with the second input tensor and axis from the third input. Semantics of this operation is identical to TensorFlow* Gather operation but also includes support of negative indices.

Detailed description

output[p_0, p_1, ..., p_{axis-1}, i_b, ..., i_{M-1}, p_{axis+1}, ..., p_{N-1}] =
data[p_0, p_1, ..., p_{axis-1}, indices[p_0, p_1, ..., p_{b-1}, i_b, ..., i_{M-1}], p_{axis+1}, ..., p_{N-1}]


Where data, indices and axis are tensors from first, second and third inputs correspondingly, b is the number of batch dimensions. N and M are numbers of dimensions of data and indices tensors, respectively. Allowed values for indices are in the range [-data.shape[axis], data.shape[axis] - 1]. If index value exceed allowed range output data for corresponding index will be filled with zeros (Example 7).

Attributes :

• batch_dims

• Description : batch_dims (also denoted as b) is a leading number of dimensions of data tensor and indices representing the batches, and Gather starts to gather from the b dimension. It requires the first b dimensions in data and indices tensors to be equal. If batch_dims is less than zero, normalized value is used batch_dims = indices.rank + batch_dims.

• Range of values : [-min(data.rank, indices.rank); min(data.rank, indices.rank)] and batch_dims <= axis’ . Where batch_dims’ and axis’ stand for normalized batch_dims and axis values.

• Type : T_AXIS

• Default value : 0

• Required : no

Example 1 with default batch_dims value:

batch_dims = 0
axis = 0

indices = [0, 0, 4]
data    = [1, 2, 3, 4, 5]
output  = [1, 1, 5]

Example 2 with non-default batch_dims value:

batch_dims = 1
axis = 1

indices = [[0, 0, 4], <-- this is applied to the first batch
[4, 0, 0]]  <-- this is applied to the second batch
indices_shape = (2, 3)

data    = [[1, 2, 3, 4, 5],  <-- the first batch
[6, 7, 8, 9, 10]]  <-- the second batch
data_shape = (2, 5)

output  = [[ 1, 1, 5],
[10, 6, 6]]
output_shape = (2, 3)

Example 3 with non-default batch_dims value:

batch_dims = 2
axis = 2

indices = [[[0, 0, 4],  <-- this is applied to the first batch, index = (0, 0)
[4, 0, 0]],  <-- this is applied to the second batch, index = (0, 1)

[[1, 2, 4],  <-- this is applied to the third batch, index = (1, 0)
[4, 3, 2]]]  <-- this is applied to the fourth batch, index = (1, 1)
indices_shape = (2, 2, 3)

data    = [[[1, 2, 3, 4, 5],  <-- the first batch, index = (0, 0)
[6, 7, 8, 9, 10]],  <-- the second batch, index = (0, 1)

[[11, 12, 13, 14, 15],  <-- the third batch, index = (1, 0)
[16, 17, 18, 19, 20]]]  <-- the fourth batch, index = (1, 1)
data_shape = (2, 2, 5)

output  = [[[ 1, 1, 5],
[10, 6, 6]],

[[12, 13, 15],
[20, 19, 18]]]
output_shape = (2, 2, 3)

Example 4 with axis> batch_dims :

batch_dims = 1
axis = 2

indices = [[1, 2, 4],  <-- this is applied to the first batch
[4, 3, 2]]  <-- this is applied to the second batch
indices_shape = (2, 3)

data = [[[[ 1,  2,  3,  4], <-- first batch
[ 5,  6,  7,  8],
[ 9, 10, 11, 12],
[13, 14, 15, 16],
[17, 18, 19, 20]]],

[[[21, 22, 23, 24], <-- second batch
[25, 26, 27, 28],
[29, 30, 31, 32],
[33, 34, 35, 36],
[37, 38, 39, 40]]]]
data_shape = (2, 1, 5, 4)

output = [[[[ 5,  6,  7,  8],
[ 9, 10, 11, 12],
[17, 18, 19, 20]]],

[[[37, 38, 39, 40],
[33, 34, 35, 36],
[29, 30, 31, 32]]]]
output_shape = (2, 1, 3, 4)

Example 5 with negative batch_dims value:

batch_dims = -1  <-- normalized value will be indices.rank + batch_dims = 2 - 1 = 1
axis = 1

indices = [[0, 0, 4], <-- this is applied to the first batch
[4, 0, 0]]  <-- this is applied to the second batch
indices_shape = (2, 3)

data    = [[1, 2, 3, 4, 5],  <-- the first batch
[6, 7, 8, 9, 10]]  <-- the second batch
data_shape = (2, 5)

output  = [[ 1, 1, 5],
[10, 6, 6]]
output_shape = (2, 3)

Example 6 with negative indices:

batch_dims = 0
axis = 0

indices = [0, -2, -1]
data    = [1, 2, 3, 4, 5]
output  = [1, 4, 5]

Example 7 with indices out of the range:

batch_dims = 0
axis = 0

indices = [3, 10, -20]
data    = [1, 2, 3, 4, 5]
output  = [4, 0, 0]

Inputs

• 1 : data tensor of type T with arbitrary data. Required.

• 2 : indices tensor of type T_IND with indices to gather. 0D tensor (scalar) for indices is also allowed. The values for indices are in the range [-data.shape[axis], data.shape[axis] - 1]. Negative values of indices indicate reverse indexing from data.shape[axis]. Required.

• 3 : Scalar or 1D tensor axis of T_AXIS type is a dimension index to gather data from. For example, axis equal to 1 means that gathering is performed over the first dimension. Negative axis means reverse indexing and will be normalized to value axis = data.rank + axis. Allowed values are from [-len(data.shape), len(data.shape) - 1] and axis>= batch_dims’ . Where axis’ and batch_dims’ stand for normalized batch_dims and axis values. Required.

Outputs

• 1 : The resulting tensor of type T that consists of elements from data tensor gathered by indices. The shape of the output tensor is data.shape[:axis] + indices.shape[batch_dims:] + data.shape[axis + 1:]

Types

• T : any supported type.

• T_IND : any supported integer types.

• T_AXIS : any supported integer types.

Example

<layer ... type="Gather" version="opset8">
<data batch_dims="1" />
<input>
<port id="0">
<dim>2</dim>
<dim>64</dim>
<dim>128</dim>
</port>
<port id="1">
<dim>2</dim>
<dim>32</dim>
<dim>21</dim>
</port>
<port id="2"/>   <!--  axis = 1  -->
</input>
<output>
<port id="2">
<dim>2</dim>
<dim>32</dim>
<dim>21</dim>
<dim>128</dim>
</port>
</output>
</layer>