GatherND#
Versioned name: GatherND-8
Category: Data movement
Short description: GatherND gathers slices from input tensor into a tensor of the shape specified by indices.
Detailed description: GatherND gathers slices from data
by indices
and forms a tensor of the shape specified by indices
.
indices
is K
-dimensional integer tensor or K-1
-dimensional tensor of tuples with indices by which the operation
gathers elements or slices from data
tensor. A position i_0, ..., i_{K-2}
in the indices
tensor corresponds to
a tuple with indices indices[i_0, ..., i_{K-2}]
of a length equal to indices.shape[-1]
. By this tuple with indices
the operation gathers a slice or an element from data
tensor and inserts it into the output at the position
i_0, ..., i_{K-2}
as described in the following formula:
output[i_0, ..., i_{K-2},:,...,:] = data[indices[i_0, ..., i_{K-2}],:,...,:]
The last dimension of indices
tensor must be not greater than a rank of data
tensor, meaning
indices.shape[-1] <= data.rank
.
The shape of the output is calculated as indices.shape[:batch_dims] + indices.shape[batch_dims:-1]
if indices.shape[-1] == data.rank - batch_dims
, else
indices.shape[:batch_dims] + list(indices.shape)[batch_dims:-1] + list(data.shape)[batch_dims + indices.shape[-1]:]
.
Attributes:
batch_dims
Description: batch_dims (denoted as
b
) is a leading number of dimensions ofdata
tensor andindices
representing the batches, and GatherND starts to gather from theb+1
dimension. It requires the firstb
dimensions indata
andindices
tensors to be equal.Range of values: integer number that belongs to
[0; min(data.rank, indices.rank))
Type: int
Default value: 0
Required: no
Inputs:
1:
data
tensor of type T. A tensor of a rank not less than 1. Required.2:
indices
tensor of type T_IND. A tensor of a rank not less than 1. It requires all indices from this tensor to be in the range[0, s-1]
wheres
is the corresponding dimension to which this index is applied. Required.
Outputs:
1: Tensor with gathered values of type T.
Types
T: any supported type.
T_IND: any supported integer types.
Examples
Example 1 shows how GatherND operates with elements from data
tensor:
indices = [[0, 0],
[1, 0]]
data = [[1, 2],
[3, 4]]
output = [1, 3]
Example 2 shows how GatherND operates with slices from data
tensor:
indices = [[1], [0]]
data = [[1, 2],
[3, 4]]
output = [[3, 4],
[1, 2]]
Example 3 shows how GatherND operates when indices
tensor has leading dimensions:
indices = [[[1]], [[0]]]
data = [[1, 2],
[3, 4]]
output = [[[3, 4]],
[[1, 2]]]
Example 4 shows how GatherND operates gathering elements for non-default batch_dims value:
batch_dims = 1
indices = [[1], <--- this is applied to the first batch
[0]] <--- this is applied to the second batch, shape = (2, 1)
data = [[1, 2], <--- the first batch
[3, 4]] <--- the second batch, shape = (2, 2)
output = [2, 3], shape = (2)
Example 5 shows how GatherND operates gathering slices for non-default batch_dims value:
batch_dims = 1
indices = [[1], <--- this is applied to the first batch
[0]] <--- this is applied to the second batch, shape = (2, 1)
data = [[[1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]] <--- the first batch
[[13, 14, 15, 16], [17, 18, 19, 20], [21, 22, 23, 24]]] <--- the second batch, shape = (2, 3, 4)
output = [[ 5, 6, 7, 8], [13, 14, 15, 16]], shape = (2, 4)
More complex examples 6 and 7 show how GatherND operates gathering slices with leading dimensions for non-default batch_dims value:
batch_dims = 2
indices = [[[[1]], <--- this is applied to the first batch
[[0]],
[[2]]],
[[[0]],
[[2]],
[[2]]] <--- this is applied to the sixth batch
], shape = (2, 3, 1, 1)
data = [[[ 1, 2, 3, 4], <--- this is the first batch
[ 5, 6, 7, 8],
[ 9, 10, 11, 12]]
[[13, 14, 15, 16],
[17, 18, 19, 20],
[21, 22, 23, 24]] <--- this is the sixth batch
] <--- the second batch, shape = (2, 3, 4)
output = [[[ 2], [ 5], [11]], [[13], [19], [23]]], shape = (2, 3, 1)
batch_dims = 3
indices = [[[[1],
[0]],
[[3],
[2]]]
], shape = (1, 2, 2, 1)
data = [[[[ 1 2 3 4],
[ 5 6 7 8]],
[[ 9 10 11 12],
[13 14 15 16]]]
], shape = (1, 2, 2, 4)
output = [[[ 2 5],
[12 15]]
], shape = (1, 2, 2)
<layer id="1" type="GatherND" version="opset8">
<data batch_dims="0" />
<input>
<port id="0">
<dim>1000</dim>
<dim>256</dim>
<dim>10</dim>
<dim>15</dim>
</port>
<port id="1">
<dim>25</dim>
<dim>125</dim>
<dim>3</dim>
</port>
</input>
<output>
<port id="3">
<dim>25</dim>
<dim>125</dim>
<dim>15</dim>
</port>
</output>
</layer>
<layer id="1" type="GatherND" version="opset8">
<data batch_dims="2" />
<input>
<port id="0">
<dim>30</dim>
<dim>2</dim>
<dim>100</dim>
<dim>35</dim>
</port>
<port id="1">
<dim>30</dim>
<dim>2</dim>
<dim>3</dim>
<dim>1</dim>
</port>
</input>
<output>
<port id="3">
<dim>30</dim>
<dim>2</dim>
<dim>3</dim>
<dim>35</dim>
</port>
</output>
</layer>
<layer id="1" type="GatherND" version="opset8">
<data batch_dims="3" />
<input>
<port id="0">
<dim>1</dim>
<dim>64</dim>
<dim>64</dim>
<dim>320</dim>
</port>
<port id="1">
<dim>1</dim>
<dim>64</dim>
<dim>64</dim>
<dim>1</dim>
<dim>1</dim>
</port>
</input>
<output>
<port id="3">
<dim>1</dim>
<dim>64</dim>
<dim>64</dim>
<dim>1</dim>
</port>
</output>
</layer>