GatherND

Versioned name: GatherND-5

Category: Data movement operations

Short description: GatherND gathers slices from input tensor into a tensor of a shape specified by indices.

Detailed description: GatherND gathers slices from data by indices and forms a tensor of a 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 insert it into the output at position i_0, ..., i_{K-2} as 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, i.e. indices.shape[-1] <= data.rank. The shape of the output can be computed as indices.shape[:-1] + data.shape[indices.shape[-1]:].

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]]]

Attributes:

• batch_dims
  • Description: batch_dims (denoted as b) is a leading number of dimensions of data tensor and indices representing the batches, and GatherND starts to gather from the b+1 dimension. It requires the first b dimensions in data and indices tensors to be equal. In case non default value for batch_dims the output shape is calculated as (multiplication of indices.shape[:b]) + indices.shape[b:-1] + data.shape[(indices.shape[-1] + b):].
  • Range of values: integer number and belongs to [0; min(data.rank, indices.rank))
  • Type: int
  • Default value: 0
  • Required: no

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 example 6 shows 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 = (6, 1)

Inputs:

• 1: data tensor of type T. This is a tensor of a rank not less than 1. Required.
• 2: indices tensor of type T_IND. This is a tensor of a rank not less than 1. It requires that all indices from this tensor will be in a range [0, s-1] where s is 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

<layer id="1" type="GatherND">
    <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">
    <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>60</dim>
            <dim>3</dim>
            <dim>35</dim>
        </port>
    </output>
</layer>