# GatherND¶

## GatherND - 13¶

### Version¶

• name: GatherND (GitHub)

• domain: main

• since_version: 13

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 13.

### Summary¶

Given data tensor of rank r >= 1, indices tensor of rank q >= 1, and batch_dims integer b, this operator gathers slices of data into an output tensor of rank q + r - indices_shape[-1] - 1 - b.

indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data, where each element defines a slice of data

batch_dims (denoted as b) is an integer indicating the number of batch dimensions, i.e the leading b number of dimensions of data tensor and indices are representing the batches, and the gather starts from the b+1 dimension.

Some salient points about the inputs’ rank and shape:

1. r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q

2. The first b dimensions of the shape of indices tensor and data tensor must be equal.

3. b < min(q, r) is to be honored.

4. The indices_shape[-1] should have a value between 1 (inclusive) and rank r-b (inclusive)

5. All values in indices are expected to be within bounds [-s, s-1] along axis of size s (i.e.) -data_shape[i] <= indices[...,i] <= data_shape[i] - 1. It is an error if any of the index values are out of bounds.

The output is computed as follows:

The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.

1. If indices_shape[-1] > r-b => error condition

2. If indices_shape[-1] == r-b, since the rank of indices is q, indices can be thought of as N (q-b-1)-dimensional tensors containing 1-D tensors of dimension r-b, where N is an integer equals to the product of 1 and all the elements in the batch dimensions of the indices_shape. Let us think of each such r-b ranked tensor as indices_slice. Each scalar value corresponding to data[0:b-1,indices_slice] is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Example 1 below)

3. If indices_shape[-1] < r-b, since the rank of indices is q, indices can be thought of as N (q-b-1)-dimensional tensor containing 1-D tensors of dimension < r-b. Let us think of each such tensors as indices_slice. Each tensor slice corresponding to data[0:b-1, indices_slice , :] is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Examples 2, 3, 4 and 5 below)

This operator is the inverse of ScatterND.

Example 1

batch_dims = 0
data    = [[0,1],[2,3]]   # data_shape    = [2, 2]
indices = [[0,0],[1,1]]   # indices_shape = [2, 2]
output  = [0,3]           # output_shape  = [2]


Example 2

batch_dims = 0
data    = [[0,1],[2,3]]  # data_shape    = [2, 2]
indices = [[1],[0]]      # indices_shape = [2, 1]
output  = [[2,3],[0,1]]  # output_shape  = [2, 2]


Example 3

batch_dims = 0
data    = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape    = [2, 2, 2]
indices = [[0,1],[1,0]]                 # indices_shape = [2, 2]
output  = [[2,3],[4,5]]                 # output_shape  = [2, 2]


Example 4

batch_dims = 0
data    = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape    = [2, 2, 2]
indices = [[[0,1]],[[1,0]]]             # indices_shape = [2, 1, 2]
output  = [[[2,3]],[[4,5]]]             # output_shape  = [2, 1, 2]


Example 5

batch_dims = 1
data    = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape    = [2, 2, 2]
indices = [[1],[0]]                     # indices_shape = [2, 1]
output  = [[2,3],[4,5]]                 # output_shape  = [2, 2]


### Attributes¶

• batch_dims - INT (default is '0'):

The number of batch dimensions. The gather of indexing starts from dimension of data[batch_dims:]

### Inputs¶

• data (heterogeneous) - T:

Tensor of rank r >= 1.

• indices (heterogeneous) - tensor(int64):

Tensor of rank q >= 1. All index values are expected to be within bounds [-s, s-1] along axis of size s. It is an error if any of the index values are out of bounds.

### Outputs¶

• output (heterogeneous) - T:

Tensor of rank q + r - indices_shape[-1] - 1.

### Type Constraints¶

• T in ( tensor(bfloat16), tensor(bool), tensor(complex128), tensor(complex64), tensor(double), tensor(float), tensor(float16), tensor(int16), tensor(int32), tensor(int64), tensor(int8), tensor(string), tensor(uint16), tensor(uint32), tensor(uint64), tensor(uint8) ):

Constrain input and output types to any tensor type.

## GatherND - 12¶

### Version¶

• name: GatherND (GitHub)

• domain: main

• since_version: 12

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 12.

### Summary¶

Given data tensor of rank r >= 1, indices tensor of rank q >= 1, and batch_dims integer b, this operator gathers slices of data into an output tensor of rank q + r - indices_shape[-1] - 1 - b.

indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data, where each element defines a slice of data

batch_dims (denoted as b) is an integer indicating the number of batch dimensions, i.e the leading b number of dimensions of data tensor and indices are representing the batches, and the gather starts from the b+1 dimension.

Some salient points about the inputs’ rank and shape:

1. r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q

2. The first b dimensions of the shape of indices tensor and data tensor must be equal.

3. b < min(q, r) is to be honored.

4. The indices_shape[-1] should have a value between 1 (inclusive) and rank r-b (inclusive)

5. All values in indices are expected to be within bounds [-s, s-1] along axis of size s (i.e.) -data_shape[i] <= indices[...,i] <= data_shape[i] - 1. It is an error if any of the index values are out of bounds.

The output is computed as follows:

The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.

1. If indices_shape[-1] > r-b => error condition

2. If indices_shape[-1] == r-b, since the rank of indices is q, indices can be thought of as N (q-b-1)-dimensional tensors containing 1-D tensors of dimension r-b, where N is an integer equals to the product of 1 and all the elements in the batch dimensions of the indices_shape. Let us think of each such r-b ranked tensor as indices_slice. Each scalar value corresponding to data[0:b-1,indices_slice] is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Example 1 below)

3. If indices_shape[-1] < r-b, since the rank of indices is q, indices can be thought of as N (q-b-1)-dimensional tensor containing 1-D tensors of dimension < r-b. Let us think of each such tensors as indices_slice. Each tensor slice corresponding to data[0:b-1, indices_slice , :] is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Examples 2, 3, 4 and 5 below)

This operator is the inverse of ScatterND.

Example 1

batch_dims = 0

data = [[0,1],[2,3]] # data_shape = [2, 2]

indices = [[0,0],[1,1]] # indices_shape = [2, 2]

output = [0,3] # output_shape = [2]

Example 2

batch_dims = 0

data = [[0,1],[2,3]] # data_shape = [2, 2]

indices = [[1],[0]] # indices_shape = [2, 1]

output = [[2,3],[0,1]] # output_shape = [2, 2]

Example 3

batch_dims = 0

data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]

indices = [[0,1],[1,0]] # indices_shape = [2, 2]

output = [[2,3],[4,5]] # output_shape = [2, 2]

Example 4

batch_dims = 0

data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]

indices = [[[0,1]],[[1,0]]] # indices_shape = [2, 1, 2]

output = [[[2,3]],[[4,5]]] # output_shape = [2, 1, 2]

Example 5

batch_dims = 1

data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]

indices = [[1],[0]] # indices_shape = [2, 1]

output = [[2,3],[4,5]] # output_shape = [2, 2]

### Attributes¶

• batch_dims - INT (default is '0'):

The number of batch dimensions. The gather of indexing starts from dimension of data[batch_dims:]

### Inputs¶

• data (heterogeneous) - T:

Tensor of rank r >= 1.

• indices (heterogeneous) - tensor(int64):

Tensor of rank q >= 1. All index values are expected to be within bounds [-s, s-1] along axis of size s. It is an error if any of the index values are out of bounds.

### Outputs¶

• output (heterogeneous) - T:

Tensor of rank q + r - indices_shape[-1] - 1.

### Type Constraints¶

• T in ( tensor(bool), tensor(complex128), tensor(complex64), tensor(double), tensor(float), tensor(float16), tensor(int16), tensor(int32), tensor(int64), tensor(int8), tensor(string), tensor(uint16), tensor(uint32), tensor(uint64), tensor(uint8) ):

Constrain input and output types to any tensor type.

## GatherND - 11¶

### Version¶

• name: GatherND (GitHub)

• domain: main

• since_version: 11

• function: False

• support_level: SupportType.COMMON

• shape inference: True

This version of the operator has been available since version 11.

### Summary¶

Given data tensor of rank r >= 1, and indices tensor of rank q >= 1, this operator gathers slices of data into an output tensor of rank q + r - indices_shape[-1] - 1.

indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data, where each element defines a slice of data

Some salient points about the inputs’ rank and shape:

1. r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q

2. The indices_shape[-1] should have a value between 1 (inclusive) and rank r (inclusive)

3. All values in indices are expected to be within bounds [-s, s-1] along axis of size s (i.e.) -data_shape[i] <= indices[...,i] <= data_shape[i] - 1. It is an error if any of the index values are out of bounds.

The output is computed as follows:

The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.

1. If indices_shape[-1] > r => error condition

2. If indices_shape[-1] == r, since the rank of indices is q, indices can be thought of as a (q-1)-dimensional tensor containing 1-D tensors of dimension r. Let us think of each such r ranked tensor as indices_slice. Each scalar value corresponding to data[indices_slice] is filled into the corresponding location of the (q-1)-dimensional tensor to form the output tensor (Example 1 below)

3. If indices_shape[-1] < r, since the rank of indices is q, indices can be thought of as a (q-1)-dimensional tensor containing 1-D tensors of dimension < r. Let us think of each such tensors as indices_slice. Each tensor slice corresponding to data[indices_slice , :] is filled into the corresponding location of the (q-1)-dimensional tensor to form the output tensor (Examples 2, 3, and 4 below)

This operator is the inverse of ScatterND.

Example 1

data = [[0,1],[2,3]] # data_shape = [2, 2]

indices = [[0,0],[1,1]] # indices_shape = [2, 2]

output = [0,3] # output_shape = [2]

Example 2

data = [[0,1],[2,3]] # data_shape = [2, 2]

indices = [[1],[0]] # indices_shape = [2, 1]

output = [[2,3],[0,1]] # output_shape = [2, 2]

Example 3

data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]

indices = [[0,1],[1,0]] # indices_shape = [2, 2]

output = [[2,3],[4,5]] # output_shape = [2, 2]

Example 4

data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]

indices = [[[0,1]],[[1,0]]] # indices_shape = [2, 1, 2]

output = [[[2,3]],[[4,5]]] # output_shape = [2, 1, 2]

### Inputs¶

• data (heterogeneous) - T:

Tensor of rank r >= 1.

• indices (heterogeneous) - tensor(int64):

Tensor of rank q >= 1. All index values are expected to be within bounds [-s, s-1] along axis of size s. It is an error if any of the index values are out of bounds.

### Outputs¶

• output (heterogeneous) - T:

Tensor of rank q + r - indices_shape[-1] - 1.

### Type Constraints¶

• T in ( tensor(bool), tensor(complex128), tensor(complex64), tensor(double), tensor(float), tensor(float16), tensor(int16), tensor(int32), tensor(int64), tensor(int8), tensor(string), tensor(uint16), tensor(uint32), tensor(uint64), tensor(uint8) ):

Constrain input and output types to any tensor type.