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: The number of batch dimensions. The gather of indexing starts from dimension of data[batch_dims:] Default value is 0.

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.

Examples

int32

node = onnx.helper.make_node(
    'GatherND',
    inputs=['data', 'indices'],
    outputs=['output'],
)

data = np.array([[0, 1], [2, 3]], dtype=np.int32)
indices = np.array([[0, 0], [1, 1]], dtype=np.int64)
output = gather_nd_impl(data, indices, 0)
expected_output = np.array([0, 3], dtype=np.int32)
assert (np.array_equal(output, expected_output))
expect(node, inputs=[data, indices], outputs=[output],
       name='test_gathernd_example_int32')

float32

node = onnx.helper.make_node(
    'GatherND',
    inputs=['data', 'indices'],
    outputs=['output'],
)

data = np.array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]], dtype=np.float32)
indices = np.array([[[0, 1]], [[1, 0]]], dtype=np.int64)
output = gather_nd_impl(data, indices, 0)
expected_output = np.array([[[2, 3]], [[4, 5]]], dtype=np.float32)
assert (np.array_equal(output, expected_output))
expect(node, inputs=[data, indices], outputs=[output],
       name='test_gathernd_example_float32')

int32_batchdim_1

node = onnx.helper.make_node(
    'GatherND',
    inputs=['data', 'indices'],
    outputs=['output'],
    batch_dims=1,
)

data = np.array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]], dtype=np.int32)
indices = np.array([[1], [0]], dtype=np.int64)
output = gather_nd_impl(data, indices, 1)
expected_output = np.array([[2, 3], [4, 5]], dtype=np.int32)
assert (np.array_equal(output, expected_output))
expect(node, inputs=[data, indices], outputs=[output],
       name='test_gathernd_example_int32_batch_dim1')

Differences

0	0	Given data tensor of rank r >= 1, indices tensor of rank q >= 1, and batch_dims integer b, this operator gathers	Given data tensor of rank r >= 1, indices tensor of rank q >= 1, and batch_dims integer b, this operator gathers
1	1	slices of data into an output tensor of rank q + r - indices_shape[-1] - 1 - b.	slices of data into an output tensor of rank q + r - indices_shape[-1] - 1 - b.
2	2
3	3	indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data,	indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data,
4	4	where each element defines a slice of data	where each element defines a slice of data
5	5
6	6	batch_dims (denoted as b) is an integer indicating the number of batch dimensions, i.e the leading b number of dimensions of	batch_dims (denoted as b) is an integer indicating the number of batch dimensions, i.e the leading b number of dimensions of
7	7	data tensor and indices are representing the batches, and the gather starts from the b+1 dimension.	data tensor and indices are representing the batches, and the gather starts from the b+1 dimension.
8	8
9	9	Some salient points about the inputs' rank and shape:	Some salient points about the inputs' rank and shape:
10	10
11	11	1) r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q	1) r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q
12	12
13	13	2) The first b dimensions of the shape of indices tensor and data tensor must be equal.	2) The first b dimensions of the shape of indices tensor and data tensor must be equal.
14	14
15	15	3) b < min(q, r) is to be honored.	3) b < min(q, r) is to be honored.
16	16
17	17	4) The indices_shape[-1] should have a value between 1 (inclusive) and rank r-b (inclusive)	4) The indices_shape[-1] should have a value between 1 (inclusive) and rank r-b (inclusive)
18	18
19	19	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.	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.
20	20	It is an error if any of the index values are out of bounds.	It is an error if any of the index values are out of bounds.
21	21
22	22	The output is computed as follows:	The output is computed as follows:
23	23
24	24	The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.	The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.
25	25
26	26	1) If indices_shape[-1] > r-b => error condition	1) If indices_shape[-1] > r-b => error condition
27	27
28	28	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	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
29	29	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	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
30	30	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]	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]
31	31	is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Example 1 below)	is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Example 1 below)
32	32
33	33	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	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
34	34	containing 1-D tensors of dimension < r-b. Let us think of each such tensors as indices_slice. Each *tensor slice* corresponding	containing 1-D tensors of dimension < r-b. Let us think of each such tensors as indices_slice. Each *tensor slice* corresponding
35	35	to data[0:b-1, indices_slice , :] is filled into the corresponding location of the (q-b-1)-dimensional tensor	to data[0:b-1, indices_slice , :] is filled into the corresponding location of the (q-b-1)-dimensional tensor
36	36	to form the output tensor (Examples 2, 3, 4 and 5 below)	to form the output tensor (Examples 2, 3, 4 and 5 below)
37	37
38	38	This operator is the inverse of ScatterND.	This operator is the inverse of ScatterND.
39	39
40	40	Example 1	Example 1
41	41
42	42	batch_dims = 0	batch_dims = 0
43	43
44	44	data = [[0,1],[2,3]] # data_shape = [2, 2]	data = [[0,1],[2,3]] # data_shape = [2, 2]
45	45
46	46	indices = [[0,0],[1,1]] # indices_shape = [2, 2]	indices = [[0,0],[1,1]] # indices_shape = [2, 2]
47	47
48	48	output = [0,3] # output_shape = [2]	output = [0,3] # output_shape = [2]
49	49
50	50	Example 2	Example 2
51	51
52	52	batch_dims = 0	batch_dims = 0
53	53
54	54	data = [[0,1],[2,3]] # data_shape = [2, 2]	data = [[0,1],[2,3]] # data_shape = [2, 2]
55	55
56	56	indices = [[1],[0]] # indices_shape = [2, 1]	indices = [[1],[0]] # indices_shape = [2, 1]
57	57
58	58	output = [[2,3],[0,1]] # output_shape = [2, 2]	output = [[2,3],[0,1]] # output_shape = [2, 2]
59	59
60	60	Example 3	Example 3
61	61
62	62	batch_dims = 0	batch_dims = 0
63	63
64	64	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]
65	65
66	66	indices = [[0,1],[1,0]] # indices_shape = [2, 2]	indices = [[0,1],[1,0]] # indices_shape = [2, 2]
67	67
68	68	output = [[2,3],[4,5]] # output_shape = [2, 2]	output = [[2,3],[4,5]] # output_shape = [2, 2]
69	69
70	70	Example 4	Example 4
71	71
72	72	batch_dims = 0	batch_dims = 0
73	73
74	74	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]
75	75
76	76	indices = [[[0,1]],[[1,0]]] # indices_shape = [2, 1, 2]	indices = [[[0,1]],[[1,0]]] # indices_shape = [2, 1, 2]
77	77
78	78	output = [[[2,3]],[[4,5]]] # output_shape = [2, 1, 2]	output = [[[2,3]],[[4,5]]] # output_shape = [2, 1, 2]
79	79
80	80	Example 5	Example 5
81	81
82	82	batch_dims = 1	batch_dims = 1
83	83
84	84	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]
85	85
86	86	indices = [[1],[0]] # indices_shape = [2, 1]	indices = [[1],[0]] # indices_shape = [2, 1]
87	87
88	88	output = [[2,3],[4,5]] # output_shape = [2, 2]	output = [[2,3],[4,5]] # output_shape = [2, 2]
89	89
90	90	**Attributes**	**Attributes**
91	91
92	92	* **batch_dims**:	* **batch_dims**:
93	93	The number of batch dimensions. The gather of indexing starts from	The number of batch dimensions. The gather of indexing starts from
94	94	dimension of data[batch_dims:] Default value is 0.	dimension of data[batch_dims:] Default value is 0.
95	95
96	96	**Inputs**	**Inputs**
97	97
98	98	* **data** (heterogeneous) - **T**:	* **data** (heterogeneous) - **T**:
99	99	Tensor of rank r >= 1.	Tensor of rank r >= 1.
100	100	* **indices** (heterogeneous) - **tensor(int64)**:	* **indices** (heterogeneous) - **tensor(int64)**:
101	101	Tensor of rank q >= 1. All index values are expected to be within	Tensor of rank q >= 1. All index values are expected to be within
102	102	bounds [-s, s-1] along axis of size s. It is an error if any of the	bounds [-s, s-1] along axis of size s. It is an error if any of the
103	103	index values are out of bounds.	index values are out of bounds.
104	104
105	105	**Outputs**	**Outputs**
106	106
107	107	* **output** (heterogeneous) - **T**:	* **output** (heterogeneous) - **T**:
108	108	Tensor of rank q + r - indices_shape[-1] - 1.	Tensor of rank q + r - indices_shape[-1] - 1.
109	109
110	110	**Type Constraints**	**Type Constraints**
111	111
112	112	* **T** in (	* **T** in (
	113		tensor(bfloat16),
113	114	tensor(bool),	tensor(bool),
114	115	tensor(complex128),	tensor(complex128),
115	116	tensor(complex64),	tensor(complex64),
116	117	tensor(double),	tensor(double),
117	118	tensor(float),	tensor(float),
118	119	tensor(float16),	tensor(float16),
119	120	tensor(int16),	tensor(int16),
120	121	tensor(int32),	tensor(int32),
121	122	tensor(int64),	tensor(int64),
122	123	tensor(int8),	tensor(int8),
123	124	tensor(string),	tensor(string),
124	125	tensor(uint16),	tensor(uint16),
125	126	tensor(uint32),	tensor(uint32),
126	127	tensor(uint64),	tensor(uint64),
127	128	tensor(uint8)	tensor(uint8)
128	129	):	):
129	130	Constrain input and output types to any tensor type.	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: The number of batch dimensions. The gather of indexing starts from dimension of data[batch_dims:] Default value is 0.

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.

Differences

0	0	Given data tensor of rank r >= 1, and indices tensor of rank q >= 1, this operator gathers	Given data tensor of rank r >= 1, indices tensor of rank q >= 1, and batch_dims integer b, this operator gathers
1	1	slices of data into an output tensor of rank q + r - indices_shape[-1] - 1.	slices of data into an output tensor of rank q + r - indices_shape[-1] - 1 - b.
2	2
3	3	indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data,	indices is an q-dimensional integer tensor, best thought of as a (q-1)-dimensional tensor of index-tuples into data,
4	4	where each element defines a slice of data	where each element defines a slice of data
5	5
	6		batch_dims (denoted as b) is an integer indicating the number of batch dimensions, i.e the leading b number of dimensions of
	7		data tensor and indices are representing the batches, and the gather starts from the b+1 dimension.
	8
6	9	Some salient points about the inputs' rank and shape:	Some salient points about the inputs' rank and shape:
7	10
8	11	1) r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q	1) r >= 1 and q >= 1 are to be honored. There is no dependency condition to be met between ranks r and q
9	12
	13		2) The first b dimensions of the shape of indices tensor and data tensor must be equal.
	14
	15		3) b < min(q, r) is to be honored.
	16
10	17	2) The indices_shape[-1] should have a value between 1 (inclusive) and rank r (inclusive)	4) The indices_shape[-1] should have a value between 1 (inclusive) and rank r-b (inclusive)
11	18
12	19	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.	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.
13	20	It is an error if any of the index values are out of bounds.	It is an error if any of the index values are out of bounds.
14	21
15	22	The output is computed as follows:	The output is computed as follows:
16	23
17	24	The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.	The output tensor is obtained by mapping each index-tuple in the indices tensor to the corresponding slice of the input data.
18	25
19	26	1) If indices_shape[-1] > r => error condition	1) If indices_shape[-1] > r-b => error condition
20	27
21	28	2) If indices_shape[-1] == r, since the rank of indices is q, indices can be thought of as a (q-1)-dimensional tensor	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
22	29	containing 1-D tensors of dimension r. Let us think of each such r ranked tensor as indices_slice.	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
23		Each *scalar value* corresponding to data[indices_slice] is filled into the corresponding location of the (q-1)-dimensional tensor
24	30	to form the output tensor (Example 1 below)	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]
	31		is filled into the corresponding location of the (q-b-1)-dimensional tensor to form the output tensor (Example 1 below)
25	32
26	33	3) If indices_shape[-1] < r, since the rank of indices is q, indices can be thought of as a (q-1)-dimensional tensor	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
27	34	containing 1-D tensors of dimension < r. Let us think of each such tensors as indices_slice.	containing 1-D tensors of dimension < r-b. Let us think of each such tensors as indices_slice. Each *tensor slice* corresponding
28	35	Each *tensor slice* corresponding to data[indices_slice , :] is filled into the corresponding location of the (q-1)-dimensional tensor	to data[0:b-1, indices_slice , :] is filled into the corresponding location of the (q-b-1)-dimensional tensor
29	36	to form the output tensor (Examples 2, 3, and 4 below)	to form the output tensor (Examples 2, 3, 4 and 5 below)
30	37
31	38	This operator is the inverse of ScatterND.	This operator is the inverse of ScatterND.
32	39
33	40	Example 1	Example 1
34	41
	42		batch_dims = 0
	43
35	44	data = [[0,1],[2,3]] # data_shape = [2, 2]	data = [[0,1],[2,3]] # data_shape = [2, 2]
36	45
37	46	indices = [[0,0],[1,1]] # indices_shape = [2, 2]	indices = [[0,0],[1,1]] # indices_shape = [2, 2]
38	47
39	48	output = [0,3] # output_shape = [2]	output = [0,3] # output_shape = [2]
40	49
41	50	Example 2	Example 2
42	51
	52		batch_dims = 0
	53
43	54	data = [[0,1],[2,3]] # data_shape = [2, 2]	data = [[0,1],[2,3]] # data_shape = [2, 2]
44	55
45	56	indices = [[1],[0]] # indices_shape = [2, 1]	indices = [[1],[0]] # indices_shape = [2, 1]
46	57
47	58	output = [[2,3],[0,1]] # output_shape = [2, 2]	output = [[2,3],[0,1]] # output_shape = [2, 2]
48	59
49	60	Example 3	Example 3
50	61
	62		batch_dims = 0
	63
51	64	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]
52	65
53	66	indices = [[0,1],[1,0]] # indices_shape = [2, 2]	indices = [[0,1],[1,0]] # indices_shape = [2, 2]
54	67
55	68	output = [[2,3],[4,5]] # output_shape = [2, 2]	output = [[2,3],[4,5]] # output_shape = [2, 2]
56	69
57	70	Example 4	Example 4
58	71
	72		batch_dims = 0
	73
59	74	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]	data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]
60	75
61	76	indices = [[[0,1]],[[1,0]]] # indices_shape = [2, 1, 2]	indices = [[[0,1]],[[1,0]]] # indices_shape = [2, 1, 2]
62	77
63	78	output = [[[2,3]],[[4,5]]] # output_shape = [2, 1, 2]	output = [[[2,3]],[[4,5]]] # output_shape = [2, 1, 2]
64	79
	80		Example 5
	81
	82		batch_dims = 1
	83
	84		data = [[[0,1],[2,3]],[[4,5],[6,7]]] # data_shape = [2, 2, 2]
	85
	86		indices = [[1],[0]] # indices_shape = [2, 1]
	87
	88		output = [[2,3],[4,5]] # output_shape = [2, 2]
	89
	90		**Attributes**
	91
	92		* **batch_dims**:
	93		The number of batch dimensions. The gather of indexing starts from
	94		dimension of data[batch_dims:] Default value is 0.
	95
65	96	**Inputs**	**Inputs**
66	97
67	98	* **data** (heterogeneous) - **T**:	* **data** (heterogeneous) - **T**:
68	99	Tensor of rank r >= 1.	Tensor of rank r >= 1.
69	100	* **indices** (heterogeneous) - **tensor(int64)**:	* **indices** (heterogeneous) - **tensor(int64)**:
70	101	Tensor of rank q >= 1. All index values are expected to be within	Tensor of rank q >= 1. All index values are expected to be within
71	102	bounds [-s, s-1] along axis of size s. It is an error if any of the	bounds [-s, s-1] along axis of size s. It is an error if any of the
72	103	index values are out of bounds.	index values are out of bounds.
73	104
74	105	**Outputs**	**Outputs**
75	106
76	107	* **output** (heterogeneous) - **T**:	* **output** (heterogeneous) - **T**:
77	108	Tensor of rank q + r - indices_shape[-1] - 1.	Tensor of rank q + r - indices_shape[-1] - 1.
78	109
79	110	**Type Constraints**	**Type Constraints**
80	111
81	112	* **T** in (	* **T** in (
82	113	tensor(bool),	tensor(bool),
83	114	tensor(complex128),	tensor(complex128),
84	115	tensor(complex64),	tensor(complex64),
85	116	tensor(double),	tensor(double),
86	117	tensor(float),	tensor(float),
87	118	tensor(float16),	tensor(float16),
88	119	tensor(int16),	tensor(int16),
89	120	tensor(int32),	tensor(int32),
90	121	tensor(int64),	tensor(int64),
91	122	tensor(int8),	tensor(int8),
92	123	tensor(string),	tensor(string),
93	124	tensor(uint16),	tensor(uint16),
94	125	tensor(uint32),	tensor(uint32),
95	126	tensor(uint64),	tensor(uint64),
96	127	tensor(uint8)	tensor(uint8)
97	128	):	):
98	129	Constrain input and output types to any tensor type.	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.

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