modeci_mdf.functions.onnx.gathernd

modeci_mdf.functions.onnx.gathernd(*args, **kwargs)

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]