Ensure that every column in a matrix has at least `e` non-zero elements

I would like to ensure that each column in a matrix has at least e non-zero elements, and for each column that does not randomoly replace zero-valued elements with the value y until the column contains e non-zero elements. Consider the following matrix where some columns have 0, 1 or 2 elements. After the operation, each column should have at least e elements of value y.

before

tensor([[0, 7, 0, 0],
        [0, 0, 0, 0],
        [0, 1, 0, 4]], dtype=torch.int32)

after, e = 2

tensor([[y, 7, 0, y],
        [y, 0, y, 0],
        [0, 1, y, 4]], dtype=torch.int32)

I have a very slow and naive loop-based solution that works:

def scatter_elements(x, e, y):
  for i in range(x.shape[1]):
    col = x.data[:, i]
    num_connections = col.count_nonzero()
    to_add = torch.clip(e - num_connections, 0, None)
    indices = torch.where(col == 0)[0]
    perm = torch.randperm(indices.shape[0])[:to_add]
    col.data[indices[perm]] = y

Is it possible to do this without loops? I've thought about using torch.scatter and generate an index array first, but since the number of elements to be added varies per column, I see no straightforward way to use it. Any suggestions or hints would be greatly appreciated!

Edit: swapped indices and updated title and description based on comment.

source https://stackoverflow.com/questions/73501398/ensure-that-every-column-in-a-matrix-has-at-least-e-non-zero-elements

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