Implement torch.tril_indices and torch.triu_indices (#12653) (#14904)
Summary:
This is an optimized implementation that does the following:
1. created an empty Tensor of correct size.
2. fill the Tensor with correct values.
The following three designs to fill in the Tensor result in roughly the same performance. Hence, the 2nd option is taken for simpler code, and to return contiguous tensors.
1. Sequential: fill row coordinates first, then columns. This results in two for-loop and more arithmetic operations.
2. Interleaved: fill in index coordinates one by one, which jumps between the two output Tensor rows in every iteration.
3. Transpose: create a n X 2 Tensor, fill the Tensor sequentially, and then transpose it.
<img width="352" alt="screen shot 2018-12-10 at 3 54 39 pm" src="https://user-images.githubusercontent.com/16999635/49769172-07bd3580-fc94-11e8-8164-41839185e9f9.png">
NOTE:
This implementation returns a 2D tensor, instead of a tuple of two tensors. It means that users will not be able to do the following:
```python
x = torch.ones(3, 3)
i = torch.tril_indices(3, 3)
x[i] # need to first convert the 2D tensor into a tuple of two 1D tensors.
```
Pull Request resolved: https://github.com/pytorch/pytorch/pull/14904
Reviewed By: zou3519
Differential Revision: D13433027
Pulled By: mrshenli
fbshipit-source-id: 41c876aafcf584832d7069f7c5929ffb59e0ae6a
