Summary:
As per title.
Numerical stability increased by replacing inverses with solutions to systems of linear triangular equations.
Unblocks computing `torch.det` for FULL-rank inputs of complex dtypes via the LU decomposition once https://github.com/pytorch/pytorch/pull/48125/files is merged:
```
LU, pivots = input.lu()
P, L, U = torch.lu_unpack(LU, pivots)
det_input = P.det() * torch.prod(U.diagonal(0, -1, -2), dim=-1) # P is not differentiable, so we are fine even if it is complex.
```
Unfortunately, since `lu_backward` is implemented as `autograd.Function`, we cannot support both autograd and scripting at the moment.
The solution would be to move all the lu-related methods to ATen, see https://github.com/pytorch/pytorch/issues/53364.
Resolves https://github.com/pytorch/pytorch/issues/52891
TODOs:
* extend lu_backward for tall/wide matrices of full rank.
* move lu-related functionality to ATen and make it differentiable.
* handle rank-deficient inputs.
Pull Request resolved: https://github.com/pytorch/pytorch/pull/53994
Reviewed By: pbelevich
Differential Revision: D27188529
Pulled By: anjali411
fbshipit-source-id: 8e053b240413dbf074904dce01cd564583d1f064
Summary:
Pull Request resolved: https://github.com/pytorch/pytorch/pull/53424
Fixes https://github.com/pytorch/pytorch/issues/24807 and supersedes the stale https://github.com/pytorch/pytorch/issues/25093 (Cc Microsheep). If you now run the reproduction
```python
import torch
if __name__ == "__main__":
t = torch.tensor([1, 2, 3], dtype=torch.float64)
```
with `pylint==2.6.0`, you get the following output
```
test_pylint.py:1:0: C0114: Missing module docstring (missing-module-docstring)
test_pylint.py:4:8: E1101: Module 'torch' has no 'tensor' member; maybe 'Tensor'? (no-
member)
test_pylint.py:4:38: E1101: Module 'torch' has no 'float64' member (no-member)
```
Now `pylint` doesn't recognize `torch.tensor` at all, but it is promoted in the stub. Given that it also doesn't recognize `torch.float64`, I think fixing this is out of scope of this PR.
---
## TL;DR
This BC-breaking only for users that rely on unintended behavior. Since `torch/__init__.py` loaded `torch/tensor.py` it was populated in `sys.modules`. `torch/__init__.py` then overwrote `torch.tensor` with the actual function. With this `import torch.tensor as tensor` does not fail, but returns the function rather than the module. Users that rely on this import need to change it to `from torch import tensor`.
Reviewed By: zou3519
Differential Revision: D26223815
Pulled By: bdhirsh
fbshipit-source-id: 125b9ff3d276e84a645cd7521e8d6160b1ca1c21
