🐛 There are two bugs:

Error 1: RunTimeError: torch.det does not support automatic differentiation for outputs with complex dtype.
Error 2: To avoid Error 1, I also tried to calculate determinant of a complex matrix by using LU-Decomposition. However, lu.backforward() only supports floating data type. I am sure that my matrix has full rank. That problems only occur if input matrix is a tensor which requires auto_grad.

Just wondering if there is any plan for supporting complex auto_grad in the future. Thanks a lot for your help!!!

To Reproduce

Steps to reproduce Error 1:

x = torch.randn(4, 4, requires_grad=True, dtype=torch.cdouble)
torch.det(x)

Error messages for Error 1:
RuntimeError: det does not support automatic differentiation for outputs with complex dtype.

Steps to reproduce Error 2:

A = torch.ones(4, 4, requires_grad=True, dtype=torch.cdouble)
A_LU, pivots = A.lu()

Error messages for Error 2:
ValueError: lu.backward works only with batches of squared full-rank matrices of floating types.

Expected behavior

Environment

Please copy and paste the output from our
environment collection script
(or fill out the checklist below manually).

You can get the script and run it with:

wget https://raw.githubusercontent.com/pytorch/pytorch/master/torch/utils/collect_env.py
# For security purposes, please check the contents of collect_env.py before running it.
python collect_env.py

• PyTorch Version (e.g., 1.0): nightly 1.9.0
• OS (e.g., Linux): Windows 10
• How you installed PyTorch (conda, pip, source): conda
• Build command you used (if compiling from source):
• Python version: 3.7
• CUDA/cuDNN version: CUDA 10.2, CUDNN 8
• GPU models and configuration: GTX 1080Ti
• Any other relevant information:

Additional context

cc @ezyang @anjali411 @dylanbespalko @mruberry @jianyuh @nikitaved @pearu @heitorschueroff @walterddr @IvanYashchuk