Potential Bug in torch.symeig() #10345
Description
Issue description
The eigenvectors produced by torch.symeig() are not always orthonormal.
Code example
import torch
# Create a random symmetric matrix
p, q = 10, 3
torch.manual_seed(0)
in_tensor = torch.rand(p, q, dtype=torch.float64, requires_grad=True).cuda()
cov_in = torch.mm(in_tensor.t(), in_tensor)
_, eig_vecs = torch.symeig(cov_in)
print(eig_vecs)
print(torch.mm(eig_vecs, eig_vecs.t()))
print(torch.mm(eig_vecs.t(), eig_vecs))
print(eig_vecs.norm(dim=0))
print(eig_vecs.norm(dim=1))Here is the result:
tensor([[ 0.3573, 0.0288, 0.4334],
[ 3.1050, 6.5767, -3.2518],
[ 2.3730, 2.2232, 2.1961]],
device='cuda:0', dtype=torch.float64, grad_fn=<SymeigBackward>)
tensor([[ 0.3164, -0.1103, 1.8639],
[-0.1103, 63.4675, 14.8483],
[ 1.8639, 14.8483, 15.3969]],
device='cuda:0', dtype=torch.float64, grad_fn=<MmBackward>)
tensor([[ 15.3995, 25.7064, -4.7303],
[ 25.7064, 48.1965, -16.4908],
[ -4.7303, -16.4908, 15.5848]],
device='cuda:0', dtype=torch.float64, grad_fn=<MmBackward>)
tensor([3.9242, 6.9424, 3.9478],
device='cuda:0', dtype=torch.float64, grad_fn=<NormBackward1>)
tensor([0.5625, 7.9667, 3.9239],
device='cuda:0', dtype=torch.float64, grad_fn=<NormBackward1>)
System Info
PyTorch version: 0.4.1
Is debug build: No
CUDA used to build PyTorch: 9.0.176
OS: Ubuntu 14.04.5 LTS
GCC version: (Ubuntu 4.8.4-2ubuntu1~14.04.4) 4.8.4
CMake version: version 3.11.1
Python version: 2.7
Is CUDA available: Yes
CUDA runtime version: 8.0.61
GPU models and configuration:
GPU 0: Tesla K80
Nvidia driver version: 384.111
cuDNN version: Probably one of the following:
/usr/local/cuda-7.5/lib64/libcudnn.so.5.1.3
/usr/local/cuda-7.5/lib64/libcudnn_static.a
Versions of relevant libraries:
[pip] numpy (1.13.3)
[conda] Could not collect