[Bug] _compute_shear_matrix and get_affine_matrix2d yield different results

🐛 Bug

_compute_shear_matrix and get_affine_matrix2d yield different results.

To Reproduce

import functools
import torch
from kornia.geometry.transform.affwarp import _compute_shear_matrix
from kornia import get_affine_matrix2d

translations = torch.zeros(1, 2)
center = torch.zeros(1, 2)
scale = torch.ones(1)
angle = torch.zeros(1)
get_affine_matrix2d_shear = functools.partial(
    get_affine_matrix2d, translations, center, scale, angle
)

# just making sure that the defaults for the other parameters are correct
assert torch.norm(get_affine_matrix2d_shear() - torch.eye(3)) < 1e-6


torch.manual_seed(0)
sx, sy = torch.rand(1), torch.rand(1)
shear = torch.stack((sx, sy), dim=1)

print(_compute_shear_matrix(shear))
print(get_affine_matrix2d_shear(sx=sx, sy=sy))

tensor([[[1.0000, 0.4963, 0.0000],
         [0.7682, 1.0000, 0.0000],
         [0.0000, 0.0000, 1.0000]]])
tensor([[[ 1.0000, -0.5415,  0.0000],
         [-0.9662,  1.5232,  0.0000],
         [ 0.0000,  0.0000,  1.0000]]])

Expected behavior

Maybe I’m missing something obvious, but I imagined both functions should yield the same results if fed with the same shear parameters.

Environment

kornia == 0.4.1+86185fb

PyTorch version: 1.6.0
Is debug build: False
CUDA used to build PyTorch: 10.2

OS: Ubuntu 18.04.4 LTS (x86_64)
GCC version: (Ubuntu 7.5.0-3ubuntu1~18.04) 7.5.0
Clang version: Could not collect
CMake version: version 3.10.2

Python version: 3.6 (64-bit runtime)
Is CUDA available: True
CUDA runtime version: 10.2.89
GPU models and configuration: GPU 0: GeForce GTX 1080
Nvidia driver version: 440.33.01
cuDNN version: /usr/lib/x86_64-linux-gnu/libcudnn.so.7.6.5

Versions of relevant libraries:
[pip3] light-the-torch==0.2.0
[pip3] numpy==1.19.1
[pip3] torch==1.6.0
[conda] Could not collect

[shijianjian]

Yes. The order does not matter since they are diagonal matrices but it is not equivalent to the x-and-y shearing. They are different mathematically:

Not sure about the source implementations. @ducha-aiki may know where to find it.

[stale[bot]]

This issue has been automatically marked as stale because it has not had recent activity. It will be closed if no further activity occurs. Thank you for your contributions, and happy coding day 😎