关于旋转矩阵的生成，有一些困惑

[GluttonK]

`def _get_rotation_matrix(thetas): bs, g = thetas.shape device = thetas.device thetas = thetas.reshape(-1) # [bs, n] --> [bs x n]

x = torch.cos(thetas)
y = torch.sin(thetas)
x = x.unsqueeze(0).unsqueeze(0)  # shape = [1, 1, bs * g]
y = y.unsqueeze(0).unsqueeze(0)
a = x - y
b = x * y
c = x + y

rot_mat_positive = torch.cat((
    torch.cat((a, 1-a, torch.zeros(1, 7, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 1, bs*g, device=device), x-b, b, torch.zeros(1, 1, bs*g, device=device), 1-c+b, y-b, torch.zeros(1, 3, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 2, bs*g, device=device), a, torch.zeros(1, 2, bs*g, device=device), 1-a, torch.zeros(1, 3, bs*g, device=device)), dim=1),
    torch.cat((b, y-b, torch.zeros(1,1 , bs*g, device=device), x-b, 1-c+b, torch.zeros(1, 4, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 4, bs*g, device=device), torch.ones(1, 1, bs*g, device=device), torch.zeros(1, 4, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 4, bs*g, device=device), 1-c+b, x-b, torch.zeros(1, 1, bs*g, device=device), y-b, b), dim=1),
    torch.cat((torch.zeros(1, 3, bs*g, device=device), 1-a, torch.zeros(1, 2, bs*g, device=device), a, torch.zeros(1, 2, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 3, bs*g, device=device), y-b, 1-c+b, torch.zeros(1, 1, bs*g, device=device), b, x-b, torch.zeros(1, 1, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 7, bs*g, device=device), 1-a, a), dim=1)
), dim=0)  # shape = [k^2, k^2, bs*g]

rot_mat_negative = torch.cat((
    torch.cat((c, torch.zeros(1, 2, bs*g, device=device), 1-c, torch.zeros(1, 5, bs*g, device=device)), dim=1),
    torch.cat((-b, x+b, torch.zeros(1, 1, bs*g, device=device), b-y, 1-a-b, torch.zeros(1, 4, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 1, bs*g, device=device), 1-c, c, torch.zeros(1, 6, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 3, bs*g, device=device), x+b, 1-a-b, torch.zeros(1, 1, bs*g, device=device), -b, b-y, torch.zeros(1, 1, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 4, bs*g, device=device), torch.ones(1, 1, bs*g, device=device), torch.zeros(1, 4, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 1, bs*g, device=device), b-y, -b, torch.zeros(1, 1, bs*g, device=device), 1-a-b, x+b, torch.zeros(1, 3, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 6, bs*g, device=device), c, 1-c, torch.zeros(1, 1, bs*g, device=device)), dim=1),
    torch.cat((torch.zeros(1, 4, bs*g, device=device), 1-a-b, b-y, torch.zeros(1, 1, bs*g, device=device), x+b, -b), dim=1),
    torch.cat((torch.zeros(1, 5, bs*g, device=device), 1-c, torch.zeros(1, 2, bs*g, device=device), c), dim=1)
), dim=0)  # shape = [k^2, k^2, bs*g]

mask = (thetas >= 0).unsqueeze(0).unsqueeze(0)
mask = mask.float()                                                   # shape = [1, 1, bs*g]
rot_mat = mask * rot_mat_positive + (1 - mask) * rot_mat_negative     # shape = [k*k, k*k, bs*g]
rot_mat = rot_mat.permute(2, 0, 1)                                    # shape = [bs*g, k*k, k*k]
rot_mat = rot_mat.reshape(bs, g, rot_mat.shape[1], rot_mat.shape[2])  # shape = [bs, g, k*k, k*k]
return rot_mat`

在这个生成旋转矩阵的函数中，我不太理解得到rot_mat_positive 和rot_mat_negative这两个矩阵 的拼接原理。这只适用于旋转3x3标准卷积，我希望理解这段代码以试图将其扩展到更大的卷积上。 能否提供一些理论上的支持，非常感谢

[yifanpu001]

can you schedule a remote meeting with me, and I'll explain the meaning of this code to you

[GluttonK]

Thank for your answer . Here is my email and QQ : 2287512349@qq.com You can send an email or Add Friends with me to schedule a remote meeting I will set aside sufficient time to wait for your reply

[Anm-pinellia]

I also have the same confusion about the code, it seems it only work with kernel size of 3. Can you give more explaination about it? Thanks very much.

[yifanpu001]

@Anm-pinellia @GluttonK Hi, this can be taken a fast implementation of torch.nn.functional.affine_grid and torch.nn.functional.grid_sample. These two operations can be simplified when only rotating a 3x3 kernel.

[aleeyang]

我也有点confused 这个代码，最后通过这个卷积，输出的特征图 是已经纠正旋转的特征图吗

[wind-waves-fll]

I don't understand the rot_mat_positive and rot_mat_negative. why can we get the rot_mat by this way?maybe my math is bad.

[yifanpu001]

Hi, the math derivation behind this code snippet is quiet complicated, so that I cannot make it clear by using several sentences. I will make some slides to show the derivation process when I'm free (maybe in the summer vacation).

[wind-waves-fll]

OK, thank you very much.

[DenverLiao]

For the mathematical formula here, I also have some confusion. Could you please provide a detailed derivation of the formula?

[qing-yao]

Hello, I don't quite understand the principles of obtaining the matrices rot_mat_positive and rot_mat_negative. Could you please explain? Thank you.

[Nu1sance]

looking forward to further details from authors