Computing matrix derivatives with torch.autograd.grad (PyTorch) - pytorch

Question

I am trying to compute matrix derivatives in PyTorch using torch.autograd.grad however I am running into few issues. Here is a minimal working example to reproduce the error.
theta = torch.tensor(np.random.uniform(low=-np.pi, high=np.pi), requires_grad=True)
rot_mat = torch.tensor([[torch.cos(theta), torch.sin(theta), 0],
[-torch.sin(theta), torch.cos(theta), 0]],
dtype=torch.float, requires_grad=True)
torch.autograd.grad(outputs=rot_mat,
inputs=theta, grad_outputs=torch.ones_like(rot_mat),
create_graph=True, retain_graph=True)
This code results in the error "One of the differentiated Tensors appears to not have been used in the graph. Set allow_unused=True if this is the desired behavior."
I tried using allow_unused=True but the gradients are returned as None. I am not sure what is causing the graph to be disconnected here.

Answer 1

Pytorch autograd graph will be created only if pytorch functions are used.
I think python 2d list used while creating rot_mat disconnects the graph. So using torch functions create rotation matrix and also just use backward() function to compute gradients. Here's sample code:
import torch
import numpy as np
theta = torch.tensor(np.random.uniform(low=-np.pi, high=np.pi), requires_grad=True)
# create required values and convert it to torch 1d tensor
cos_t = torch.cos(theta).view(1)
sin_t = torch.sin(theta).view(1)
msin_t = -sin_t
zero = torch.zeros(1)
# create rotation matrix using only pytorch functions
rot_1d = torch.cat((cos_t, sin_t, zero, msin_t, cos_t, zero))
rot_mat = rot_1d.view((2, 3))
# Autograd
rot_mat.backward(torch.ones_like(rot_mat))
# gradient
print(theta.grad)