Install with
python -m pip install git+https://github.com/mariogeiger/hessian.git
import torch
from hessian import hessian
x = torch.tensor([1.5, 2.5], requires_grad=True)
h = hessian(x.pow(2).prod(), x, create_graph=True)
print(h)
# tensor([[12.5, 15],
# [15, 4.5]], grad_fn=<CopySlices>)
h2 = hessian(h.sum(), x)
print(h2)
# tensor([[4, 8],
# [8, 4]])
The hessian is computed naively assuming the commutativity of the derivatives.
import torch
from hessian import jacobian
x = torch.tensor([1.5, 2.5], requires_grad=True)
y = torch.tensor([5.5, -4.], requires_grad=True)
j = jacobian(x.pow(y), [x, y])
print(j)
# tensor([[34.1, -0.00, 3.77, 0.00],
# [ 0.0, -0.04, 0.00, 0.02]])