Setting a `complex` tensor to `linalg.norm()` returns a `float` tensor

[hyperkai]

🐛 Describe the bug

Setting an int tensor to linalg.norm() gets the error message as shown below:

import torch
from torch import linalg

my_tensor = torch.tensor([8, -3, 0, 1])

linalg.norm(input=my_tensor) # Error

RuntimeError: linalg.vector_norm: Expected a floating point or complex tensor as input. Got Long

But, setting a complex tensor to linalg.norm() returns a float tensor as shown below:

import torch
from torch import linalg

my_tensor = torch.tensor([8.+0.j, -3.+0.j, 0.+0.j, 1.+0.j])

linalg.norm(input=my_tensor)
# tensor(8.6023)

linalg.norm(input=my_tensor).dtype
# torch.float32

So, I set dtype=torch.complex64 to linalg.norm() but it still returns a float tensor as shown below:

import torch
from torch import linalg

my_tensor = torch.tensor([8.+0.j, -3.+0.j, 0.+0.j, 1.+0.j])
                           # ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
linalg.norm(input=my_tensor, dtype=torch.complex64)
# tensor(8.6023)

linalg.norm(input=my_tensor, dtype=torch.complex64).dtype
# torch.float32

Versions

import torch

torch.__version__ # '2.3.0'

cc @svekars @sekyondaMeta @AlannaBurke @ezyang @anjali411 @dylanbespalko @mruberry @nikitaved @amjames @jianyuh @walterddr @lezcano @pearu @xwang233

[soulitzer]

This sounds expected - the docs say that int is not supported, and real-valued tensor is returned even if the input is complex.

[lezcano]

This is expected. See the docs for dtype:

dtype (torch.dtype, optional) – If specified, the input tensor is cast to dtype before performing the operation, and the returned tensor’s type will be dtype. Default: None

[lezcano]

Actually, no, we say that the output will be of the given dtype. We should probably specify that the output will be of the associated real dtype in the case of it being complex. We would accept a PR fixing the docs for norm* operators.