*Memos:
- My post explains linalg.norm().
- My post explains linalg.vector_norm().
linalg.matrix_norm() can get the 0D or more D tensor of the one or more elements computed with matrix norm from the 2D or more D tensor of zero or more elements as shown below:
*Memos:
-
linalg.matrix_norm()can be used with torch but not with a tensor. - The 1st argument with
torchisinput(Required-Type:tensoroffloatorcomplex): *Memos:- It must be the 2D or more D tensor of zero or more elements.
- A
complextensor returns afloattensor even ifdtype=torch.complex64is set tolinalg.norm()which is a bug.
- The 2nd argument with
torchisord(Optional-Default:None-Type:int,floatorstr). *It sets a norm. - The 3rd argument with
torchisdim(Optional-Default:None-Type:tupleorlistofint). *The length oftupleorlistofintmust be2. - The 4th argument with
torchiskeepdim(Optional-Default:False-Type:bool). *My post explainskeepdimargument. - There is
dtypeargument withtorch(Optional-Default:None-Type:dtype): *Memos:- If it's
None, it's inferred frominput. -
dtype=must be used. -
My post explains
dtypeargument.
- If it's
- There is
outargument withtorch(Optional-Default:None-Type:tensor): *Memos:-
out=must be used. -
My post explains
outargument.
-
-
ordsupports the following norms: *Memos:-
infcan betorch.inf,float('inf'), etc: - For vector, there are also L3 norm(
ord=3), L4 norm(ord=4) etc.
-
ord |
Matrix norm |
|---|---|
'fro'(Default) |
Frobenius norm |
'nuc' |
Nuclear norm |
inf |
max(sum(abs(x), dim=1)) |
-inf |
min(sum(abs(x), dim=1)) |
0 |
Not supported |
1 |
max(sum(abs(x), dim=0)) |
-1 |
min(sum(abs(x), dim=0)) |
2 |
The largest singular value of SVD(Singular Value Decomposition) |
-2 |
The smallest singular value of SVD |
Other int or float
|
Not supported |
import torch
from torch import linalg
my_tensor = torch.tensor([[-3., -2., -1., 0.],
[1., 2., 3., 4.]])
linalg.matrix_norm(input=my_tensor) # Frobenius norm
# tensor(6.6332)
linalg.matrix_norm(input=my_tensor, ord=1)
# tensor(4.)
linalg.matrix_norm(input=my_tensor, ord=-1)
# tensor(4.)
linalg.matrix_norm(input=my_tensor, ord=2)
# tensor(5.8997)
linalg.matrix_norm(input=my_tensor, ord=-2)
# tensor(3.0321)
linalg.matrix_norm(input=my_tensor, ord=torch.inf)
# tensor(10.)
linalg.matrix_norm(input=my_tensor, ord=-torch.inf)
# tensor(6.)
linalg.matrix_norm(input=my_tensor, ord='fro') # Frobenius norm
# tensor(6.6332)
linalg.matrix_norm(input=my_tensor, ord='nuc') # Nuclear norm
# tensor(8.9318)
my_tensor = torch.tensor([[[-3., -2.], [-1., 0.]],
[[1., 2.], [3., 4.]]])
linalg.matrix_norm(input=my_tensor) # Frobenius norm
# tensor([3.7417, 5.4772])
linalg.matrix_norm(input=my_tensor, ord=1)
linalg.matrix_norm(input=my_tensor, ord=1, dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord=1, dim=(-2, -1))
# tensor([4., 6.])
linalg.matrix_norm(input=my_tensor, ord=-1)
linalg.matrix_norm(input=my_tensor, ord=-1, dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord=-1, dim=(-2, -1))
# tensor([2., 4.])
linalg.matrix_norm(input=my_tensor, ord=2)
linalg.matrix_norm(input=my_tensor, ord=2, dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord=2, dim=(-2, -1))
# tensor([3.7025, 5.4650])
linalg.matrix_norm(input=my_tensor, ord=-2)
linalg.matrix_norm(input=my_tensor, ord=-2, dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord=-2, dim=(-2, -1))
# tensor([0.5402, 0.3660])
linalg.matrix_norm(input=my_tensor, ord=torch.inf)
linalg.matrix_norm(input=my_tensor, ord=torch.inf, dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord=torch.inf, dim=(-2, -1))
# tensor([5., 7.])
linalg.matrix_norm(input=my_tensor, ord=-torch.inf)
linalg.matrix_norm(input=my_tensor, ord=-torch.inf, dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord=-torch.inf, dim=(-2, -1))
# tensor([1., 3.])
# Frobenius norm
linalg.matrix_norm(input=my_tensor, ord='fro')
linalg.matrix_norm(input=my_tensor, ord='fro', dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord='fro', dim=(-2, -1))
# tensor([3.7417, 5.4772])
# Nuclear norm
linalg.matrix_norm(input=my_tensor, ord='nuc')
linalg.matrix_norm(input=my_tensor, ord='nuc', dim=(1, 2))
linalg.matrix_norm(input=my_tensor, ord='nuc', dim=(-2, -1))
# tensor([4.2426, 5.8310])
my_tensor = torch.tensor([[[-3.+0.j, -2.+0.j], [-1.+0.j, 0.+0.j]],
[[1.+0.j, 2.+0.j], [3.+0.j, 4.+0.j]]])
linalg.matrix_norm(input=my_tensor, dtype=torch.complex64) # Frobenius norm
# tensor([3.7417, 5.4772])
Top comments (0)