DEV Community

Super Kai (Kazuya Ito)
Super Kai (Kazuya Ito)

Posted on • Edited on

linalg.matrix_norm in PyTorch

Buy Me a Coffee

*Memos:

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 torch is input(Required-Type:tensor of float or complex): *Memos:
    • It must be the 2D or more D tensor of zero or more elements.
    • A complex tensor returns a float tensor even if dtype=torch.complex64 is set to linalg.norm() which is a bug.
  • The 2nd argument with torch is ord(Optional-Default:None-Type:int, float or str). *It sets a norm.
  • The 3rd argument with torch is dim(Optional-Default:None-Type:tuple or list of int). *The length of tuple or list of int must be 2.
  • The 4th argument with torch is keepdim(Optional-Default:False-Type:bool). *My post explains keepdim argument.
  • There is dtype argument with torch(Optional-Default:None-Type:dtype): *Memos:
    • If it's None, it's inferred from input.
    • dtype= must be used.
    • My post explains dtype argument.
  • There is out argument with torch(Optional-Default:None-Type:tensor): *Memos:
    • out= must be used.
    • My post explains out argument.
  • ord supports the following norms: *Memos:
    • inf can be torch.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])
Enter fullscreen mode Exit fullscreen mode

Image of Datadog

Master Mobile Monitoring for iOS Apps

Monitor your app’s health with real-time insights into crash-free rates, start times, and more. Optimize performance and prevent user churn by addressing critical issues like app hangs, and ANRs. Learn how to keep your iOS app running smoothly across all devices by downloading this eBook.

Get The eBook

Top comments (0)

👋 Kindness is contagious

Please leave a ❤️ or a friendly comment on this post if you found it helpful!

Okay