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

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linalg.matrix_norm in PyTorch

#python #pytorch #linalgmatrixnorm #regularization

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*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])
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