adjoint(), mH and mT in PyTorch

#pytorch #adjoint #mh #mt

*Memos:

My post explains transpose() and t().
My post explains reshape() and view().
My post explains permute().
My post explains movedim().

adjoint() or mH can get the view of the 2D or more D transposed and conjugated tensor of zero or more elements without losing data from the 2D or more D tensor of zero or more elements as shown below:

adjoint() can be used with torch or a tensor while mH can be used with a tensor but not with torch.
For adjoint(), the 1st argument(input) with torch or using a tensor(Required-Type:tensor of int, float, complex or bool).
For mH, using a tensor(Required-Type:tensor of int, float, complex or bool).
adjoint() is equivalent to mH, equivalent to transpose(-2, -1) for an int, float or bool tensor and equivalent to transpose(-2, -1).conj() for a complex tensor.
adjoint() or mH can also get the 0D tensor of zero or more elements but it's deprecated.

import torch

my_tensor = torch.tensor([[0, 1, 2], [3, 4, 5],
                          [6, 7, 8], [9, 10, 11]])
torch.adjoint(input=my_tensor)
my_tensor.adjoint()
my_tensor.mH
# tensor([[0, 3, 6, 9],
#         [1, 4, 7, 10],
#         [2, 5, 8, 11]])

my_tensor = torch.tensor([[[0, 1, 2], [3, 4, 5]],
                          [[6, 7, 8], [9, 10, 11]],
                          [[12, 13, 14], [15, 16, 17]],
                          [[18, 19, 20], [21, 22, 23]]])
torch.adjoint(input=my_tensor)
my_tensor.mH
# tensor([[[0, 3], [1, 4], [2, 5]],
#         [[6, 9], [7, 10], [8, 11]],
#         [[12, 15], [13, 16], [14, 17]],
#         [[18, 21], [19, 22], [20, 23]]])

my_tensor = torch.tensor([[[0., 1., 2.], [3., 4., 5.]],
                          [[6., 7., 8.], [9., 10., 11.]],
                          [[12., 13., 14.], [15., 16., 17.]],
                          [[18., 19., 20.], [21., 22., 23.]]])
torch.adjoint(input=my_tensor)
my_tensor.mH
# tensor([[[0., 3.], [1., 4.], [2., 5.]],
#         [[6., 9.], [7., 10.], [8., 11.]],
#         [[12., 15.], [13., 16.], [14., 17.]],
#         [[18., 21.], [19., 22.], [20., 23.]]])

my_tensor = torch.tensor([[[0.+0.j, 1.+0.j, 2.+0.j],
                           [3.+0.j, 4.+0.j, 5.+0.j]],
                          [[6.+0.j, 7.+0.j, 8.+0.j],
                           [9.+0.j, 10.+0.j, 11.+0.j]],
                          [[12.+0.j, 13.+0.j, 14.+0.j],
                           [15.+0.j, 16.+0.j, 17.+0.j]],
                          [[18.+0.j, 19.+0.j, 20.+0.j],
                           [21.+0.j, 22.+0.j, 23.+0.j]]])
torch.adjoint(input=my_tensor)
my_tensor.mH
# tensor([[[0.-0.j, 3.-0.j], [1.-0.j, 4.-0.j], [2.-0.j, 5.-0.j]],
#         [[6.-0.j, 9.-0.j], [7.-0.j, 10.-0.j], [8.-0.j, 11.-0.j]],
#         [[12.-0.j, 15.-0.j], [13.-0.j, 16.-0.j], [14.-0.j, 17.-0.j]],
#         [[18.-0.j, 21.-0.j], [19.-0.j, 22.-0.j], [20.-0.j, 23.-0.j]]])

my_tensor = torch.tensor([[[True, False, True], [True, False, True]],
                          [[False, True, False], [False, True, False]],
                          [[True, False, True], [True, False, True]],
                          [[False, True, False], [False, True, False]]])
torch.adjoint(input=my_tensor)
my_tensor.mH
# tensor([[[True, True], [False, False], [True, True]],
#         [[False, False], [True, True], [False, False]],
#         [[True, True], [False, False], [True, True]],
#         [[False, False], [True, True], [False, False]]])

mT can get the view of the 2D or more D transposed tensor of zero or more elements without losing data from the 2D or more D tensor of zero or more elements as shown below:

mT can be used with a tensor but not with torch.
Using a tensor(Required-Type:tensor of int, float, complex or bool).
mT can also get the 0D tensor of zero or more elements but it's deprecated.

import torch

my_tensor = torch.tensor([[0, 1, 2], [3, 4, 5],
                          [6, 7, 8], [9, 10, 11]])
my_tensor.mT
# tensor([[0, 3, 6, 9],
#         [1, 4, 7, 10],
#         [2, 5, 8, 11]])

my_tensor = torch.tensor([[[0, 1, 2], [3, 4, 5]],
                          [[6, 7, 8], [9, 10, 11]],
                          [[12, 13, 14], [15, 16, 17]],
                          [[18, 19, 20], [21, 22, 23]]])
my_tensor.mT
# tensor([[[0, 3], [1, 4], [2, 5]],
#         [[6, 9], [7, 10], [8, 11]],
#         [[12, 15], [13, 16], [14, 17]],
#         [[18, 21], [19, 22], [20, 23]]])

my_tensor = torch.tensor([[[0., 1., 2.], [3., 4., 5.]],
                          [[6., 7., 8.], [9., 10., 11.]],
                          [[12., 13., 14.], [15., 16., 17.]],
                          [[18., 19., 20.], [21., 22., 23.]]])
my_tensor.mT
# tensor([[[0., 3.], [1., 4.], [2., 5.]],
#        [[6., 9.],  [7., 10.], [8., 11.]],
#        [[12., 15.], [13., 16.], [14., 17.]],
#        [[18., 21.], [19., 22.], [20., 23.]]])

my_tensor = torch.tensor([[[0.+0.j, 1.+0.j, 2.+0.j],
                           [3.+0.j, 4.+0.j, 5.+0.j]],
                          [[6.+0.j, 7.+0.j, 8.+0.j],
                           [9.+0.j, 10.+0.j, 11.+0.j]],
                          [[12.+0.j, 13.+0.j, 14.+0.j],
                           [15.+0.j, 16.+0.j, 17.+0.j]],
                          [[18.+0.j, 19.+0.j, 20.+0.j],
                           [21.+0.j, 22.+0.j, 23.+0.j]]])
my_tensor.mT
# tensor([[[0.+0.j, 3.+0.j], [ 1.+0.j, 4.+0.j], [2.+0.j, 5.+0.j]],
#         [[6.+0.j, 9.+0.j], [7.+0.j, 10.+0.j], [8.+0.j, 11.+0.j]],
#         [[12.+0.j, 15.+0.j], [13.+0.j, 16.+0.j], [14.+0.j, 17.+0.j]],
#         [[18.+0.j, 21.+0.j], [19.+0.j, 22.+0.j], [20.+0.j, 23.+0.j]]])

my_tensor = torch.tensor([[[True, False, True], [True, False, True]],
                          [[False, True, False], [False, True, False]],
                          [[True, False, True], [True, False, True]],
                          [[False, True, False], [False, True, False]]])
my_tensor.mT
# tensor([[[True, True], [False, False], [True, True]],
#         [[False, False], [True, True], [False, False]],
#         [[True, True], [False, False], [True, True]],
#         [[False, False], [True, True], [False, False]]])

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adjoint(), mH and mT in PyTorch

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