sum(), prod() and cartesian_prod() in PyTorch

sum() can get the one or more sum elements of a 0D or more tensor from a 0D or more D tensor as shown below:

*Memos:

• sum() can be used with torch or a tensor.
• The 1st argument(tensor of int, float, complex or bool) with torch or using a tensor(tensor of int, float, complex or bool) is input(Required).
• The 2nd argument(int, tuple of int or list of int) with torch or the 1st argument(int, tuple of int or list of int) with a tensor is dim(Optional).
• The 3rd argument(bool) with torch or the 2nd argument(bool) with a tensor is keepdim(Optional-Default:False) which keeps the dimension of the input tensor. *keepdim= must be used with dim=.
• There is dtype argument(torch.dtype) (Optional) with torch. *Memos:
  • If None, the type of input is used.
  • dtype can also accept int(), float() and bool() but not complex() which are python built-in functions.
  • dtype= must be used.

import torch

my_tensor = torch.tensor([1, 2, 3])

torch.sum(input=my_tensor)
my_tensor.sum()
torch.sum(input=my_tensor, dim=0)
torch.sum(input=my_tensor, dim=-1)
torch.sum(input=my_tensor, dim=(0,))
torch.sum(input=my_tensor, dim=(-1,))
# tensor(6)

torch.sum(input=my_tensor, dim=0, keepdim=True)
# tensor([6])

my_tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])

torch.sum(input=my_tensor)
torch.sum(input=my_tensor, dim=(0, 1))
torch.sum(input=my_tensor, dim=(0, -1))
torch.sum(input=my_tensor, dim=(1, 0))
torch.sum(input=my_tensor, dim=(1, -2))
torch.sum(input=my_tensor, dim=(-1, 0))
torch.sum(input=my_tensor, dim=(-1, -2))
torch.sum(input=my_tensor, dim=(-2, 1))
torch.sum(input=my_tensor, dim=(-2, -1))
# tensor(21)

torch.sum(input=my_tensor, dim=0)
torch.sum(input=my_tensor, dim=-2)
torch.sum(input=my_tensor, dim=(0,))
torch.sum(input=my_tensor, dim=(-2,))
# tensor([5, 7, 9])

torch.sum(input=my_tensor, dim=1)
torch.sum(input=my_tensor, dim=-1)
torch.sum(input=my_tensor, dim=(1,))
torch.sum(input=my_tensor, dim=(-1,))
# tensor([6, 15])

torch.sum(input=my_tensor, dim=(0, 1), keepdim=True)
# tensor([[21]])

my_tensor = torch.tensor([[1., 2., 3.], [4., 5., 6.]])

torch.sum(input=my_tensor, dtype=torch.float64)
torch.sum(input=my_tensor, dtype=float)
# tensor(21., dtype=torch.float64)

my_tensor = torch.tensor([[1.+9.j, 2.-4.j, 3.+6.j],
                          [4.+0.j, 5.+8.j, 6.-5.j]])
torch.sum(input=my_tensor, dtype=torch.complex64)
# tensor(21.+14.j)

my_tensor = torch.tensor([[True, False, True, False],
                          [False, True, False, True]])
torch.sum(input=my_tensor)
# tensor(4)

torch.sum(input=my_tensor, dtype=torch.bool)
torch.sum(input=my_tensor, dtype=bool)
# tensor(True)

prod() can get the one or more product values of a 0D or more D tensor from a 0D or more D tensor as shown below:

*Memos:

• prod() can be used with torch or a tensor.
• The 1st argument(tensor of int, float, complex or bool) with torch or using a tensor(tensor of int, float, complex or bool) is input(Required).
• The 2nd argument(int) with torch or the 1st argument(int) with a tensor is dim(Optional).
• The 3rd argument(bool) with torch or the 2nd argument(bool) with a tensor is keepdim(Optional-Default:False) which keeps the dimension of the input tensor. *keepdim= must be used with dim=.
• There is dtype argument(torch.dtype) (Optional) with torch. *Memos:
  • If None, the type of input is used.
  • dtype can also accept int(), float() and bool() but not complex() which are python built-in functions.
  • dtype= must be used.

import torch

my_tensor = torch.tensor([1, 2, 3])

torch.prod(input=my_tensor)
my_tensor.prod()
torch.prod(input=my_tensor, dim=0)
torch.prod(input=my_tensor, dim=-1)
# tensor(6)

torch.prod(input=my_tensor, dim=0, keepdim=True)
# tensor([6])

my_tensor = torch.tensor([[1, 2, 3], [4, 5, 6]])

torch.prod(input=my_tensor)
# tensor(720)

torch.prod(input=my_tensor, dim=0)
torch.prod(input=my_tensor, dim=-2)
# tensor([4, 10, 18])

torch.prod(input=my_tensor, dim=1)
torch.prod(input=my_tensor, dim=-1)
# tensor([6, 120])

torch.prod(input=my_tensor, dim=0, keepdim=True)
# tensor([[4, 10, 18]])

my_tensor = torch.tensor([[1., 2., 3.],
                          [4., 5., 6.]])
torch.prod(input=my_tensor, dtype=torch.float64)
torch.prod(input=my_tensor, dtype=float)
# tensor(720., dtype=torch.float64)

my_tensor = torch.tensor([[1.+9.j, 2.-4.j, 3.+6.j],
                          [4.+0.j, 5.+8.j, 6.-5.j]])
torch.prod(input=my_tensor, dtype=torch.complex64)
# tensor(-16440.+78360.j)

my_tensor = torch.tensor([[True, False, True, False],
                          [False, True, False, True]])
torch.prod(input=my_tensor)
# tensor(0)

torch.prod(input=my_tensor, dtype=torch.bool)
# tensor(False)

cartesian_prod() can do cartesian product with one or more 1D tensors as shown below:

*Memos:

• cartesian_prod() can be used with torch but not with a tensor.
• The 1st or more arguments(tensor of int, float, complex or bool) with torch are *tensors(Required at least one tensor). *Memos:
  • Don't use *tensors= or tensors= with torch.
  • Tensors must be the same type.

import torch

my_tensor = torch.tensor([1, 2, 3])

torch.cartesian_prod(my_tensor)
# tensor([1, 2, 3])

my_tensor = torch.tensor([1., 2., 3.])

torch.cartesian_prod(my_tensor)
# tensor([1., 2., 3.])

my_tensor = torch.tensor([1.+9.j, 2.-4.j, 3.+6.j])

torch.cartesian_prod(my_tensor)
# tensor([1.+9.j, 2.-4.j, 3.+6.j])

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

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

tensor1 = torch.tensor([1, 2, 3])
tensor2 = torch.tensor([4, 5])

torch.cartesian_prod(tensor1, tensor2)
# tensor([[1, 4],
#         [1, 5],
#         [2, 4],
#         [2, 5],
#         [3, 4],
#         [3, 5]])

tensor1 = torch.tensor([1, 2, 3])
tensor2 = torch.tensor([4, 5])
tensor3 = torch.tensor([6, 7, 8, 9])

torch.cartesian_prod(tensor1, tensor2, tensor3)
# tensor([[1, 4, 6],
#         [1, 4, 7],
#         [1, 4, 8],
#         [1, 4, 9],
#         [1, 5, 6],
#         [1, 5, 7],
#         [1, 5, 8],
#         [1, 5, 9],
#         [2, 4, 6],
#         [2, 4, 7],
#         [2, 4, 8],
#         [2, 4, 9],
#         [2, 5, 6],
#         [2, 5, 7],
#         [2, 5, 8],
#         [2, 5, 9],
#         [3, 4, 6],
#         [3, 4, 7],
#         [3, 4, 8],
#         [3, 4, 9],
#         [3, 5, 6],
#         [3, 5, 7],
#         [3, 5, 8],
#         [3, 5, 9]])