The arithmetic operations with `nan` and `inf` in PyTorch

#python #pytorch #arithmeticoperations #nan

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*Memos:

My post explains how to create nan and inf in PyTorch.
My post explains the comparisons with nan and inf in PyTorch.

The arithmetic operations with torch.nan and 100.0, torch.nan or torch.inf as shown below:

*Memos:

The arithmetic operations with nan are always nan:
complex type cannot do mod(modulo) calculation with %.

import torch

""" `float` type """
torch.nan + 100.0      # nan
torch.nan + torch.nan  # nan
torch.nan + -torch.nan # nan
torch.nan + torch.inf  # nan
torch.nan + -torch.inf # nan

torch.nan - 100.0      # nan
torch.nan - torch.nan  # nan
torch.nan - -torch.nan # nan
torch.nan - torch.inf  # nan
torch.nan - -torch.inf # nan

torch.nan * 100.0      # nan
torch.nan * torch.nan  # nan
torch.nan * -torch.nan # nan
torch.nan * torch.inf  # nan
torch.nan * -torch.inf # nan

torch.nan / 100.0      # nan
torch.nan / torch.nan  # nan
torch.nan / -torch.nan # nan
torch.nan / torch.inf  # nan
torch.nan / -torch.inf # nan

torch.nan % 100.0      # nan
torch.nan % torch.nan  # nan
torch.nan % -torch.nan # nan
torch.nan % torch.inf  # nan
torch.nan % -torch.inf # nan

""" `complex` type """
complex(torch.nan, torch.nan) + (100.0+0.j)                     # (nan+nanj)
complex(torch.nan, torch.nan) + complex(torch.nan, torch.nan)   # (nan+nanj)
complex(torch.nan, torch.nan) + complex(torch.nan, -torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) + complex(-torch.nan, torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) + complex(-torch.nan, -torch.nan) # (nan+nanj)
complex(torch.nan, torch.nan) + complex(torch.inf, torch.inf)   # (nan+nanj)
complex(torch.nan, torch.nan) + complex(torch.inf, -torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) + complex(-torch.inf, torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) + complex(-torch.inf, -torch.inf) # (nan+nanj)

complex(torch.nan, torch.nan) - (100.0+0.j)                     # (nan+nanj)
complex(torch.nan, torch.nan) - complex(torch.nan, torch.nan)   # (nan+nanj)
complex(torch.nan, torch.nan) - complex(torch.nan, -torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) - complex(-torch.nan, torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) - complex(-torch.nan, -torch.nan) # (nan+nanj)
complex(torch.nan, torch.nan) - complex(torch.inf, torch.inf)   # (nan+nanj)
complex(torch.nan, torch.nan) - complex(torch.inf, -torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) - complex(-torch.inf, torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) - complex(-torch.inf, -torch.inf) # (nan+nanj)

complex(torch.nan, torch.nan) * (100.0+0.j)                     # (nan+nanj)
complex(torch.nan, torch.nan) * complex(torch.nan, torch.nan)   # (nan+nanj)
complex(torch.nan, torch.nan) * complex(torch.nan, -torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) * complex(-torch.nan, torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) * complex(-torch.nan, -torch.nan) # (nan+nanj)
complex(torch.nan, torch.nan) * complex(torch.inf, torch.inf)   # (nan+nanj)
complex(torch.nan, torch.nan) * complex(torch.inf, -torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) * complex(-torch.inf, torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) * complex(-torch.inf, -torch.inf) # (nan+nanj)

complex(torch.nan, torch.nan) / (100.0+0.j)                     # (nan+nanj)
complex(torch.nan, torch.nan) / complex(torch.nan, torch.nan)   # (nan+nanj)
complex(torch.nan, torch.nan) / complex(torch.nan, -torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) / complex(-torch.nan, torch.nan)  # (nan+nanj)
complex(torch.nan, torch.nan) / complex(-torch.nan, -torch.nan) # (nan+nanj)
complex(torch.nan, torch.nan) / complex(torch.inf, torch.inf)   # (nan+nanj)
complex(torch.nan, torch.nan) / complex(torch.inf, -torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) / complex(-torch.inf, torch.inf)  # (nan+nanj)
complex(torch.nan, torch.nan) / complex(-torch.inf, -torch.inf) # (nan+nanj)

The arithmetic operations with torch.inf and 100.0 or torch.inf as shown below. *complex type cannot do mod(modulo) calculation with %:

import torch

""" `float` type """
torch.inf + 100.0      # inf
torch.inf + torch.inf  # inf
torch.inf + -torch.inf # nan

torch.inf - 100.0      # inf
torch.inf - torch.inf  # nan
torch.inf - -torch.inf # inf

torch.inf * 100.0      # inf
torch.inf * torch.inf  # inf
torch.inf * -torch.inf # -inf

torch.inf / 100.0      # inf
torch.inf / torch.inf  # nan
torch.inf / -torch.inf # nan

torch.inf % 100.0      # nan
torch.inf % torch.inf  # nan
torch.inf % -torch.inf # nan

""" `complex` type """
complex(torch.inf, torch.inf) + (100.0+0.j)                     # (inf+infj)
complex(torch.inf, torch.inf) + complex(torch.inf, torch.inf)   # (inf+infj)
complex(torch.inf, torch.inf) + complex(torch.inf, -torch.inf)  # (inf+nanj)
complex(torch.inf, torch.inf) + complex(-torch.inf, torch.inf)  # (nan+infj)
complex(torch.inf, torch.inf) + complex(-torch.inf, -torch.inf) # (nan+nanj)

complex(torch.inf, torch.inf) - (100.0+0.j)                     # (inf+infj)
complex(torch.inf, torch.inf) - complex(torch.inf, torch.inf)   # (nan+nanj)
complex(torch.inf, torch.inf) - complex(torch.inf, -torch.inf)  # (nan+infj)
complex(torch.inf, torch.inf) - complex(-torch.inf, torch.inf)  # (inf+nanj)
complex(torch.inf, torch.inf) - complex(-torch.inf, -torch.inf) # (inf+infj)

complex(torch.inf, torch.inf) * (100.0+0.j)                     # (nan+nanj)
complex(torch.inf, torch.inf) * complex(torch.inf, torch.inf)   # (nan+infj)
complex(torch.inf, torch.inf) * complex(torch.inf, -torch.inf)  # (inf+nanj)
complex(torch.inf, torch.inf) * complex(-torch.inf, torch.inf)  # (-inf+nanj)
complex(torch.inf, torch.inf) * complex(-torch.inf, -torch.inf) # (nan-infj)

complex(torch.inf, torch.inf) / (100.0+0.j)                     # (nan+nanj)
complex(torch.inf, torch.inf) / complex(torch.inf, torch.inf)   # (nan+nanj)
complex(torch.inf, torch.inf) / complex(torch.inf, -torch.inf)  # (nan+nanj)
complex(torch.inf, torch.inf) / complex(-torch.inf, torch.inf)  # (nan+nanj)
complex(torch.inf, torch.inf) / complex(-torch.inf, -torch.inf) # (nan+nanj)

Additionally, the arithmetic operations with nan and 100.0, nan or inf with float() and complex() which are Python's built-in functions as shown below:

*Memos:

The arithmetic operations with nan are always nan:
complex type cannot do mod(modulo) calculation with %.

import torch

""" `float` type """
float('nan') + 100.0         # nan
float('nan') + float('nan')  # nan
float('nan') + float('-nan') # nan
float('nan') + float('inf')  # nan
float('nan') + float('-inf') # nan

float('nan') - 100.0         # nan
float('nan') - float('nan')  # nan
float('nan') - float('-nan') # nan
float('nan') - float('inf')  # nan
float('nan') - float('-inf') # nan

float('nan') * 100.0         # nan
float('nan') * float('nan')  # nan
float('nan') * float('-nan') # nan
float('nan') * float('inf')  # nan
float('nan') * float('-inf') # nan

float('nan') / 100.0         # nan
float('nan') / float('nan')  # nan
float('nan') / float('-nan') # nan
float('nan') / float('inf')  # nan
float('nan') / float('-inf') # nan

float('nan') % 100.0         # nan
float('nan') % float('nan')  # nan
float('nan') % float('-nan') # nan
float('nan') % float('inf')  # nan
float('nan') % float('-inf') # nan

""" `complex` type """
complex('nan+nanj') + (100.0+0.j)          # (nan+nanj)
complex('nan+nanj') + complex('nan+nanj')  # (nan+nanj)
complex('nan+nanj') + complex('nan-nanj')  # (nan+nanj)
complex('nan+nanj') + complex('-nan+nanj') # (nan+nanj)
complex('nan+nanj') + complex('-nan-nanj') # (nan+nanj)
complex('nan+nanj') + complex('inf+infj')  # (nan+nanj)
complex('nan+nanj') + complex('inf-infj')  # (nan+nanj)
complex('nan+nanj') + complex('-inf+infj') # (nan+nanj)
complex('nan+nanj') + complex('-inf-infj') # (nan+nanj)

complex('nan+nanj') - (100.0+0.j)          # (nan+nanj)
complex('nan+nanj') - complex('nan+nanj')  # (nan+nanj)
complex('nan+nanj') - complex('nan-nanj')  # (nan+nanj)
complex('nan+nanj') - complex('-nan+nanj') # (nan+nanj)
complex('nan+nanj') - complex('-nan-nanj') # (nan+nanj)
complex('nan+nanj') - complex('inf+infj')  # (nan+nanj)
complex('nan+nanj') - complex('inf-infj')  # (nan+nanj)
complex('nan+nanj') - complex('-inf+infj') # (nan+nanj)
complex('nan+nanj') - complex('-inf-infj') # (nan+nanj)

complex('nan+nanj') * (100.0+0.j)          # (nan+nanj)
complex('nan+nanj') * complex('nan+nanj')  # (nan+nanj)
complex('nan+nanj') * complex('nan-nanj')  # (nan+nanj)
complex('nan+nanj') * complex('-nan+nanj') # (nan+nanj)
complex('nan+nanj') * complex('-nan-nanj') # (nan+nanj)
complex('nan+nanj') * complex('inf+infj')  # (nan+nanj)
complex('nan+nanj') * complex('inf-infj')  # (nan+nanj)
complex('nan+nanj') * complex('-inf+infj') # (nan+nanj)
complex('nan+nanj') * complex('-inf-infj') # (nan+nanj)

complex('nan+nanj') / (100.0+0.j)          # (nan+nanj)
complex('nan+nanj') / complex('nan+nanj')  # (nan+nanj)
complex('nan+nanj') / complex('nan-nanj')  # (nan+nanj)
complex('nan+nanj') / complex('-nan+nanj') # (nan+nanj)
complex('nan+nanj') / complex('-nan-nanj') # (nan+nanj)
complex('nan+nanj') / complex('inf+infj')  # (nan+nanj)
complex('nan+nanj') / complex('inf-infj')  # (nan+nanj)
complex('nan+nanj') / complex('-inf+infj') # (nan+nanj)
complex('nan+nanj') / complex('-inf-infj') # (nan+nanj)

Additionally, the arithmetic operations with inf and 100.0 or inf with float() and complex() which are Python's built-in functions as shown below. *complex type cannot do mod(modulo) calculation with %:

import torch

""" `float` type """
float('inf') + 100.0         # inf
float('inf') + float('inf')  # inf
float('inf') + float('-inf') # nan

float('inf') - 100.0         # inf
float('inf') - float('inf')  # nan
float('inf') - float('-inf') # inf

float('inf') * 100.0         # inf
float('inf') * float('inf')  # inf
float('inf') * float('-inf') # -inf

float('inf') / 100.0         # inf
float('inf') / float('inf')  # nan
float('inf') / float('-inf') # nan

float('inf') % 100.0         # nan
float('inf') % float('inf')  # nan
float('inf') % float('-inf') # nan

""" `complex` type """
complex('inf+infj') + (100.0+0.j)          # (inf+infj)
complex('inf+infj') + complex('inf+infj')  # (inf+infj)
complex('inf+infj') + complex('inf-infj')  # (inf+nanj)
complex('inf+infj') + complex('-inf+infj') # (nan+infj)
complex('inf+infj') + complex('-inf-infj') # (nan+nanj)

complex('inf+infj') - (100.0+0.j)          # (inf+infj)
complex('inf+infj') - complex('inf+infj')  # (nan+nanj)
complex('inf+infj') - complex('inf-infj')  # (nan+infj)
complex('inf+infj') - complex('-inf+infj') # (inf+nanj)
complex('inf+infj') - complex('-inf-infj') # (inf+infj)

complex('inf+infj') * (100.0+0.j)          # (nan+nanj)
complex('inf+infj') * complex('inf+infj')  # (nan+infj)
complex('inf+infj') * complex('inf-infj')  # (inf+nanj)
complex('inf+infj') * complex('-inf+infj') # (-inf+nanj)
complex('inf+infj') * complex('-inf-infj') # (nan-infj)

complex('inf+infj') / (100.0+0.j)          # (nan+nanj)
complex('inf+infj') / complex('inf+infj')  # (nan+nanj)
complex('inf+infj') / complex('inf-infj')  # (nan+nanj)
complex('inf+infj') / complex('-inf+infj') # (nan+nanj)
complex('inf+infj') / complex('-inf-infj') # (nan+nanj)