The simplest and best solution is to use torch.sum().
To sum all elements of a tensor:
torch.sum(x) # gives back a scalar
To sum over all rows (i.e. for each column):
torch.sum(x, dim=0) # size = [ncol]
To sum over all columns (i.e. for each row):
torch.sum(x, dim=1) # size = [nrow]
It should be noted that the dimension summed over is eliminated from the resulting tensor.