# Torch sum a tensor along an axis

## Question:

How do I sum over the columns of a tensor?

``````torch.Size([10, 100])    --->    torch.Size([10])
``````

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.

Alternatively, you can use `tensor.sum(axis)` where `axis` indicates `0` and `1` for summing over rows and columns respectively, for a 2D tensor.

``````In [210]: X
Out[210]:
tensor([[  1,  -3,   0,  10],
[  9,   3,   2,  10],
[  0,   3, -12,  32]])

In [211]: X.sum(1)
Out[211]: tensor([ 8, 24, 23])

In [212]: X.sum(0)
Out[212]: tensor([ 10,   3, -10,  52])
``````

As, we can see from the above outputs, in both cases, the output is a 1D tensor. If you, on the other hand, wish to retain the dimension of the original tensor in the output as well, then you’ve set the boolean kwarg `keepdim` to `True` as in:

``````In [217]: X.sum(0, keepdim=True)
Out[217]: tensor([[ 10,   3, -10,  52]])

In [218]: X.sum(1, keepdim=True)
Out[218]:
tensor([[ 8],
[24],
[23]])
``````

If you have tensor `my_tensor`, and you wish to sum across the second array dimension (that is, the one with index 1, which is the column-dimension, if the tensor is 2-dimensional, as yours is), use `torch.sum(my_tensor,1)` or equivalently `my_tensor.sum(1)` see documentation here.

One thing that is not mentioned explicitly in the documentation is: you can sum across the last array-dimension by using `-1` (or the second-to last dimension, with `-2`, etc.)

So, in your example, you could use: `outputs.sum(1)` or `torch.sum(outputs,1)`, or, equivalently, `outputs.sum(-1)` or `torch.sum(outputs,-1)`. All of these would give the same result, an output tensor of size `torch.Size([10])`, with each entry being the sum over the all rows in a given column of the tensor `outputs`.

To illustrate with a 3-dimensional tensor:

``````In [1]: my_tensor = torch.arange(24).view(2, 3, 4)
Out[1]:
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]]])

In [2]: my_tensor.sum(2)
Out[2]:
tensor([[ 6, 22, 38],
[54, 70, 86]])

In [3]: my_tensor.sum(-1)
Out[3]:
tensor([[ 6, 22, 38],
[54, 70, 86]])
``````

it should be

dim (int or tuple of python:ints) – the dimension or dimensions to reduce.

dim=0 means reduce row dimensions: condense all rows = sum by col
dim=1 means reduce col dimensions: condense cols= sum by row

#### Torch sum along multiple axis or dimensions

Just for the sake of completeness (I could not find it easily) I include how to sum along multiple dimensions with `torch.sum` which is heavily used in computer vision tasks where you have to reduce along `H` and `W` dimensions.

If you have an image `x` with shape `C x H x W` and want to compute the average pixel intensity value per channel you could do:

``````avg = torch.sum(x, dim=(1,2)) / (H*W)     # Sum along (H,W) and norm
``````
Categories: questions Tags: , ,
Answers are sorted by their score. The answer accepted by the question owner as the best is marked with
at the top-right corner.