*Concatenating joins a sequence of tensors along an existing axis. The PyTorch function for concatenation is cat(). Stacking joins a sequence of tensors along a new axis. The PyTorch function for stacking is stack().*

*This tutorial will go through the two PyTorch functions with code examples.*

## PyTorch Cat

We can use the PyTorch `cat()`

function to concatenate a sequence of tensors along the same dimension. The tensors must have the same shape (except in the concatenating dimension) or be empty.

### Syntax

torch.cat(tensors, dim=0, *, out=None)

**Parameters**

**tensors**(sequence of Tensors):*Required*. Any Python sequence of tensors of the same type. Non-empty tensors must have the same shape except in the concatenating dimension.**dim**(int):*Optional*. The dimension to concatenate the tensors over.

**Keyword Arguments**

**out**(Tensor):*Optional*. Output tensor

### Example

Let’s look at an example where we concatenate three tensors into one tensor using `cat()`

. First, we have to import the PyTorch library and then use the `tensor()`

function to create the tensors:

import torch x = torch.tensor([2, 3, 4, 5]) y = torch.tensor([4, 10, 30]) z = torch.tensor([7, 22, 4, 8, 3, 6])

Next, we can concatenate the tensors along the 0th dimension, the only available axis.

xyz = torch.cat( (x, y, z), dim=0 ) print(xyz) print(xyz.shape)

Let’s run the code to see the result:

tensor([ 2, 3, 4, 5, 4, 10, 30, 7, 22, 4, 8, 3, 6])

## PyTorch Stack

We can use the PyTorch `stack()`

function to concatenate a sequence of tensors along a new dimension. The tensors must have the same shape.

### Syntax

torch.stack(tensors, dim=0, *, out=None)

**Parameters**

**tensors**(sequence of Tensors):*Required*. Python sequence of tensors of the same size.**dim**(int):*Optional*. The new dimension to insert. The dimension must be between 0 and the number of dimensions of concatenated tensors.

**Keyword Arguments**

**out**(Tensor):*Optional*. Output tensor

### Example

Let’s look at an example where we stack three tensors into one tensor using `stack()`

. First, we have to import the PyTorch library and then use the `tensor()`

function to create the tensors:

import torch x = torch.tensor([2, 3, 4, 5]) y = torch.tensor([4, 10, 30, 40]) z = torch.tensor([8, 7, 16, 14])

In the above code, the tensors `x`

, `y`

, and `z`

are one-dimensional, each having four elements. Next, we will stack the tensors along `dim=0`

and `dim=1`

.

# Stacking Tensors using dimension 0 stacked_0 = torch.stack( (x, y, z), dim=0 ) # Stacking Tensors using dimension 1 stacked_1 = torch.stack( (x,y, z), dim=1 ) # Resultant combined tensor with new axes along dimension 0 print(stacked_0) # Shape of combined tensor print(stacked_0.shape) # Resultant combined tensor with new axes along dimension 1 print(stacked_1) # Shape of combined tensor print(stacked_1.shape)

Let’s run the code to get the result:

tensor([[ 2, 3, 4, 5], [ 4, 10, 30, 40], [ 8, 7, 16, 14]]) torch.Size([3, 4]) tensor([[ 2, 4, 8], [ 3, 10, 7], [ 4, 30, 16], [ 5, 40, 14]]) torch.Size([4, 3])

The resultant concatenated tensor is two-dimensional. As the individual tensors are one-dimensional, we can stack them with dimensions 0 and 1.

With `dim=0`

the tensors are stacked row-wise, giving us a 3×4 matrix. With `dim=1`

we transpose the tensors and stack them column-wise, giving us a 4×3 matrix.

## PyTorch Cat Vs Stack

The two PyTorch functions offer similar functionality but differ in how they concatenate tensors. The `cat()`

function concatenates tensors along the existing dimension. The `stack()`

function concatenates tensors along a new dimension not present in the individual tensors.

We can derive the same results of the `stack()`

function using the `cat()`

function. We can apply the unsqueeze operation to each tensor before passing them to the cat() function to get the same result. Let’s look at the result with the tensors from the previous example

import torch x = torch.tensor([2, 3, 4, 5]) y = torch.tensor([4, 10, 30, 40]) z = torch.tensor([8, 7, 16, 14]) xyz = torch.cat((x.unsqueeze(0), y.unsqueeze(0), z.unsqueeze(0)), dim=0) print(xyz) print(xyz.shape)

The unsqueeze operation adds a new dimension of length one to the tensors, and then we concatenate along the first axis. Let’s run the code to get the result:

tensor([[ 2, 3, 4, 5], [ 4, 10, 30, 40], [ 8, 7, 16, 14]]) torch.Size([3, 4])

Therefore `torch.stack((A, B), dim=0)`

is equivalent to `torch.cat((A.unsqueeze(0), B.unsqueeze(0)), dim=0`

## Summary

Congratulations on reading to the end of this tutorial. We have gone through how to concatenate tensors using both `cat()`

and `stack()`

and explained the differences between the two functions.

For further reading on PyTorch, go to the article: How to Convert NumPy Array to PyTorch Tensor.

To learn more about Python for data science and machine learning, go to the online courses page on Python for the most comprehensive courses available.

Have fun and happy researching!

Suf is a research scientist at Moogsoft, specializing in Natural Language Processing and Complex Networks. Previously he was a Postdoctoral Research Fellow in Data Science working on adaptations of cutting-edge physics analysis techniques to data-intensive problems in industry. In another life, he was an experimental particle physicist working on the ATLAS Experiment of the Large Hadron Collider. His passion is to share his experience as an academic moving into industry while continuing to pursue research. Find out more about the creator of the Research Scientist Pod here and sign up to the mailing list here!