**Table of Contents**

- Introduction
- The
`numpy.concatenate`

Function `numpy.vstack`

: Joining Arrays Vertically`numpy.hstack`

: Joining Arrays Horizontally`numpy.stack`

: Joining Arrays Along a New Axis

## Introduction

Concatenation means **joining** of two or more arrays into a single array. Several functions are available in NumPy to perform concatenation including `numpy.concatenate`

, `numpy.vstack`

, `numpy.hstack`

and `numpy.stack`

.

## The numpy.concatenate Function

The `numpy.concatenate`

function joins a sequence of arrays along an **existing** axis.

Syntax

**The**.

`numpy.concatenate`

function```
1numpy.concatenate((a1, a2, ...), axis=0, out=None, dtype=None)
```

Parameter | Required? | Default Value | Description |
---|---|---|---|

`a1, a2, ...` |
✔️ Yes | NA | Input arrays must have the same shape, except in the dimension corresponding to `axis` . |

`axis` |
❌ No | 0 | The axis along which the arrays will be joined. If `axis` is `None` , arrays are flattened before use. |

`out` |
❌ No | `None` |
If provided, the destination to place the result. The shape must be correct, matching that of what concatenate would have returned if no out argument were specified. |

`dtype` |
❌ No | `None` |
If provided, the destination array will have this dtype. Cannot be provided together with out. |

**Note**

All the input arrays must have same number of dimensions.

### Joining 1-D Arrays

We begin by first by creating a few arrays to be used in subsequent examples. In the following, `ar`

is a 2-D array and `x`

, `y`

and `z`

are 1-D arrays sliced from `ar`

.

```
1import numpy as np
2ar = np.arange(1, 10).reshape((3, 3)) # create 2D array
3print(ar)
4x = ar[0,:] # 3 1-D arrays (each one is a row)
5print(x)
6y = ar[1,:]
7print(y)
8z = ar[2,:]
9print(z)
```

```
[[1 2 3]
[4 5 6]
[7 8 9]]
[1 2 3]
[4 5 6]
[7 8 9]
```

Example

Concatenating two 1-D arrays.```
1np.concatenate((x, y))
```

```
array([1, 2, 3, 4, 5, 6])
```

Example

Concatenating three 1-D arrays.```
1np.concatenate((x, y, z))
```

```
array([1, 2, 3, 4, 5, 6, 7, 8, 9])
```

Example

Concatenating three 1-D arrays with`dtype=float`

.
```
1np.concatenate((x, y, z),dtype=float)
```

```
array([1., 2., 3., 4., 5., 6., 7., 8., 9.])
```

**Caution**

It's **not possible** to concatenate 1-D arrays along `axis=1`

(and hoping that the arrays will stack row by row) since the `numpy.concatenate`

function only concatenates arrays along an **existing** axis.

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### Joining 2-D Arrays

We begin by first by creating two more 2-D arrays to be used in subsequent examples.

```
1ar2 = np.arange(10, 19).reshape((3, 3))
2print(ar2)
3ar3 = np.arange(19, 28).reshape((3, 3))
4print(ar3)
```

```
[[10 11 12]
[13 14 15]
[16 17 18]]
[[19 20 21]
[22 23 24]
[25 26 27]]
```

Example

Concatenating two 2-D arrays along first axis (default).```
1np.concatenate((ar2, ar3))
```

```
array([[10, 11, 12],
[13, 14, 15],
[16, 17, 18],
[19, 20, 21],
[22, 23, 24],
[25, 26, 27]])
```

Example

Concatenating two 2-D arrays along second axis.```
1np.concatenate((ar2, ar3),axis=1)
```

```
array([[10, 11, 12, 19, 20, 21],
[13, 14, 15, 22, 23, 24],
[16, 17, 18, 25, 26, 27]])
```

Example

Concatenating two 2-D arrays with`axis=None`

.
```
1np.concatenate((ar2, ar3),axis=None)
```

```
array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27])
```

In the above, the input arrays are flattened before concatenation.

Example

Concatenating three 2-D arrays along second axis.```
1np.concatenate((ar, ar2, ar3), axis=1)
```

```
array([[ 1, 2, 3, 10, 11, 12, 19, 20, 21],
[ 4, 5, 6, 13, 14, 15, 22, 23, 24],
[ 7, 8, 9, 16, 17, 18, 25, 26, 27]])
```

Example

Concatenate a 1-D array with a 2-D array results in error.```
1np.concatenate((x, ar2))
```

```
File "<__array_function__ internals>", line 5, in concatenate
ValueError: all the input arrays must have same number of dimensions, but the array at index 0 has 1 dimension(s) and the array at index 1 has 2 dimension(s)
```

**Caution**

All the input arrays must have same number of dimensions.

However, it is still possible to concatenate arrays with different dimensions. For the above example, one way is to convert the 1-D array into a 2-D array using either the `newaxis`

method or `reshape()`

method.

Example

Concatenate a 1-D array with a 2-D array by using`newaxis`

.
```
1np.concatenate((x[np.newaxis, :], ar2))
```

```
array([[ 1, 2, 3],
[10, 11, 12],
[13, 14, 15],
[16, 17, 18]])
```

Example

Concatenate a 1-D array with a 2-D array by using`reshape()`

method.
```
1np.concatenate((x.reshape(1,3), ar2))
```

```
array([[ 1, 2, 3],
[10, 11, 12],
[13, 14, 15],
[16, 17, 18]])
```

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## numpy.vstack: Joining Arrays Vertically

The `numpy.vstack`

function stacks arrays in sequence vertically (row wise). In contrast to the `numpy.concatenate`

function, it is possible to stack two 1-D arrays along the second axis which would result in putting them one on top of the other, or even stacking arrays of different dimensions.

Example

Stack two 1-D arrays vertically using`numpy.vstack`

.
```
1np.vstack((x, y))
```

```
array([[1, 2, 3],
[4, 5, 6]])
```

Example

Stack two 2-D arrays vertically using`numpy.vstack`

.
```
1np.vstack((ar, ar2))
```

```
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 7, 8, 9],
[10, 11, 12],
[13, 14, 15],
[16, 17, 18]])
```

Example

Stack two arrays (of different dimensions) vertically using`numpy.vstack`

.
```
1np.vstack((x, ar2))
```

```
array([[ 1, 2, 3],
[10, 11, 12],
[13, 14, 15],
[16, 17, 18]])
```

## numpy.hstack: Joining Arrays Horizontally

The `numpy.hstack`

function stacks arrays in sequence horizontally (column wise). This is equivalent to concatenation along the second axis, except for 1-D arrays where it concatenates along the first axis.

**Note**

The arrays must have the same shape along all but the *second axis*, except 1-D arrays which can be any length.

Example

Stack two 1-D arrays horizontally using`numpy.hstack`

.
```
1np.hstack((x, y))
```

```
array([1, 2, 3, 4, 5, 6])
```

The above can also be reproduced using `np.concatenate((x, y))`

.

Example

Stack two 2-D arrays horizontally using`numpy.hstack`

.
```
1np.hstack((ar, ar2))
```

```
array([[ 1, 2, 3, 10, 11, 12],
[ 4, 5, 6, 13, 14, 15],
[ 7, 8, 9, 16, 17, 18]])
```

The above can also be reproduced using `np.concatenate((ar, ar2), axis=1)`

.

**Tip**

The advantage of using `numpy.hstack`

over `numpy.concatenate`

is that there is no need to specify the `axis`

parameter.

It is possible to stack two arrays of different shapes horizontally as long as the they have the same size along the interface. In other words, the arrays must have the same shape along all but the second axis.

Example

Stack two arrays (of different shapes) horizontally using`numpy.hstack`

.
```
1ar4 = np.arange(0, 15).reshape((3, 5)) # create a 3X5 array
2print(ar4)
3print(np.hstack((ar2, ar4)))
```

```
[[ 0 1 2 3 4]
[ 5 6 7 8 9]
[10 11 12 13 14]]
[[10 11 12 0 1 2 3 4]
[13 14 15 5 6 7 8 9]
[16 17 18 10 11 12 13 14]]
```

It is meaningless to stack two arrays that do not have the same size along the interface. Instead, we may reshape one of the arrays to ensure they can be stacked properly.

Example

Stack two (unmatched) arrays horizontally using`numpy.hstack`

.
```
1np.hstack((x.reshape(3,1), ar2))
```

```
array([[ 1, 10, 11, 12],
[ 2, 13, 14, 15],
[ 3, 16, 17, 18]])
```

As another example, we can extract a single row from the 2-D array `ar2`

so that it can then be stacked horizontally with the 1-D array `x`

.

Example

Stack two (unmatched) arrays horizontally using`numpy.hstack`

.
```
1np.hstack((x, ar2[0,:] ))
```

```
array([ 1, 2, 3, 10, 11, 12])
```

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## numpy.stack: Joining Arrays Along a New Axis

While the `concatenate`

, `hstack`

and `vstack`

functions join arrays along an existing axis, the `numpy.stack`

function joins a sequence of arrays along a new axis.

Syntax

**The**.

`numpy.stack`

function```
1numpy.stack((a1, a2, ...), axis=0, out=None)
```

Parameter | Required? | Default Value | Description |
---|---|---|---|

`a1, a2, ...` |
✔️ Yes | NA | Each array must have the same shape. |

`axis` |
❌ No | 0 | The axis in the result array along which the input arrays are stacked. |

`out` |
❌ No | `None` |
If provided, the destination to place the result. The shape must be correct, matching that of what stack would have returned if no out argument were specified. |

The axis parameter specifies the index of the new axis in the dimensions of the result. For example, if `axis=0`

it will be the first dimension and if `axis=-1`

it will be the last dimension.

Example

Stack two 2-D arrays along`axis=0`

using `numpy.stack`

.
```
1np.stack((ar, ar2),axis=0) # size=2 along axis=0
```

```
array([[[ 1, 2, 3],
[ 4, 5, 6],
[ 7, 8, 9]],
[[10, 11, 12],
[13, 14, 15],
[16, 17, 18]]])
```

```
1np.stack((ar, ar2),axis=0).shape # output shape
```

```
(2, 3, 3)
```

**Note**

The size along the axis that is stacked is always equal to the number of input arrays.

In the above example, there are *two* input arrays which are stacked along `axis=0`

. Therefore, the size of the output array for `axis=0`

(first dimension) will also be *two*.

Example

Stack two 2-D arrays along`axis=1`

using `numpy.stack`

.
```
1np.stack((ar, ar2),axis=1) # size=2 along axis=1
```

```
array([[[ 1, 2, 3],
[10, 11, 12]],
[[ 4, 5, 6],
[13, 14, 15]],
[[ 7, 8, 9],
[16, 17, 18]]])
```

```
1np.stack((ar, ar2),axis=1).shape # output shape
```

```
(3, 2, 3)
```

In this case, there are two input arrays which are stacked along `axis=1`

(second dimension). Therefore, the size of the output array for the second dimension will also be two.

**Tip**

An easy way to visualize stacking is to simply swap the axes so that the input arrays are stacked along the specified axis.

Example

Stack two 2-D arrays along`axis=2`

using `numpy.stack`

.
```
1np.stack((ar, ar2),axis=2) # size=2 along axis=2
```

```
array([[[ 1, 10],
[ 2, 11],
[ 3, 12]],
[[ 4, 13],
[ 5, 14],
[ 6, 15]],
[[ 7, 16],
[ 8, 17],
[ 9, 18]]])
```

```
1np.stack((ar, ar2),axis=2).shape # output shape
```

```
(3, 3, 2)
```

In this case, there are two input arrays which are stacked along `axis=2`

(third dimension). Therefore, the size of the output array for the third dimension will also be two.