NumPy - Concatenating Arrays

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Concatenating NumPy Array

By concatenating a NumPy array, we mean to combine two or more arrays across different dimensions and axes to create a new array. This is helpful for combining arrays either vertically (along rows) or horizontally (along columns), depending on the need.

You can join arrays in Numpy using the concatenate() function available in the NumPy module.

The concatenate() Function

The concatenate() function in NumPy is used to concatenate (join together) arrays along a specified axis. It allows you to combine arrays either along rows or columns, depending on the axis parameter provided. Following is the syntax −

numpy.concatenate((a1, a2, ...), axis=0, out=None)

Where,

• a1, a2, ... − These are the sequence of arrays to be joined. These arrays must have the same shape along all axes except the one specified by axis. Default is 0 (along rows). Use 1 for joining along columns.

• axis − Specifies the axis along which the arrays will be joined.

• out (optional) − This allows you to specify an output array where the result of concatenation will be stored.

Concatenating Arrays Along Rows

Concatenating arrays along rows in NumPy means stacking arrays vertically, placing one array on top of another to create a larger array. This is useful for combining datasets or expanding data vertically.

In NumPy, you can achieve this using the numpy.concatenate() function with "axis" argument set to "0".

Example

In the following example, we are concatenating two NumPy arrays "arr1" and "arr2" along rows using the numpy.concatenate() function −

import numpy as np

arr1 = np.array([[1, 2, 3],
                 [4, 5, 6]])

arr2 = np.array([[7, 8, 9],
                 [10, 11, 12]])

# Concatenate along rows
concatenated_arr = np.concatenate((arr1, arr2), axis=0)
print("Concatenated Array along rows:",concatenated_arr)

Following is the output obtained −

Concatenated Array along rows:
[[ 1  2  3]
 [ 4  5  6]
 [ 7  8  9]
 [10 11 12]]

Concatenating Arrays Along Columns

We can also concatenate arrays along columns in NumPy by stacking arrays horizontally, placing one array beside another to extend data horizontally. This is useful for combining datasets where each array represents columns of data that need to be joined.

In NumPy, you achieve this using the numpy.concatenate() function with the "axis" argument set to "1".

Example

In the example below, we are concatenating two NumPy arrays "arr1" and "arr2" along columns using the numpy.concatenate() function −

import numpy as np

# Create two arrays
arr1 = np.array([[1, 2],
                 [3, 4]])

arr2 = np.array([[5, 6],
                 [7, 8]])

# Concatenate along columns 
concatenated_arr = np.concatenate((arr1, arr2), axis=1)
print("Concatenated Array along columns:")
print(concatenated_arr)

This will produce the following result −

Concatenated Array along columns:
[[1 2 5 6]
 [3 4 7 8]]

Concatenating Arrays with Mixed Dimensions

Concatenating arrays with mixed dimensions in NumPy involves combining arrays that initially have different shapes.

To achieve this, we use broadcasting techniques to adjust the shapes of the arrays so they are compatible for concatenation. This involves expanding the dimensions of the smaller arrays to match the larger arrays along the concatenation axis.

In NumPy, you can adjust the dimensions of arrays using functions such as np.reshape(), np.expand_dims(), and slicing.

Example: Concatenate 1D array with 2D array

Let us consider concatenating a 1D array with a 2D array. The 1D array will be expanded along the appropriate dimension to match the 2D array −

import numpy as np

# Create a 1D array
arr1 = np.array([1, 2, 3])

# Create a 2D array
arr2 = np.array([[4, 5, 6],
                 [7, 8, 9]])

# Expand dimensions of the 1D array to match the 2D array for concatenation along rows
expanded_arr1 = np.expand_dims(arr1, axis=0)

# Concatenate along rows (axis=0)
concatenated_arr = np.concatenate((expanded_arr1, arr2), axis=0)
print("Concatenated Array with Mixed Dimensions along rows:")
print(concatenated_arr)

Following is the output of the above code −

Concatenated Array with Mixed Dimensions along rows:
[[1 2 3]
 [4 5 6]
 [7 8 9]]
 

Example: Concatenate 2D array with 3D array

If you have arrays with more dimensions, you can similarly expand their dimensions to match each other. For example, concatenating a 2D array with a 3D array involves expanding the dimensions of the 2D array −

import numpy as np

# Create a 2D array
arr1 = np.array([[1, 2],
                 [3, 4]])

# Create a 3D array
arr2 = np.array([[[5, 6],
                  [7, 8]],
                 
                 [[9, 10],
                  [11, 12]]])

# Expand dimensions of the 2D array to match the 3D array for concatenation along the third dimension (axis=2)
expanded_arr1 = np.expand_dims(arr1, axis=2)

# Concatenate along the third dimension (axis=2)
concatenated_arr = np.concatenate((expanded_arr1, arr2), axis=2)
print("Concatenated Array with Mixed Dimensions along axis=2:")
print(concatenated_arr)

The output obtained is as shown below −

Concatenated Array with Mixed Dimensions along axis=2:
[[[ 1  5  6]
  [ 2  7  8]]

 [[ 3  9 10]
  [ 4 11 12]]]

Concatenating Arrays Along Specific Axes

You can concatenate arrays along axes other than "0" and "1" using the axis parameter of the concatenate() function. This parameter determines the dimension along which the arrays will be joined. By changing the value of axis, you can control whether the arrays are concatenated along rows, columns, or higher dimensions.

For arrays with more than two dimensions, you can specify higher axes for concatenation. For example, concatenating along the third axis (axis=2) involves combining arrays along their depth.

Example

In the following example, we are concatenating two 3D arrays along the third dimension −

import numpy as np

# 3D arrays
arr1 = np.array([[[1, 2],
                  [3, 4]],
                 
                 [[5, 6],
                  [7, 8]]])

arr2 = np.array([[[9, 10],
                  [11, 12]],
                 
                 [[13, 14],
                  [15, 16]]])

# Concatenate along the third dimension (axis=2)
result = np.concatenate((arr1, arr2), axis=2)
print("Concatenated along third dimension:")
print(result)

After executing the above code, we get the following output −

Concatenated along third dimension:
[[[ 1  2  9 10]
  [ 3  4 11 12]]

 [[ 5  6 13 14]
  [ 7  8 15 16]]]

Concatenating Arrays Using stack() Function

The NumPy stack() function can also be used to concatenate arrays along a new axis. Unlike numpy.concatenate(), which joins arrays along an existing axis, numpy.stack() adds an additional dimension, creating a new axis in the result. Following is the syntax −

numpy.stack(arrays, axis=0)

Where,

• arrays − A sequence of arrays to be stacked. All arrays must have the same shape.

• axis − The axis along which the arrays will be stacked. The default is 0.

Example

In the example below, we are stacking two 2D arrays along a new third axis (axis=2) using the NumPy stack() function −

import numpy as np

# Example 2D arrays
arr1 = np.array([[1, 2],
                 [3, 4]])

arr2 = np.array([[5, 6],
                 [7, 8]])

# Stack along a new third axis 
result = np.stack((arr1, arr2), axis=2)
print("Stacked along a new axis:")
print(result)

The result produced is as follows −

Stacked along a new axis:
[[[1 5]
  [2 6]]

 [[3 7]
  [4 8]]]