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Numpy: Index 3D array with index of last axis stored in 2D array

How to get the indices of the sorted array using NumPy in Python?

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NumPy, or Numerical Python, is a powerful library for efficient numerical computation in Python. One of the key features of NumPy is its ability to perform advanced indexing, which allows to access and manipulate specific elements of an array based on complex conditions.

In this article, we will explore how to index a 3D array using a 2D array of indices in NumPy. This is a powerful technique that can be used to perform complex data manipulation and analysis tasks efficiently.

Table of Content

  • Indexing 3D Arrays with 2D Indices
  • Step-by-Step Guide: Mastering 3D Indexing with 2D Indices
    • Create the 3D array and the 2D index array:
    • Step 2: Expand the Dimensions of the Index Array
    • Step 3: Use numpy.take_along_axis to Index the 3D Array
    • Step 4: Squeeze the Result to Remove the Extra Dimension
  • Indexing 3D array with index of last axis stored in 2D array – Full Implementation Code

Indexing 3D Arrays with 2D Indices

Traditional indexing in NumPy employs integer positions to access specific elements within an array. Advanced indexing, however, extends this capability by enabling selection based on masks, boolean arrays, and even other arrays containing indices. This grants us the flexibility to target and operate on specific subsets of data within a multidimensional array.

In this specific scenario, we’ll focus on using a 2D array of indices to select elements from a 3D array along a particular axis. This technique is particularly useful when dealing with scenarios where the selection criteria for each element in a higher dimension depends on corresponding values in a lower dimension.

To index a 3D NumPy array using indices stored in a 2D array, we can use the numpy.take_along_axis function, which is designed for such tasks. This function allows you to select elements from an array along a specified axis using indices from another array.

Step-by-Step Guide: Mastering 3D Indexing with 2D Indices

Step-by-step guide to achieve this:

  • Step 1: We create a 3D array val_arr with shape (3, 3, 3) and a 2D array z_indices with shape (3, 3) that contains the indices along the z-axis.
  • Step 2: We use np.expand_dims to add an extra dimension to z_indices, making its shape (3, 3, 1). This is necessary because take_along_axis requires the indices array to have the same number of dimensions as the array being indexed.
  • Step 3: We use np.take_along_axis to select elements from val_arr along the z-axis (axis=0) using the indices from z_indices_expanded.
  • Step 4: We use np.squeeze to remove the extra dimension added by expand_dims, resulting in the final 2D array result_arr.

Create the 3D array and the 2D index array:

Python 
import numpy as np

# Create a 3D array of shape (3, 3, 3)
val_arr = np.arange(27).reshape(3, 3, 3)

# Create a 2D array of indices of shape (3, 3)
z_indices = np.array([[1, 0, 2],
                      [0, 0, 1],
                      [2, 0, 1]])

Step 2: Expand the Dimensions of the Index Array

Next, we use np.expand_dims to add an extra dimension to z_indices, making its shape (3, 3, 1). This is necessary because take_along_axis requires the indices array to have the same number of dimensions as the array being indexed.

Python 
# Expand the dimensions of z_indices to match the dimensions of val_arr
z_indices_expanded = np.expand_dims(z_indices, axis=-1)

Step 3: Use numpy.take_along_axis to Index the 3D Array

We then use np.take_along_axis to select elements from val_arr along the z-axis (axis=0) using the indices from z_indices_expanded.

Python 
# Use take_along_axis to select the elements
result_arr = np.take_along_axis(val_arr, z_indices_expanded, axis=0)

Step 4: Squeeze the Result to Remove the Extra Dimension

Finally, we use np.squeeze to remove the extra dimension added by expand_dims, resulting in the final 2D array result_arr.

Python 
# Squeeze the result to remove the extra dimension
result_arr = np.squeeze(result_arr, axis=-1)

print(result_arr)

Output:

[[ 9  1 20]
 [ 3  4 14]
 [24  7 17]]

Indexing 3D array with index of last axis stored in 2D array – Full Implementation Code

Python 
import numpy as np

# Create a 3D array of shape (3, 3, 3)
val_arr = np.arange(27).reshape(3, 3, 3)

# Create a 2D array of indices of shape (3, 3)
z_indices = np.array([[1, 0, 2],
                      [0, 0, 1],
                      [2, 0, 1]])

# Expand the dimensions of z_indices to match the dimensions of val_arr
z_indices_expanded = np.expand_dims(z_indices, axis=-1)

# Use take_along_axis to select the elements
result_arr = np.take_along_axis(val_arr, z_indices_expanded, axis=0)

# Squeeze the result to remove the extra dimension
result_arr = np.squeeze(result_arr, axis=-1)

print(result_arr)

Conclusion

In this article, we have demonstrated how to index a 3D NumPy array using indices stored in a 2D array. This technique leverages the numpy.take_along_axis function to efficiently select elements from a multidimensional array based on complex indexing conditions. By following the step-by-step guide, you can apply this method to your own data manipulation and analysis tasks, making your code more efficient and easier to understand.

NumPy’s advanced indexing capabilities are a testament to its power and flexibility, making it an indispensable tool for anyone working with numerical data in Python. Whether you are a data scientist, a machine learning engineer, or a researcher, mastering these techniques will enable you to handle complex data structures with ease and precision.



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