How to Fill Values in an Array Between Two Index Arrays Using NumPy ?

Published: December 14, 2024
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Published: December 14, 2024

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Introduction

Filling specific ranges of values into a NumPy array based on given start and end indexes is a common task in data analysis, image processing, and simulations. This article explains how to achieve this using NumPy's broadcasting capabilities through illustrative examples.

Table of contents

Note: This approach has been used to vectorize a research code and improve its performance. More details can be found How to Plot CloudSat 2B-CLDCLASS-LIDAR Product Using Python ?.

Example 1: Filling Values Between Two Indexes in a Matrix

Let's consider the problem where we have two arrays defining the start and end indexes of a range. The task is to fill a matrix with values between these indexes.

Problem Definition

We are given:

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import numpy as np

start_idx = np.array([67, 67, 67, 62, 62, 63, 62, 62, 24, 24])
end_idx = np.array([70, 70, 70, 71, 71, 71, 71, 71, 26, 26])

The goal is to create a matrix and fill values in the columns between start_idx and end_idx for each row.

Step 1: Create a Matrix of Indexes Using meshgrid

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x_idx_max = 10
y_idx_max = 200

x = np.arange(0, y_idx_max)
y = np.arange(0, x_idx_max)

xx, yy = np.meshgrid(x, y)

print(xx)

Output:

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array([[  0,   1,   2, ..., 197, 198, 199],
       [  0,   1,   2, ..., 197, 198, 199],
       [  0,   1,   2, ..., 197, 198, 199],
       ...,
       [  0,   1,   2, ..., 197, 198, 199],
       [  0,   1,   2, ..., 197, 198, 199],
       [  0,   1,   2, ..., 197, 198, 199]])

The matrix xx represents column indices repeated across rows.

Step 2: Apply Broadcasting to Fill Values

Using broadcasting, we compare the start and end indexes with the column indices (xx) to create a boolean matrix:

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heatmap = ((start_idx.reshape(x_idx_max, 1) <= xx) &
           (xx <= end_idx.reshape(x_idx_max, 1)))

For a specific row, you can observe the filled ranges:

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print(heatmap[0, :])

Output:

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array([False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False,  True,  True,  True,  True, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False])

Example 2: Filling Values Using One-Dimensional Arrays

This example demonstrates how to fill a matrix with ranges defined by two one-dimensional arrays.

Step 1: Define Start and End Index Arrays

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import numpy as np

r = np.arange(12)[:, None]  # Creates a column vector
start = [0, 1, 2, 3, 4, 4, 3, 2, 1, 0]
end = [9, 8, 7, 6, 5, 5, 6, 7, 8, 9]

Step 2: Apply Broadcasting

Using broadcasting, compare each element in r with start and end:

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out = ((start <= r) & (r <= end)).astype(int)

print(out)

Output:

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array([[1, 0, 0, 0, 0, 0, 0, 0, 0, 1],
       [1, 1, 0, 0, 0, 0, 0, 0, 1, 1],
       [1, 1, 1, 0, 0, 0, 0, 1, 1, 1],
       [1, 1, 1, 1, 0, 0, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
       [1, 1, 1, 1, 0, 0, 1, 1, 1, 1],
       [1, 1, 1, 0, 0, 0, 0, 1, 1, 1],
       [1, 1, 0, 0, 0, 0, 0, 0, 1, 1],
       [1, 0, 0, 0, 0, 0, 0, 0, 0, 1],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

The result shows ranges of 1s for indices between start and end.

NumPy's broadcasting is a powerful tool for efficiently filling values in matrices based on index ranges. The examples presented illustrate how to solve such problems for both one-dimensional and two-dimensional scenarios, enabling seamless data manipulation in various applications.

References

Links Site
Fill in values between given indices of 2d numpy array stackoverflow.com
Fill values into an array given indexes array and values array in Numpy stackoverflow.com
meshgrid numpy.org
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Benjamin

Hi, I'm Ben, the Founder of moonbooks.org. I work as a research scientist specializing in Earth satellite remote sensing, particularly focusing on Fire detection using VIIRS and ABI sensors. My areas of expertise include Python, Machine Learning, and Open Science. Feel free to reach out if you notice any errors on the site. I am constantly striving to enhance it. Thank you!

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