NumPy: Generate a generic 2D Gaussian-like array
Generate 2D Gaussian-Like Array
Write a NumPy program to generate a generic 2D Gaussian-like array.
Sample Solution:
Python Code:
# Importing the NumPy library and aliasing it as 'np'
import numpy as np
# Generating 2D grids 'x' and 'y' using meshgrid with 10 evenly spaced points from -1 to 1
x, y = np.meshgrid(np.linspace(-1, 1, 10), np.linspace(-1, 1, 10))
# Calculating the Euclidean distance 'd' from the origin using the generated grids 'x' and 'y'
d = np.sqrt(x*x + y*y)
# Defining parameters sigma and mu for a Gaussian-like distribution
sigma, mu = 1.0, 0.0
# Calculating the Gaussian-like distribution 'g' based on the distance 'd', sigma, and mu
g = np.exp(-((d - mu)**2 / (2.0 * sigma**2)))
# Printing a message indicating a 2D Gaussian-like array will be displayed
print("2D Gaussian-like array:")
# Printing the calculated 2D Gaussian-like array 'g'
print(g)
Sample Output:
2D Gaussian-like array: [[ 0.36787944 0.44822088 0.51979489 0.57375342 0.60279818 0.60279818 0.57375342 0.51979489 0.44822088 0.36787944] [ 0.44822088 0.54610814 0.63331324 0.69905581 0.73444367 0.73444367 0.69905581 0.63331324 0.54610814 0.44822088] [ 0.51979489 0.63331324 0.73444367 0.81068432 0.85172308 0.85172308 0.81068432 0.73444367 0.63331324 0.51979489] [ 0.57375342 0.69905581 0.81068432 0.89483932 0.9401382 0.9401382 0.89483932 0.81068432 0.69905581 0.57375342] [ 0.60279818 0.73444367 0.85172308 0.9401382 0.98773022 0.98773022 0.9401382 0.85172308 0.73444367 0.60279818] [ 0.60279818 0.73444367 0.85172308 0.9401382 0.98773022 0.98773022 0.9401382 0.85172308 0.73444367 0.60279818] [ 0.57375342 0.69905581 0.81068432 0.89483932 0.9401382 0.9401382 0.89483932 0.81068432 0.69905581 0.57375342] [ 0.51979489 0.63331324 0.73444367 0.81068432 0.85172308 0.85172308 0.81068432 0.73444367 0.63331324 0.51979489] [ 0.44822088 0.54610814 0.63331324 0.69905581 0.73444367 0.73444367 0.69905581 0.63331324 0.54610814 0.44822088] [ 0.36787944 0.44822088 0.51979489 0.57375342 0.60279818 0.60279818 0.57375342 0.51979489 0.44822088 0.36787944]]
Explanation:
In the above code –
- x, y = np.meshgrid(np.linspace(-1,1,10), np.linspace(-1,1,10)): Create two 2D arrays ‘x’ and ‘y’ using np.meshgrid and np.linspace. np.linspace creates 10 evenly spaced points between -1 and 1 for both arrays.
- d = np.sqrt(x*x+y*y): Calculate the Euclidean distance from the origin (0,0) to each coordinate in the grid using the Pythagorean theorem.
- sigma, mu = 1.0, 0.0: Define the standard deviation sigma and the mean mu of the Gaussian function.
- g = np.exp(-( (d-mu)**2 / ( 2.0 * sigma**2 ) ) ): This line computes the Gaussian function values for each distance d using the given sigma and mu. This generates a 2D Gaussian-like array, where the values represent the amplitude of the Gaussian function at each grid point.
- print("2D Gaussian-like array:"): Prints a "2D Gaussian-like array:"
- print(g): Print the generated 2D Gaussian-like array g.
For more Practice: Solve these Related Problems:
- Write a NumPy program to generate a 2D array that mimics a Gaussian distribution using meshgrid and exponential functions.
- Create a function that returns a normalized 2D Gaussian-like array and verifies that the peak value is at the center.
- Generate a 2D Gaussian-like pattern and adjust parameters to observe changes in spread and amplitude.
- Implement a Gaussian filter on an image array and compare the result with a manually generated 2D Gaussian array.
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