NumPy: Generate a generic 2D Gaussian-like array

NumPy: Array Object Exercise-79 with Solution

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.

Python-Numpy Code Editor:

Previous: Write a NumPy program to create a record array from a (flat) list of arrays.
Next: Write a NumPy program to convert a NumPy array into Python list structure.