import numpy

def a(m, n):
    array = numpy.zeros((m, n))

    for i in range(m):
        for j in range(n):
            array[i, j] = i * j

    return array

def main():
    m = 3
    n = 4

    array = a(m, n)

    print(array)

if __name__ == "__main__":
    main()

1. Import statement

   import numpy
   

   This line imports the numpy library so that we can use numpy arrays and its associated functions.

2. Function definition:

   def a(m, n):
       array = numpy.zeros((m, n))
   
       for i in range(m):
           for j in range(n):
               array[i, j] = i * j
   
       return array
   

   • def a(m, n):

     This defines a function named a that takes two parameters, m and n. These parameters are integers that specify the size of the 2D array: m is the number of rows and n is the number of columns.

   • array = numpy.zeros((m, n))

     Here we create a numpy array of shape (m, n) filled with zeros. By default, numpy.zeros will create an array of type float64, which aligns with the requirement to store floating-point numbers.

   • Nested for loops:

     for i in range(m):
         for j in range(n):
             array[i, j] = i * j
     

     We iterate over each row i from 0 to m - 1, and each column j from 0 to n - 1.

     • For every position (i, j) in the array, we assign the value i * j.
     • This means the element in row i and column j will literally hold the product of the row index and the column index.

   • return array

     After filling the entire 2D array, we return it to wherever the function a was called.

3. Main function:

   def main():
       m = 3
       n = 4
   
       array = a(m, n)
   
       print(array)
   

   • We define a function main() that does the following:
     1. Sets m = 3 and n = 4.
     2. Calls the function a(m, n), which returns a 2D array with shape (3, 4) where each element at position (i, j) is i * j.
     3. Stores the result in the variable array.
     4. Prints array to the console.

4. Condition to run main():

   if __name__ == "__main__":
       main()
   

   This is a common Python idiom to ensure that main() is executed only if the script is run directly (not imported as a module by another script).

How it works all together

When main() is called:

• m is set to 3, and n is set to 4.
• a(3, 4) creates an array with 3 rows and 4 columns (all zeros initially).
• The code fills each element at (i, j) with the product i * j. This means:
  • Row 0: indices i = 0, so every product 0 * j is 0 → [0, 0, 0, 0].
  • Row 1: indices i = 1, so elements become [1 *0, 1 * 1, 1 * 2, 1 * 3] → [0, 1, 2, 3].
  • Row 2: indices i = 2, so elements become [2 * 0, 2 * 1, 2 * 2, 2 * 3] → [0, 2, 4, 6].

Thus, the resulting 2D array is:

[[0. 0. 0. 0.]
 [0. 1. 2. 3.]
 [0. 2. 4. 6.]]