def b(matrix):
    result = numpy.zeros(matrix.shape)

    sums = numpy.zeros(matrix.shape[1])

    for j in range(matrix.shape[1]):
        for i in range(matrix.shape[0]):
            sums[j] += matrix[i, j]

    for i in range(matrix.shape[0]):
        for j in range(matrix.shape[1]):
            result[i, j] = matrix[i, j] / sums[j]
        
    return result

Function definition

def b(matrix):
	...
	return result

The function is called b and takes one argument called matrix, which is assumed to be a 2D numpy array. It returns a new 2D array (called result) that is the normalised version of matrix along its columns.

Step 1: Create a Result Array of the Same Shape

result = numpy.zeros(matrix.shape)

• matrix.shape returns a tuple (num_rows, num_cols) corresponding to the dimensions of the 2D numpy array.
• numpy.zeros(matrix.shape) creates an array of zeros with the exact same dimensions as matrix.
• This result array will eventually hold the normalised values. By initialising it with zeros, the function ensures it has the right shape from the start, and then updates each element with the normalised value in the subsequent loops.

Step 2: Initialise an Array for the Column Sums

sums = numpy.zeros(matrix.shape[1])

• matrix.shape[1] is the number of columns in the matrix.
• numpy.zeros(matrix.shape[1]) creates a 1D array with length equal to the number of columns. This array, called sums, is used to store the sum of each column.
• Initially, each entry is zero. The next loop fills in the correct sums for each column.

Step 3: Calculate the Sum of Each Column

for j in range(matrix.shape[1]):
        for i in range(matrix.shape[0]):
            sums[j] += matrix[i, j]

• Here, a nested loop iterates over each column (outer loop: j) and then each row (inner loop: i).