NumPy Exercises

1. Write a function replace_zeros(A, x) that modifies the array A (of any shape) by replacing all zero elements with x.

2. Write a function centered(A) that returns an array made of the array A (of any shape) in such a way that from each of its elements it subtracts the arithmetic mean of all elements of A. The array A itself should remain unchanged.

3. Write a function below_diagonal(A) that, for a square array A (any size greater than 1), creates a one-dimensional array whose k-th element is the sum of the elements of the k-th column of A below the main diagonal.

4. Write a function checkboard(n) that creates (and returns) a square array NumPy with alternating ones and zeros, of the size given by the invocation argument n, in the form:

   >>> checkboard(2)
   array([[ 1.,  0.],
          [ 0.,  1.]])
   
   >>> checkboard(3)
   array([[ 1.,  0.,  1.],
          [ 0.,  1.,  0.],
          [ 1.,  0.,  1.]])
   
   >>> checkboard(4)
   array([[ 1.,  0.,  1.,  0.],
          [ 0.,  1.,  0.,  1.],
          [ 1.,  0.,  1.,  0.],
          [ 0.,  1.,  0.,  1.]])
   
   >>> checkboard(5)
   array([[ 1.,  0.,  1.,  0.,  1.],
          [ 0.,  1.,  0.,  1.,  0.],
          [ 1.,  0.,  1.,  0.,  1.],
          [ 0.,  1.,  0.,  1.,  0.],
          [ 1.,  0.,  1.,  0.,  1.]])