diff --git a/exercises/week4/conjugate_gradient/sources-solution/conjugate_gradient.py b/exercises/week4/conjugate_gradient/sources-solution/conjugate_gradient.py
index df14db5..2959399 100644
--- a/exercises/week4/conjugate_gradient/sources-solution/conjugate_gradient.py
+++ b/exercises/week4/conjugate_gradient/sources-solution/conjugate_gradient.py
@@ -1,46 +1,50 @@
 #!/usr/bin/env python3
 
 import numpy as np
 
 
 def solve(func, x0, jac=None, hess=None,
           max_iter=50, tol=1e-8,
           callback=None):
     'Minimize function with home-made conjugate gradient'
 
     if jac is None:
         raise RuntimeError('this method needs a jacobian to be provided')
 
     if hess is None:
         raise RuntimeError('this method needs a hessian to be provided')
 
     x_old = x0
     r_old = -jac(x0)
     p_old = r_old
 
+    # conjugate iteration loop
     for i in range(0, max_iter):
 
+        # fetch the hessian
         A = hess(x_old)
 
         Ap_old = np.einsum('ij,j->i', A, p_old)
 
         alpha = (np.einsum('i,i->', r_old, r_old) /
                  np.einsum('i,i->', p_old, Ap_old))
 
         x_new = x_old + alpha * p_old
         r_new = r_old - alpha * Ap_old
 
+        # call the callback over iterations
         if callback:
             callback(x_new)
 
+        # evaluate stop criterion
         if np.linalg.norm(x_new-x_old) < tol:
             return x_new
 
         beta = (np.einsum('i,i->', r_new, r_new) /
                 np.einsum('i,i->', r_old, r_old))
 
         p_old = r_new + beta * p_old
         r_old = r_new
         x_old = x_new
 
     return False