diff --git a/hw1-conjugate-gradient/conjugate_gradient.py b/hw1-conjugate-gradient/conjugate_gradient.py
index 1aea021b..968239c3 100644
--- a/hw1-conjugate-gradient/conjugate_gradient.py
+++ b/hw1-conjugate-gradient/conjugate_gradient.py
@@ -1,39 +1,43 @@
-#THIS PROGRAM RUNS THE CONJUGATE GRADIENT ALGORITHM
+### THIS PROGRAM RUNS THE CONJUGATE GRADIENT ALGORITHM
+
+### IMPORT LIBRARIES
 
-# Import Libraries
 import numpy as np
 import scipy as sp
-import matplotlib.pyplt as plt
+#import matplotlib.pyplt as plt
 
-# Input Arguments
-# A = np.array([[2.0, 3.0, 5.0], [2.0, 3.0 , 6.0], [3.0, 6.0, 9.0]])
-# b = np.array([2.0, 3.0, 5.0])
+### INPUT ARGUMENTS
 
+#A = np.array([[2.0, 3.0, 5.0], [2.0, 3.0 , 6.0], [3.0, 6.0, 9.0]])
+#b = np.array([2.0, 3.0, 5.0])
+#x = np.array([10.0, 20.5, 0.0]).T # initial guess
 A = np.array([[4.0, 0], [1.0, 3.0]])
-b = np.array([0.0, 1.0])
-
+b = np.array([0.0, 1.0]).T
+x = np.array([10.0, 20.5]).T # initial guess
 max_iterations = 1000
-tolerance = 0.0001
+tolerance = 0.001 
+
+
+### DEFINE FUNCTION : conjgrad
+### DOES : CG algorithm
 
-# Define the function conjgrad
-# DOES : CG algorithm
 def conjgrad(A, b, x, tolerance, max_iterations):
 	# Initialization
 	k = 0
 	r = b - np.matmul(A, x) # b - A @ x
 	p = r
-
+    
+    # Algorithm
 	for i in range(0, max_iterations):
-		alpha  =
-		x      =
-		r_next =
-		beta   =
-		p      =
-		k      = k + 1
+		alpha  = np.einsum('j,j',r,r) / np.einsum('j,j',p,np.einsum('ij,j', A, p))
+		x      = x + alpha*p
+		r_next = r - alpha*np.einsum('ij,j', A, p)
+		beta   = np.einsum('j,j',r_next,r_next)/np.einsum('j,j',r,r)
 		r      = r_next
-		# Bertil continues
+		p      = r + beta*p
+		k      = k + 1
 
-		if (np.sqrt(np.sum(r**2)) > tolerance):
+		if (np.sqrt(np.sum(r**2)) < tolerance):
 			break
 
-	return x # want to return x-array that minimizes S(x)
+	return (x,k) # want to return x-array that minimizes S(x)