Added part b and cleaned up code

Assignment 1/assignment1.py

@@ -7,10 +7,6 @@ c = np.asmatrix(np.loadtxt('c.txt'))
 b = np.transpose(b) #make b a column vector
 m = 1
 
-
-# Initialize iteration counter
-global x
-global count 
 # Define f(x)
 def f(Q,b,c,x): 
 	return np.transpose(x)*Q*x + np.transpose(b)*x + c
@@ -33,9 +29,7 @@ def armijo(alpha0,Q,b,c,D,m,x):
 		alpha = beta**m*s
 		#print('alpha is ', alpha)
 	return alpha
-		
-		
-
+			
 # Begin Gradient Descent Algorithm
 def grad_opt(epsilon,x,count,alpha):
 	#print('alpha is ', alpha)
@@ -58,6 +52,18 @@ def grad_opt(epsilon,x,count,alpha):
 	print 'epsilon is ', epsilon
 	return 0
 
+#part b
+#gradient of f * x = zero vector. solve for x by getting inverse of grad_f
+# grad f = 2*Q*x + b 
+#setting to zero gives us 2*Q*x = -b
+def partb(Q,b,x):
+	Qinv = np.linalg.inv(2*Q)
+	ans = Qinv*(-b)
+	print '\n Solving for x* using the inverse of 2*Q*x=-b is', ans
+	print f(Q,b,c,x)
+	print 'f(x*) is', f(Q,b,c,ans)
+	return 0
+	
 def run(epsilon):
 	# Make a guess for x vector
 	#x = np.asmatrix(np.zeros(np.size(b)))
@@ -66,7 +72,10 @@ def run(epsilon):
 	x = np.transpose(np.asmatrix(np.ones(np.size(b)))*1)
 	count = 0
 	alpha0 = 1.0
+	print '******** Part A ********'
 	grad_opt(epsilon,x,count,alpha0)
+	print '******** Part B ********'
+	partb(Q,b,x)
 	return 0 
 	
 run(0.00001)
\ No newline at end of file