#Insert code here...

from numpy import random
from numpy import matrix

A = matrix( random.rand( 4,4 ) )
x = matrix( random.rand( 4,1 ) )
y = matrix( random.rand( 4,1 ) )
yold = matrix( random.rand( 4,1 ) )

print( 'A before =' )
print( A )

print( 'x before =' )
print( x )

print( 'y before =' )
print( y )

import numpy as np

# Notice that A is not symmetric.  We now "symmetrize it"
Asymm = np.tril( A ) + np.transpose( np.tril( A, -1 ) )

laff.copy( y, yold )   # save the original vector y

Symv_l_unb_var1( A, x, y )

print( 'y after =' )
print( y )

print( 'y - ( Asymm * x + yold ) = ' )
print( y - ( Asymm * x + yold ) )

#Insert code here...

from numpy import random
from numpy import matrix

A = matrix( random.rand( 4,4 ) )
x = matrix( random.rand( 4,1 ) )
y = matrix( random.rand( 4,1 ) )
yold = matrix( random.rand( 4,1 ) )

print( 'A before =' )
print( A )

print( 'x before =' )
print( x )

print( 'y before =' )
print( y )

import numpy as np

# Notice that A is not symmetric.  We now "symmetrize it"
Asymm = np.tril( A ) + np.transpose( np.tril( A, -1 ) )

laff.copy( y, yold )   # save the original vector y

Symv_l_unb_var2( A, x, y )

print( 'y after =' )
print( y )

print( 'y - ( Asymm * x + yold ) = ' )
print( y - ( Asymm * x + yold ) )