#Insert code here...

from numpy import random
from numpy import matrix

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

# Notice that U is not upper triangular.  We will only use the upper triangular part.

print( 'U before =' )
print( U )

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

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

import numpy as np
laff.copy( y, yold )   # save the original vector y

Tmvmult_un_unb_var1( U, x, y )

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

print( 'y - ( np.triu( U ) * x + yold ) = ' ) #np.triu makes the matrix upper triangular
print( y - ( np.triu( U ) * x + yold ) )

#Insert code here...

from numpy import random
from numpy import matrix

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

# U is not upper triangular.  We will only use the upper triangular part.

print( 'U before =' )
print( U )

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

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

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

Tmvmult_un_unb_var2( U, x, y )

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

print( 'y - ( np.triu( U ) * x + yold ) = ' ) #np.triu makes the matrix upper triangular
print( y - ( np.triu( U ) * x + yold ) )