#Insert code here...

from numpy import random
from numpy import matrix

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

import numpy as np
laff.copy( x, xold )   # save the original vector x

Trmv_un_unb_var1( U, x )

print( 'x after =' )
print( x )

print( np.triu( U ) * xold )

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

#Insert code here...

from numpy import random
from numpy import matrix

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


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

Trmv_un_unb_var2( U, x )

print( 'x after =' )
print( x )

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