#Insert code here...

from numpy import random
from numpy import matrix

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

# Notice that L is not lower triangular.  We will only use the lower triangular part.

print( 'L before =' )
print( L )

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

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

Trmv_lt_unb_var1( L, x )

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

#np.tril makes the matrix lower triangular
print( 'x - ( np.transpose( np.tril( L ) ) * xold ) = ' )
print( x - ( np.transpose( np.tril( L ) ) * xold ) )

#Insert code here...

from numpy import random
from numpy import matrix

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

# L is not lower triangular.  We will only use the lower triangular part.

print( 'L before =' )
print( L )

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


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

Trmv_lt_unb_var2( L, x )

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

#np.tril makes the matrix lower triangular
print( 'x - ( np.transpose( np.tril( L ) ) * xold ) = ' )
print( x - ( np.transpose( np.tril( L ) ) * xold ) )