#Insert code here...

from numpy import random
from numpy import matrix

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

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

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

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

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

Tmvmult_ln_unb_var1( L, x, y )

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

print( 'y - ( np.tril( L ) * x + yold ) = ' ) #np.tril makes the matrix lower triangular
print( y - ( np.tril( L ) * x + yold ) )

#Insert code here...

from numpy import random
from numpy import matrix

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

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

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

Tmvmult_ln_unb_var2( L, x, y )

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

print( 'y - ( np.tril( L ) * x + yold ) = ' ) #np.tril makes the matrix lower triangular
print( y - ( np.tril( L ) * x + yold ) )