import numpy as np    # This imports a package called "numpy" that will make working with matrices 
                      # simpler

# create two two-dimensional matrices of only one column each.  
x = np.matrix( '1.;2.;3.' )
print( 'x = ' )
print( x )

y = np.matrix( '-1.;0.;-2.' )
print( 'y = ' )
print( y )

alpha = np.transpose( x ) * y

print( 'alpha:' )
print( alpha )

alpha[0,0]

alpha = 0.

for i in range( 3 ):
    alpha = x[ i, 0 ] * y[ i, 0 ] + alpha

print( 'alpha' )
print( alpha )

print( 'compare alpha to  np.transpose(x) * y:' )
alpha_reference = np.transpose(x) * y

print( alpha - alpha_reference[0,0]  )

def dot( x, y ):
    
    m, n = np.shape( x )
    
    alpha = 0.0
    
    for i in range( m ):
        alpha = x[ i, 0 ] * y[ i, 0 ] + alpha
    
    return alpha

alpha = 0.

alpha = dot( x, y )

print( 'alpha' )
print( alpha )

print( 'compare alpha to  np.transpose(x) * y:' )
alpha_reference = np.transpose(x) * y

print( alpha - alpha_reference[0,0]  )

import laff

alpha = 0.

alpha = laff.dot( x, y )

print( 'alpha' )
print( alpha )

print( 'compare alpha to  np.transpose(x) * y:' )
alpha_reference = np.transpose(x) * y

print( alpha - alpha_reference[0,0]  )

def dot( x, y ):
    ### You fill in the rest!