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.  
# In the future we will also think of (column) 
# vectors as matrices with only one column.
x = np.matrix( '1.;2.;3.' )
print( 'x = ' )
print( x )

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

def dot( x, y ):

    # Check how many elements there are in vector x.  For this, 
    # np.shape( x ) return the row and column size of x, where x is a matrix.
    
    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( 'Difference between  alpha and  np.transpose(x) * y:' )
alpha_reference = np.transpose(x) * y

print( alpha - alpha_reference[0,0]  )

# Insert Code here







import laff

alpha = np.matrix( '-2.0' ) # the way we are going to program, scalars, vectors, and matrices are 
                           # all just matrices.  So, alpha here is a 1 x 1 matrix, which we 
                           # initialize to some random number, in this case -2.0.

dot_unb( x, y, alpha )    # Takes x, y, and alpha as an input, and then updates alpha with the 
                          # result of dot( x, y ).  Notice that the contents of variable alpha
                          # are updated.  This only works if alpha is passed in as an array 
                          # (a matrix in our case)

print( 'alpha' )
print( alpha )

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

print( alpha - alpha_reference[0,0]  )