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 = 2.5
print( 'alpha = ' )
print( alpha )

import laff

yold = np.matrix( '0;0;0' )

laff.copy( y, yold )

print( 'yold = ' )
print( y )

y = yold

print( 'y before axpy:')

print( y )

y = alpha * x + y

print( 'y after axpy: ' )
print( y )

print( 'compare new y to  alpha * x + yold:' )
print( y - ( alpha * x + yold ) )

laff.copy( yold, y )

print( 'y before axpy:')

print( y )

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

print( 'y after axpy: ' )
print( y )

print( 'compare new y to  alpha * x + yold:' )
print( y - ( alpha * x + yold ) )

def axpy( alpha, x, y ):

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

laff.copy( yold, y )

print( 'y before axpy:')

print( y )

axpy( alpha, x, y )

print( 'y after axpy: ' )
print( y )

print( 'compare new y to  alpha * x + yold:' )
print( y - ( alpha * x + yold ) )

import laff

laff.copy( yold, y )

print( 'y before axpy:')

print( y )

laff.axpy( alpha, x, y )

print( 'y after axpy: ' )
print( y )

print( 'compare new y to  alpha * x + yold:' )
print( y - ( alpha * x + yold ) )

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