In [112]:

    

from sympy import Function, Symbol, latex, init_printing


    

In [126]:

    

y0,y1,y2 = symbols('y^(0),y^(1),y^(2)')
x0, x1, x2, x = symbols('x^(0), x^(1), x^(2), x')
w0,w1 = symbols('w0, w1')
n = symbols('n')


    

In [127]:

    

f = (x*w1 + w0)


    

In [129]:

    

mse = ((f.subs(x, x0) - y0 )**2 + (f.subs(x, x1) - y1 )**2 + (f.subs(x, x2) - y2 )**2) /2
mse = ((f.subs(x, x0) - y0 )**2 ) 
#latex(mse)
mse


    

    
Out[129]:





$$\left(w_{0} + w_{1} x^{(0)} - y^{(0)}\right)^{2}$$

In [132]:

    

latex(mse.diff(w1))


    

    
Out[132]:





'2 x^{(0)} \\left(w_{0} + w_{1} x^{(0)} - y^{(0)}\\right)'

In [135]:

    

latex(mse.diff(w0).simplify())


    

    
Out[135]:





'2 w_{0} + 2 w_{1} x^{(0)} - 2 y^{(0)}'

In [151]:

    

expr = ( ((y0 + 0.8*x0) - 1) +  ((y0 - 0.2*x0) + 3))**2


    

In [153]:

    

expr.diff(x0)


    

    
Out[153]:





$$0.72 x^{(0)} + 2.4 y^{(0)} + 2.4$$

In [ ]: