# %%
from IPython.display import display
from sympy import Matrix, symbols

[a, b] = symbols("x_1, x_2")
x0 = Matrix([1.1, 0.9])
print("x0:")
display(x0)

f = Matrix(
    [
        [20.0 - (18.0 * a) - 2.0 * (b ** 2.0)],
        [(-4.0 * b) * (a - (b ** 2.0))]
    ])

Df = Matrix(
    [
        [-18.0, -4.0 * b],
        [-4.0 * b, (-4.0 * a) + 12.0 * (b ** 2.0)]
    ])

Df0 = Df.subs(
    {
        a: x0[0],
        b: x0[1]
    })


f0 = f.subs(
    {
        a: x0[0],
        b: x0[1]
    })

print("Df(x0):")
display(Df0)
print("f(x0):")
display(f0)
print("||f(x0)||_2")
display(f0.norm(2))

d0 = Df0.solve(-f0)

print("d0")
display(d0)
print("||d0||_2")
display(d0.norm(2))

x1 = x0 + d0
print("x1:")
display(x1)

Df1 = Df.subs(
    {
        a: x1[0],
        b: x1[1]
    })

f1 = f.subs(
    {
        a: x1[0],
        b: x1[1]
    })

print("Df(x1)")
display(Df1)
print("f(x1)")
display(f1)
print("||f(x1)||_2")
display(f1.norm(2))

d1 = Df1.solve(-f1)

print("d1")
display(d1)
print("||d1||_2")
display(d1.norm(2))

x2 = x1 + d1

print("x2")
display(x2)

# %%