lab2(CM) ver 0.0

def f1(x, y, z):
    return 9*x*z**2 + y*z + 2*y**2*x**3 + 175
def f2(x, y, z):
    return 0.5*y**3*z**2 - 0.8*x**2*y - 5.5 + 4.2
def f3(x, y, z):
    return 0.7*z**3 - 6.3*y**3 - 12.6
def f1_der_x(x, y, z):     #derivative
    return 9*z**2 + 2*y**2*3*x**2
def f1_der_y(x, y, z):
    return z + 2*2*y*x**3
def f1_der_z(x, y, z):
    return 9*x*2*z + y
def f2_der_x(x, y, z):
    return -0.8*2*x*y
def f2_der_y(x, y, z):
    return 1.5*y**2 - 0.8*x**2
def f2_der_z(x, y, z):
    return y**3*z
def f3_der_x(x, y, z):
    return 0
def f3_der_y(x, y, z):
    return -18.9*y**2
def f3_der_z(x, y, z):
    return 2.1*z**2


def w_matrix(x, y, z):
    W = [[f1_der_x(x, y, z), f1_der_y(x, y, z), f1_der_z(x, y, z)],
         [f2_der_x(x, y, z), f2_der_y(x, y, z), f2_der_z(x, y, z)],
         [f3_der_x(x, y, z), f3_der_y(x, y, z), f3_der_z(x, y, z)]]
    return W


def def_matrix(a=[]):
    return (a[0][0]*a[1][1]*a[2][2] + a[2][0]*a[0][1]*a[1][2] +
            a[1][0]*a[2][1]*a[0][2] - a[2][0]*a[1][1]*a[0][2] -
            a[0][0]*a[2][1]*a[1][2] - a[1][0]*a[0][1]*a[2][2])


def t_matrix(a=[]):
    a1 = a[0][0]
    a2 = a[1][0]
    a3 = a[2][0]
    b1 = a[0][1]
    b2 = a[1][1]
    b3 = a[2][1]
    c1 = a[0][2]
    c2 = a[1][2]
    c3 = a[2][2]
    B = [[a1*b2-a2*b1, -a2*c3+a3*c2, a2*b3-a3*b2],
         [-b1*c3+b3*c1, a1*c3-a3*c1, -a1*b3+a3*b1],
         [b1*c2-b2*c1, -a1*c2+a2*c1, a1*b2-a2*b1]]
    return B

def inverse_matrix(a=[]):
    T = t_matrix(a)
    q = def_matrix(a)
    if def_matrix(a) == 0:
        print("def_matrix = 0")
        return a
    for i in range(3):
        for k in range(3):
            a[i][k] = T[i][k]/q
    return a



def output_matrix(a=[]):
    print(a[0][0], ' ', a[0][1], ' ', a[0][2])
    print(a[1][0], ' ', a[1][1], ' ', a[1][2])
    print(a[2][0], ' ', a[2][1], ' ', a[2][2])
    print('')




x = 1
y = 1
z = 1
W = w_matrix(1, 1, 1) #[номер строки][номер столбца]
W = [[2,1,1],[1,2,1],[1,1,2]]
output_matrix(W)
T = t_matrix(W)
output_matrix(T)
I = inverse_matrix(W)
output_matrix(I)