lab4(CM) ver 1.0

import matplotlib.pyplot as plt


def sum_aij(x=[]):   # k-степень от 1 до 9 включительно
    sum = []
    for i in range(9+1):
        sum.append([])
        for j in range(9+1):
            a = 0
            for k in range(20):
                a += x[k]**(i+j)
            sum[i].append(a)

    return sum


def sum_b(x=[], y=[]):
    b = []
    for i in range(9+1):
        sum = 0
        for k in range(20):
            sum += x[k]**i * y[k]
        b.append(sum)
    return b


def diagonal(a=[], b=[]):
    tmp = 0
    for i in range(9+1):
        if a[i][i] == 0:
            for j in range(9+1):
                if j == i:
                    continue
                if (a[j][i] != 0) and (a[i][j] != 0):
                    for k in range(9+1):
                        tmp = a[j][k]
                        a[j][k] = a[i][k]
                        a[i][k] = tmp
                    tmp = b[j]
                    b[j] = b[i]
                    b[i] = tmp
                    break
    return a


def function(x, a=[]):
    sum = 0
    for i in range(9+1):
        sum += a[i]*x**i
    return sum


lst_x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
lst_y = [5, 6, 8, 10, 12, 13, 12, 10, 8, 10, 8, 11, 7, 9, 11, 10, 9, 12, 11, 6]
aij = []
aij = sum_aij(lst_x)
b = sum_b(lst_x, lst_y)
aij = diagonal(sum_aij(lst_x), sum_b(lst_x, lst_y))

for k in range(9+1):
    for i in range(k+1, 9+1):
        if aij[k][k] == 0:
            print("Solution isn't exist")
        M = aij[i][k]/aij[k][k]
        for j in range(k, 9+1):
            aij[i][j] -= M * aij[k][j]
        b[i] -= M * b[k]

i = 9
a = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
while i >= 0:
    i -= 1
    s = 0
    for j in range(i, 9+1):
        s += aij[i][j] * a[j]
    a[i] = (b[i] - s) / aij[i][i]
for i in range(9+1):
    print(a[i])

x = 1
lst_x_a = []
lst_y_a = []
while x < 20:
    lst_x_a.append(x)
    lst_y_a.append(function(x, a))
    x += 0.5
lst_x_a.append(20)
lst_y_a.append(function(20, a))

plt.plot(lst_x, lst_y, lst_x_a, lst_y_a)
plt.show()