TridiagonalMatrixAlgorythm

import numpy

def tridiagonalMatrixAlgorythm(d, c, a, b):
    alpha = [0]
    beta = [0]
    n = len(b)

    for i in range(1, n-1):
        if i == 1:
            alpha.append(-c[i] / d[i])
            beta.append(b[i] / d[i])
        else:
            alpha.append(-c[i] / (d[i] + alpha[i-1] * a[i-1]))
            beta.append((b[i] - a[i-1] * beta[i-1]) / (d[i] + a[i-1] * alpha[i-1]))

    x = [0] * n
    n -= 1
    x[n] = (b[n] - a[n-1] * beta[n-1]) / (d[n] + a[n-1] * alpha[n-1])
    for i in range(n-1, 0, -1):
        x[i] = x[i+1] * alpha[i] + beta[i]
    return x[1:]

def init_array(matrix, D):
    a, b, c, d = [0], [0], [0], [0]
    d.extend([matrix[i][i] for i in range(len(matrix[0]))])
    c.extend([matrix[i][i + 1] for i in range(len(matrix[0]) - 1)])
    a.extend([matrix[i + 1][i] for i in range(len(matrix[0]) - 1)])
    b.extend(D)
    return a, b, c, d

def valueB(matrix, x):
    b = [0] * len(x)
    for j in range(len(matrix)):
        b[j] = sum(matrix[j][i] * x[i] for i in range(len(matrix[j])))
    return b

def find_error(matrix, d1, d2, x2):
    r = [d2[i] - d1[i] for i in range(len(matrix))]
    matrix_rev = numpy.matrix(matrix).I
    matrix_rev = matrix_rev.tolist()
    e = [0 for _ in range(0, len(d1))]
    for j in range(0, len(matrix_rev)):
        e[j] = sum(matrix_rev[j][i] * r[i] for i in range(len(matrix_rev[j])))

    x = [x2[i] - e[i] for i in range(0, len(matrix_rev))]
    return x, e[0:4]


if __name__ == "__main__":
    matrix = [[4, 1, 0, 0],
              [1, 4, 1, 0],
              [0, 1, 4, 1],
              [0, 0, 1, 4]]
    D = [5, 6, 6, 5]
    a, b, c, d = init_array(matrix, D)
    x = tridiagonalMatrixAlgorythm(d, c, a, b)
    print(x)
    D_ = valueB(matrix, x)
    print(D_)
    x_real, error = find_error(matrix, D, D_, x)
    print(error)
    print(x_real)