non linear regression

from typing import List

from numpy import matrix, matmul, ndarray
from numpy.linalg import inv

tmp_m = [[0, 1],
         [1, 3],
         [2, 5],
         [3, 7]]
tmp_p = 1


def calc_a_plus(mat: matrix) -> ndarray:
    """
    Used to calcul the A+ = (A_T*A)^(-1) where x*=(A+)A_T.b

    :type mat: matrix
    :rtype: ndarray
    """
    mat_trans: ndarray = mat.transpose()
    res_matmul: ndarray = matmul(mat_trans, mat)
    a_plus: ndarray = inv(res_matmul)
    return a_plus


def line_regression(
        main_mat: List[list],
        p: int,
        debug: bool = False)-> ndarray:
    """
    Used to calcul the main elements of Ax*=b

    :param main_mat: data: [[x, y], ..., [x, y]]
    :param p: polynomial degree of the result function
    :param debug: debug
    """
    mat: List[List[float]] = list()
    vec: list = list()
    for elem in main_mat:
        tmp: List[float] = list()
        for j in range(p + 1):
            tmp.append(pow(elem[0], j))
        mat.append(tmp)
        vec.append(elem[1])
    if debug:
        print("a = {}".format(mat))
        print("b = {}".format(vec))
    a_plus: ndarray = calc_a_plus(matrix(mat))
    tmp_res: ndarray = matmul(a_plus, matrix(mat).transpose())
    res: ndarray = matmul(tmp_res, vec)
    return res


print("the result is : {}".format(line_regression(tmp_m, tmp_p, True)))