Python script to solve approximate equation with least squares method.

least_squares_method.py

#! /usr/local/bin/python3.6
"""
Solving approximate equation with least squares method
"""
import sys
import traceback


class LeastSquaresMethod:
    N, M = 7, 5                    # Number of data, Dimension of curve
    X = [-3, -2, -1,  0, 1, 2, 3]  # Measurement data x
    Y = [ 5, -2, -3, -1, 1, 4, 5]  # Measurement data y

    def __init__(self):
        self.a = [[0.0 for _ in range(self.M + 2)] for _ in range(self.M + 1)]
        self.s = [0.0 for _ in range(2 * self.M + 1)]
        self.t = [0.0 for _ in range(self.M + 1)]

    def exec(self):
        """ Executeion """
        try:
            self.__calc_st()
            self.__ins_st()
            self.__sweep_out()
            self.__display()
        except Exception as e:
            raise

    def __calc_st(self):
        """ Calculation of s and t """
        try:
            for i in range(self.N):
                for j in range(2 * self.M + 1):
                    self.s[j] += (self.X[i] ** j)
                for j in range(self.M + 1):
                    self.t[j] += (self.X[i] ** j) * self.Y[i]
        except Exception as e:
            raise

    def __ins_st(self):
        """ Insertion of s and t into a """
        try:
            for i in range(self.M + 1):
                for j in range(self.M + 1):
                    self.a[i][j] = self.s[i + j]
                self.a[i][self.M + 1] = self.t[i]
        except Exception as e:
            raise

    def __sweep_out(self):
        """ Sweeping out """
        try:
            for k in range(self.M + 1):
                p = self.a[k][k]
                for j in range(k, self.M + 2):
                    self.a[k][j] /= p
                for i in range(self.M + 1):
                    if i == k:
                        continue
                    d = self.a[i][k]
                    for j in range(k, self.M + 2):
                        self.a[i][j] -= d * self.a[k][j]
        except Exception as e:
            raise

    def __display(self):
        """ Computation of y value and display """
        try:
            for k in range(self.M + 1):
                print("a{:d} = {:10.6f}".format(k, self.a[k][self.M + 1]))
            print("    x    y")
            for px in [0.5 * i for i in range(-6, 7)]:
                p = 0
                for k in range(self.M + 1):
                    p += self.a[k][self.M + 1] * (px ** k)
                print("{:5.1f}{:5.1f}".format(px, p))
        except Exception as e:
            raise


if __name__ == '__main__':
    try:
        obj = LeastSquaresMethod()
        obj.exec()
    except Exception as e:
        traceback.print_exc()
        sys.exit(1)