8_week_class2.py - master - mrFeld/Test

8_week_class2.py
92 строки2 KB
Vladimir N.
Approx
05 ноя 2024, 01:42
05 ноя 2024, 01:4213a670c
import numpy as np
import matplotlib.pyplot as plt


x_vals=np.array([0,0.5,0.7,1])
y_vals= (x_vals+1)**2

# Расчёт коэффииентом встроенным методом 
# A=np.vstack([np.ones_like(x_vals), x_vals, x_vals**2]).T
# coef = np.linalg.lstsq(A, y_vals)[0]
# c0, c1, c2 = coef

# Расчёт коэффииентом методом квадратных корней (в лоб)
# m1 = np.mean(x_vals)
# m2 = np.mean(x_vals ** 2)
# m3 = np.mean(x_vals ** 3)
# m4 = np.mean(x_vals ** 4)

# K01 = np.mean(y_vals)
# K11 = np.mean(x_vals * y_vals)
# K21 = np.mean(x_vals ** 2 * y_vals)

# s11 = 1
# s12 = m1
# s13 = m2
# s22 = (np.abs(m2 - m1 ** 2)) ** 0.5
# s23 = (m3 - m1 * m2) / s22
# s33 = (np.abs(m4 - (s13 ** 2 + s23 ** 2))) ** 0.5

# z1 = K01
# z2 = (K11 - m1 * K01) / s22
# z3 = (K21 - (s13 * z1 + s23 * z2)) / s33

# c2 = z3 / s33
# c1 = (z2 - s23 * c2) / s22
# c0 = z1 - (s12 * c1 + s13 * c2)


# Расчёт коэффииентов методом Крамера
m1 = np.mean(x_vals)
m2 = np.mean(x_vals ** 2)
m3 = np.mean(x_vals ** 3)
m4 = np.mean(x_vals ** 4)

K01 = np.mean(y_vals)
K11 = np.mean(x_vals * y_vals)
K21 = np.mean(x_vals ** 2 * y_vals)

A = [
    [1, m1, m2],
    [m1, m2, m3],
    [m2, m3, m4]
]

B = [K01, K11, K21]

def detM(matrix):
    return (matrix[0][0] * (matrix[1][1] * matrix[2][2] - matrix[1][2] * matrix[2][1])
            - matrix[0][1] * (matrix[1][0] * matrix[2][2] - matrix[1][2] * matrix[2][0])
            + matrix[0][2] * (matrix[1][0] * matrix[2][1] - matrix[1][1] * matrix[2][0]))

det_A = detM(A)

A0 = [B, [m1, m2, m3], [m2, m3, m4]]
A1 = [[1, m1, m2], B, [m2, m3, m4]]
A2 = [[1, m1, m2], [m1, m2, m3], B]

det_A0 = detM(A0)
det_A1 = detM(A1)
det_A2 = detM(A2)

c0 = det_A0 / det_A
c1 = det_A1 / det_A
c2 = det_A2 / det_A

x_range = np.linspace(min(x_vals)-1, max(x_vals)+1, 100)
y_original = (x_range+1)**2
y_aprox = c0 + c1*x_range + c2*x_range**2
y_approx = c0 + c1*x_vals + c2*x_vals**2

errors = y_vals - y_approx
mse = np.mean(errors**2)  

print(f"Найденные коэффициенты: c0 = {c0}, c1 = {c1}, c2 = {c2}")
print("Аппроксимированные значения:", y_approx)
print("Средний квадрат ошибки:", mse)

plt.plot(x_vals, y_vals, 'o', label='Входные данные')
plt.plot(x_range, y_original , 'r', label='оригинальная функция')
plt.plot(x_range, y_aprox, 'r', label = 'Апроксимированное значение', color='black')
plt.legend()
plt.show()