Commit du premier TP

tp1/TP1.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Nov 26 10:30:38 2024
+
+@author: dlahanqu
+"""
+
+import autograd as ag
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+import scipy.linalg as nla
+
+def f(x):
+    return 0.5*x**3 - 2*x**2 +x +7
+
+Tx = np.array ([-1.1, 0.17, 1.22, -.5, 2.02, 1.81])
+p = Tx.shape[0]
+Ty_sur_la_courbe = np.array ([f(x) for x in Tx])
+perturbations = 0.5*np.array ([-1.3, 2.7, -5, 0, 1.4, 6])
+Ty_experimentaux = Ty_sur_la_courbe + perturbations
+
+erreur_initiale = np.linalg.norm(Ty_sur_la_courbe-Ty_experimentaux, 2)
+print(erreur_initiale)
+
+plt.scatter(Tx, Ty_sur_la_courbe)
+plt.xlim(-1.2,2.1)
+plt.show()
+
+A = np.array([[x**3,x**2,x,1] for x in Tx], dtype = np.float64)
+
+Q1, R1 = nla.qr(A, mode ='economic')
+
+Q1Tb = np.dot(np.transpose(Q1), Ty_experimentaux)
+
+alpha, beta, gamma, mu = nla.solve_triangular(R1, Q1Tb, lower = False)
+
+print(alpha,beta, gamma, mu)
+
+def f_ajuster(x):
+    return alpha*x**3 + beta* x**2 + gamma *x + mu
+
+erreur_mini = np.linalg.norm(Ty_experimentaux-[f_ajuster(x) for x in Tx], 2)
+print(erreur_mini)
+
+"""plt.scatter(Tx, [f_ajuster(x) for x in Tx])
+xplot = np.linspace(-1.2, 2.1, 50)
+yplot = np.array([f_ajuster(x) for x in xplot])
+plt.plot(xplot, yplot)"""
+
+
+plt.close()
+# METHODE NEWTON A UNE VARIABLE
+def f(x):
+    return x**3 - 2
+
+def f_prime(x):
+    return 3*x**2
+
+def un_suiv(x):
+    return x- f(x)/f_prime(x)
+
+Tx=[]
+un = 2
+for i in range(10):
+    Tx.append(un)
+    print('u[%d] =' % i, un)
+    un = un_suiv(un)
+
+print(un)
+
+def f(x):
+    return alpha*x**3 + beta* x**2 + gamma *x + mu
+
+xplot = np.linspace(-1,2, 50)
+yplot = np.array([f(x) for x in xplot])
+plt.scatter(Tx, [0 for x in Tx])
+plt.plot(xplot, yplot)
+    
+def f(x):
+    return alpha*x**3 + beta* x**2 + gamma *x + mu
+
+def f_prime(x):
+    return 3*alpha*x**2 + 2*beta*x +gamma
+
+def f_seconde(x):
+    return 6*alpha*x + 2*beta
+
+Tx=[]
+u = 1
+for i in range(10):
+    Tx.append(u)
+    print('u[%d] = ' %i, u)
+    u = u - f_prime(u)/f_seconde(u)
+    
+xplot = np.linspace(-1,2, 100)
+yplot = np.array([f_prime(x) for x in xplot])
+plt.scatter(Tx, [0 for x in Tx])
+plt.plot(xplot, yplot)
+plt.axhline()
+plt.show()
+
+
+
+
+
+