97 lines
1.9 KiB
Python
97 lines
1.9 KiB
Python
import matplotlib.pyplot as plt
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import numpy as np
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dich_steps = []
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new_raph_steps = []
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def f(x) -> float:
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return np.exp(x) - 2 * np.cos(x)
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def dichotomie(x_0, a, b, epsilon, n=0) -> float:
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delta = f(a) * f(x_0)
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x_1 = (a + b) / 2
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dich_steps.append(x_1)
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if np.abs(b - a) <= epsilon:
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return x_1
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if delta < 0:
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return dichotomie(x_1, a, x_0, epsilon, n+1)
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elif delta == 0:
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return x_1
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else:
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return dichotomie(x_1, x_0, b, epsilon, n+1)
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def f_prime(x) -> float:
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return np.exp(x) + 2 * np.sin(x)
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def newton_raphson(x_0, epsilon, max_iter=1_000) -> float | None:
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"""
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Condition : connaître la dérivée de f(x)
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:param x_0:
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:param epsilon:
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:param max_iter:
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:return:
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"""
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x = x_0
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for _ in range(max_iter):
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x_prev = x
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fx = f(x)
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fpx = f_prime(x)
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if np.abs(fx) < epsilon:
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return x
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elif fpx == 0:
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return None
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x = x - (fx / fpx)
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new_raph_steps.append(x)
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if np.abs(x - x_prev) < epsilon:
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return x
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return None
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def ex1() -> None:
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x = np.arange(0, 1, 0.001)
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f = [np.exp(i) - 2 * np.cos(i) for i in x]
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f1 = [np.exp(i) for i in x]
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f2 = [2 * np.cos(i) for i in x]
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for i in range(len(x)):
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if f1[i] == f2[i]:
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print(f1[i])
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plt.plot(x, f)
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plt.plot(x, f1)
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plt.plot(x, f2)
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plt.grid()
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plt.show()
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dichotomie_res = dichotomie(0, 0, 1, 10e-6)
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print(dichotomie_res)
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plt.plot(dich_steps)
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plt.title('Convergence de la dichotomie')
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plt.show()
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newton_raphson_res = newton_raphson(0.1, 10e-6)
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print(newton_raphson_res)
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plt.plot(new_raph_steps)
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plt.title('Convergence de Newton-Raphson')
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plt.show()
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"""
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La NR à moins d'étape que la dichotomie, NR à l'air rapide,
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comme Flash McQueen (Kachow)
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"""
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if __name__ == '__main__':
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ex1()
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