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feat: newton Verfahren zeit auf f(x) an

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Sandro Zimmermann 2026-04-10 14:19:17 +02:00
parent 59149464c4
commit 5f7f9c4097
1 changed files with 9 additions and 6 deletions
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15
src/optimierung/allgemeiner_newton_verfahren.py
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@ -8,8 +8,8 @@ N = 200
x = sp.Symbol("x") x = sp.Symbol("x")
# Funktion # Funktion
# f_sym = x**4 - 10 * x**2 + x f_sym = x**4 - 10 * x**2 + x
f_sym = -sp.cos(2 * sp.pi * x) #f_sym = -sp.cos(2 * sp.pi * x)
# Ableitungen # Ableitungen
f = sp.lambdify(x, f_sym, "numpy") f = sp.lambdify(x, f_sym, "numpy")
@ -18,7 +18,7 @@ f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")
# Daten # Daten
# x_data = np.linspace(-4, 4, N) # x_data = np.linspace(-4, 4, N)
x_data = np.linspace(-3, 3, N) x_data = np.linspace(-4, 4, N)
f_data = f(x_data) f_data = f(x_data)
# Plot # Plot
@ -31,7 +31,8 @@ plt.show()
# Newton Verfahren # Newton Verfahren
# Startwert # Startwert
startwerte = [0.01, 0.02, 0.05, 0.1, 0.2, 0.23, 0.24, 0.245, 0.248, 0.249, 0.2499] #startwerte = [0.01, 0.02, 0.05, 0.1, 0.2, 0.23, 0.24, 0.245, 0.248, 0.249, 0.2499]
startwerte = [1.1]
# Iterationsformel # Iterationsformel
x_n = lambda x: x - f_prime(x) / np.abs(f_second(x)) x_n = lambda x: x - f_prime(x) / np.abs(f_second(x))
@ -41,18 +42,20 @@ print(60 * "-")
for x_0 in startwerte: for x_0 in startwerte:
n = 0 n = 0
x_i = x_0 x_i = x_0
f_x = f(x_0)
f_x_prime = f_prime(x_0) f_x_prime = f_prime(x_0)
f_x_second = f_second(x_0) f_x_second = f_second(x_0)
print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n") print(f"x_{n}: {x_0}\nf(x_{n}): {f_x}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n")
limit = 1000 limit = 1000
while np.abs(f_x_prime) > 1e-10 and limit > 0: while np.abs(f_x_prime) > 1e-10 and limit > 0:
n += 1 n += 1
x_i = x_n(x_i) x_i = x_n(x_i)
f_x = f(x_i)
f_x_prime = f_prime(x_i) f_x_prime = f_prime(x_i)
f_x_second = f_second(x_i) f_x_second = f_second(x_i)
print(f"x_{n}: {x_i}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n") print(f"x_{n}: {x_i}\nf(x_{n}): {f_x}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n")
limit -= 1 limit -= 1
print(60 * "-") print(60 * "-")
# %% # %%