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refractor: Ausgabe verbessert

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This commit is contained in:
Sandro Zimmermann 2026-04-04 19:49:25 +02:00
parent d39e3fcff0
commit e5e591891d
1 changed files with 19 additions and 18 deletions
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31
src/optimierung/newton_verfahren.py
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@ -1,16 +1,16 @@
#%% # %%
import numpy as np import numpy as np
import sympy as sp import sympy as sp
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
#%% # %%
# "Einfacher" Newton Verfahren # "Einfacher" Newton Verfahren
# Parameter # Parameter
N = 200 N = 200
x = sp.Symbol('x') x = sp.Symbol("x")
# Funktion # Funktion
f_sym = sp.sin(3*x)+0.02*x**2 f_sym = sp.sin(3 * x) + 0.02 * x**2
# Ableitungen # Ableitungen
f = sp.lambdify(x, f_sym, "numpy") f = sp.lambdify(x, f_sym, "numpy")
@ -18,7 +18,7 @@ f_prime = sp.lambdify(x, sp.diff(f_sym, x), "numpy")
f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy") f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")
# Daten # Daten
x_data = np.linspace(0,10,N) x_data = np.linspace(0, 10, N)
f_data = f(x_data) f_data = f(x_data)
# Plot # Plot
@ -34,14 +34,14 @@ plt.axis("image")
startwerte = [6.6, 3.4, 8.38] startwerte = [6.6, 3.4, 8.38]
# Iterationsformel # Iterationsformel
x_n = lambda x: x - f_prime(x)/f_second(x) x_n = lambda x: x - f_prime(x) / f_second(x)
# Iteration # Iteration
for x_0 in startwerte: for x_0 in startwerte:
n = 0 n = 0
x_i = x_0 x_i = x_0
f_x_prime = f_prime(x_0) f_x_prime = f_prime(x_0)
print(f"n: {n}\nf(x): {x_0}\nf'(x): {f_x_prime}\n") print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\n")
limit = 4 limit = 4
@ -49,17 +49,17 @@ for x_0 in startwerte:
n += 1 n += 1
x_i = x_n(x_i) x_i = x_n(x_i)
f_x_prime = f_prime(x_i) f_x_prime = f_prime(x_i)
print(f"n: {n}\nf(x): {x_i}\nf'(x): {f_x_prime}\n") print(f"x_{n}: {x_i}\nf'(x_{n}): {f_x_prime}\n")
limit -= 1 limit -= 1
#%% # %%
# "Modifizierter" Newton Verfahren # "Modifizierter" Newton Verfahren
# Parameter # Parameter
N = 200 N = 200
x = sp.Symbol('x') x = sp.Symbol("x")
# Funktion # Funktion
f_sym = sp.sin(3*x)+0.02*x**2 f_sym = sp.sin(3 * x) + 0.02 * x**2
# Ableitungen # Ableitungen
f = sp.lambdify(x, f_sym, "numpy") f = sp.lambdify(x, f_sym, "numpy")
@ -67,7 +67,7 @@ f_prime = sp.lambdify(x, sp.diff(f_sym, x), "numpy")
f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy") f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")
# Daten # Daten
x_data = np.linspace(0,10,N) x_data = np.linspace(0, 10, N)
f_data = f(x_data) f_data = f(x_data)
# Plot # Plot
@ -83,14 +83,14 @@ plt.axis("image")
startwerte = [6.6, 3.4, 8.38] startwerte = [6.6, 3.4, 8.38]
# 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))
# Iteration # Iteration
for x_0 in startwerte: for x_0 in startwerte:
n = 0 n = 0
x_i = x_0 x_i = x_0
f_x_prime = f_prime(x_0) f_x_prime = f_prime(x_0)
print(f"n: {n}\nf(x): {x_0}\nf'(x): {f_x_prime}\n") print(f"x_{n}: {x_0}\nf'(x_{n}): {f_x_prime}\n")
limit = 4 limit = 4
@ -98,5 +98,6 @@ for x_0 in startwerte:
n += 1 n += 1
x_i = x_n(x_i) x_i = x_n(x_i)
f_x_prime = f_prime(x_i) f_x_prime = f_prime(x_i)
print(f"n: {n}\nf(x): {x_i}\nf'(x): {f_x_prime}\n") print(f"x_{n}: {x_i}\nf'(x_{n}): {f_x_prime}\n")
limit -= 1 limit -= 1
# %%