89 lines
2.0 KiB
Python
89 lines
2.0 KiB
Python
# %%
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import numpy as np
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# %%
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print("Aufgabe 4")
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def fixpunkt_iteration(f, x=1.0, tol=1e-7, N=1000):
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x_new = f(x)
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i = 0
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while np.abs(x_new - x) > tol:
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if i > N:
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raise RuntimeError("Keine Konvergenz erreicht")
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x = x_new
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x_new = f(x)
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i += 1
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return [x_new, i]
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# Ausgabe
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print("----------------------------------------------------------------------")
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print(__file__)
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print("----------------------------------------------------------------------")
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f = lambda x: 1 - (1 / 5) * x
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try:
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fixpunkt_a, iterationen_a = fixpunkt_iteration(f)
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except RuntimeError as error:
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print(f"a) f(x) = 1-(1/5)*x\n{error}")
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else:
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print(
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f"a) f(x) = 1-(1/5)*x\nFixpunkt: {fixpunkt_a}\nIterationen: {iterationen_a}\n"
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)
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f = np.cos
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try:
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fixpunkt_b, iterationen_b = fixpunkt_iteration(f)
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except RuntimeError as error:
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print(f"b) f(x) = cos(x)\n{error}")
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else:
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print(f"b) f(x) = cos(x)\nFixpunkt: {fixpunkt_b}\nIterationen: {iterationen_b}\n")
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f = lambda x: np.e**-x
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try:
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fixpunkt_c, iterationen_c = fixpunkt_iteration(f)
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except RuntimeError as error:
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print(f"c) f(x) = e⁻x\n{error}")
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else:
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print(f"c) f(x) = e⁻x\nFixpunkt: {fixpunkt_c}\nIterationen: {iterationen_c}\n")
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print("----------------------------------------------------------------------")
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##%
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# Parameter
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q = 2.0
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a_0 = 1.0
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pr = 16
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# Funktionen
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def f(x):
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y = 0.5 * (x + q / x)
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return y
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# Iteration
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w = 0.0
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a = a_0
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k = 0
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print("----------------------------------------------------------------------")
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print(__file__)
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print("----------------------------------------------------------------------")
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print("Iteration :")
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print(f"a_{k} = {a:#.16g}")
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while a != w:
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w = a
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k = k + 1
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a = f(a)
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print(f"a_{k} = {a:#.16g}")
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# Ausgabe :
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print("----------------------------------------------------------------------")
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print(f"Wurzel: sqrt({q:#.{pr}g}) = {a:#.{pr}g}")
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print("----------------------------------------------------------------------")
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