94 lines
2.1 KiB
Python
94 lines
2.1 KiB
Python
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#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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Created on Fri Mar 6 08:06:39 2020
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@author: suwako
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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def newton(f, df, u, xtol=1e-12, Nmax=100):
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n = 1
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v = u - f(u) / df(u)
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while abs(u - v) >= xtol:
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u, v = v, v - f(v) / df(v)
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n += 1
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if n > Nmax:
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return None
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return v, n
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def secante(f, u, v, xtol=1e-12, Nmax=100):
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n = 1
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while abs(u - v) >= xtol:
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u, v = v, (u * f(v) - v * f(u)) / (f(v) - f(u))
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n += 1
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if n > Nmax:
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return None
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return v, n
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def f(x): return x**3 - 2 * x - 5
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def df(x): return 3 * x * x - 2
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plt.figure(0)
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X = np.linspace(-3, 3, 256)
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Y = [f(x) for x in X]
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plt.plot(X,Y)
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plt.grid()
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plt.show()
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for u in range(-3, 4):
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x, n = newton(f, df, u)
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print(f"Pour u0 = {u} on obtient {x} au bout de {n} itérations'")
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nmax = 0
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for u in range(-3, 4):
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for v in range(-3, 4):
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if u != v:
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x, n = secante(f, u, v)
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if n > nmax:
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nmax = n
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(a, b) = (u, v)
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print(f"pour u0 = {a} et u1 = {b}, {nmax} itérations sont nécéssaires")
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print(secante(df, 0, 1)[0])
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print(newton(f, df, secante(df, 0, 1)[0], Nmax=200))
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def f(x): return 3 * np.sin(4*x)+x*x - 2
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def df(x): return 12*np.cos(4*x)+2*x
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plt.figure(1)
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X = np.linspace(-3, 3, 256)
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Y = [f(x) for x in X]
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plt.plot(X,Y)
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plt.grid()
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plt.show()
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def zeros(f, df, a, b, n=100):
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zer = []
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for k in range(n):
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u = a + np.random.random() * (b - a)
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x = newton(f, df, u)
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if x is not None and round(x[0], 12) not in zer:
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zer.append(round(x[0], 12))
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return zer
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from scipy.integrate import quad
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def f(x):
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return quad(lambda t : np.sqrt(1-t*t)*np.cos(x*t),-1,1)[0]
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def df(x):
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return quad(lambda t : -t*np.sqrt(1-t*t)*np.sin(x*t),-1,1)[0]
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plt.figure(2)
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X = np.linspace(0, 16, 256)
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Y = [f(x) for x in X]
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plt.plot(X,Y)
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plt.grid()
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plt.show()
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def derivee(f,x,h):
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return (f(x+h)-f(x-h)/(2*h))
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def delta(p):
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return abs(np.cos(1)-derivee(np.sin,1,10**(-p)))
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plt.figure(3)
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P= np.arange(4,8,.1)
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D=[delta(p) for p in P]
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print(D)
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plt.plot(P,D)
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plt.show()
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