File:Metodo das secantes anime.gif

<syntaxhighligh lang=python>

1. !/usr/bin/env python3
2. -*- coding: utf-8 -*-

Este trabalho está licenciado sob a Licença Creative Commons Atribuição-CompartilhaIgual 3.0 Não Adaptada. Para ver uma cópia desta licença, visite https://creativecommons.org/licenses/by-sa/3.0/ ou envie uma carta para Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Author: Picknick - 09/2016

import numpy as np import scipy as sci from scipy import optimize import matplotlib.pyplot as plt import matplotlib.animation as animation

1. canvas

fig = plt.figure(figsize=(3,3), dpi=300, linewidth=0.0, facecolor="white")

1. axes definitions

ax = plt.subplot(1,1,1) ax.set_xlim(-1,3.5) ax.set_ylim(-5,30)

ax.set_xticks([]) ax.set_yticks([])

ax.set_frame_on(False)

a = 0.25 b = 2.75

def fun(x):

   return 0.8*(x+0.5)**3-1

def rsec(x,x0,x1):

   return (fun(x1)-fun(x0))/(x1-x0)*(x-x1) + fun(x1)

x = np.array([0.,0.,0.,0.]) x[0] = 2.65 x[1] = 2.15 x[2] = x[1] - fun(x[1])*(x[1]-x[0])/(fun(x[1])-fun(x[0])) x[3] = x[2] - fun(x[2])*(x[2]-x[1])/(fun(x[2])-fun(x[1]))

def init():

   global ax
   ax.cla()

   ax.set_xlim(-1,3.5)
   ax.set_ylim(-5,30)

   ax.set_xticks([])
   ax.set_yticks([])

   ax.set_frame_on(False)

   ax.arrow(-1, 0, 4.5, 0, length_includes_head=True, facecolor='black', head_length=0.1, head_width=0.5)
   ax.text(3.25,-3.5,r"$x$")

   ax.arrow(0, -2, 0, 31, length_includes_head=True, facecolor='black', head_length=0.5, head_width=0.1)
   ax.text(-0.4, 27.5, r"$y$")

   xx = np.linspace (a, b)
   ax.plot(xx, fun(xx), lw=1.5)

   xstar = sci.optimize.fsolve(fun,a)
   ax.plot ([xstar, xstar], [0, 0], 'ro', markersize=3)
   ax.text (xstar - 0.25, 0.5, r"$x\!^{*}$")

def update(i):

   global ax, x
   print(i)
   if (i == 0):
       a = x[0]
       ax.plot ([0, a], [fun(a), fun(a)], color='gray', linestyle='dashed')
       ax.plot ([a, a], [fun(a), 0], color='gray', linestyle='dashed')
       ax.plot (a, fun(a), 'ko', markersize=3)
       ax.plot ([a, a], [-0.5, 0.5], color='black')
       ax.plot ([-0.05, 0.05], [fun(a), fun(a)], color='black')
       ax.text (-1, fun(a)-0.1, r"$f(x^{(1)})$")
       ax.text (a - 0.25, -3.5, r"$x^{(1)}$")

       a = x[1]
       ax.plot ([0, a], [fun(a), fun(a)], color='gray', linestyle='dashed')
       ax.plot ([a, a], [fun(a), 0], color='gray', linestyle='dashed')
       ax.plot (a, fun(a), 'ko', markersize=3)
       ax.plot ([a, a], [-0.5, 0.5], color='black')
       ax.plot ([-0.05, 0.05], [fun(a), fun(a)], color='black')
       ax.text (-1, fun(a)-0.1, r"$f(x^{(2)})$")
       ax.text (a - 0.25, -3.5, r"$x^{(2)}$")

   if (i == 1):
       xx = np.linspace(x[1]-0.75,x[1]+0.7)
       ax.plot(xx,rsec(xx,x[0],x[1]),color="gray",lw=0.75)

   if (i == 2):
       ax.plot ([x[2], x[2]], [-0.5, 0.5], color='black')
       
   if (i == 3):
       a = x[2]
       ax.plot ([0, a], [fun(a), fun(a)], color='gray', linestyle='dashed')
       ax.plot ([a, a], [fun(a), 0], color='gray', linestyle='dashed')
       ax.plot (a, fun(a), 'ko', markersize=3)
       ax.plot ([-0.05, 0.05], [fun(a), fun(a)], color='black')
       ax.text (-1, fun(a)-0.1, r"$f(x^{(3)})$")
       ax.text (a - 0.2, -3.5, r"$x^{(3)}$")
       
   if (i == 4):
       xx = np.linspace(x[2]-0.5,x[2]+1)
       ax.plot(xx,rsec(xx,x[1],x[2]),color="gray",lw=0.75)
       
   if (i == 5):
       ax.plot ([x[3], x[3]], [-0.5, 0.5], color='black')

   if (i == 6):
       a = x[3]
       ax.plot ([a, a], [-0.5, 0.5], color='black')
       ax.text (a - 0.3, -3.5, r"$x^{(4)}$")

anime = animation.FuncAnimation(fig, update, np.arange(7), interval=2000, repeat=True, init_func=init, repeat_delay=3000) anime.save('metodo_das_secantes_anime.gif', writer='imagemagick') </syntaxhighligh>

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