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File:Expinvsqlau GIF.gif

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Expinvsqlau_GIF.gif (800 × 600 pixels, file size: 281 KB, MIME type: image/gif, looped, 11 frames, 11 s)

Summary

Description
English: GIF version to illustrate the Laurent approximation of the function f(x)=exp(-1/x^2).
Date
Source Own work
Author IkamusumeFan

Matplotlib (Python)

# Author: Ika, 2013-08-24

import math as m
import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
# import matplotlib.animation as animation
def draw_frame(n,filename,line_color):
	fig = plt.figure()
	plt.axes([0.02,0.13,0.9,0.8])
	plt.hold(True)
	plt.xlim(-3,3)
	plt.ylim(-2,4)
	# Set up the spines
	ax = plt.gca()
	ax.spines['right'].set_color('none')
	ax.spines['top'].set_color('none')
	ax.xaxis.set_ticks_position('bottom')
	ax.spines['bottom'].set_position(('data',0))
	ax.yaxis.set_ticks_position('left')
	ax.spines['left'].set_position(('data',0))
	# Set up the label
	ax.text(2,3,'N='+str(n),fontsize=24,color=line_color)

	Q = []
	X = np.arange(-3, 3, 0.001)
	# Draw the original function (ORG) curve
	ORG = np.exp(-1/(X*X))
	a = plt.plot(X, ORG, '-', color='black', lw=4)
	Q.append(a)
	# Draw the approximation function (APPR) curve
	i=1
	APPR = 1+(-1)**i*(X**(-2*i))/m.factorial(i)
	while (i<n):
		i = i+1
		APPR = APPR+(-1)**i*(X**(-2*i))/m.factorial(i)
	a = plt.plot(X, APPR, '-', color=line_color, lw=4)
	Q.append(a)
	
	plt.savefig(filename)

draw_frame(1,'frame01.eps','#b30000')
draw_frame(2,'frame02.eps','#00b300')
draw_frame(3,'frame03.eps','#0000b3')
draw_frame(4,'frame04.eps','#b3b300')
draw_frame(5,'frame05.eps','#00b3b3')
draw_frame(6,'frame06.eps','#b300b3')
draw_frame(7,'frame07.eps','#b3b3b3')
draw_frame(10,'frame08.eps','#3300b3')
draw_frame(50,'frame09.eps','#33b300')
draw_frame(65,'frame10.eps','#0033b3')
draw_frame(80,'frame11.eps','#b3b333')

# To generate the final GIF file, use the shell command:
# convert -antialias -loop 0 -delay 100 -compress LZW frame* Expinvsqlau_GIF.gif

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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26 August 2013

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Date/TimeThumbnailDimensionsUserComment
current16:36, 26 August 2013Thumbnail for version as of 16:36, 26 August 2013800 × 600 (281 KB)IkamusumeFanRescale the image for better display.
06:20, 26 August 2013Thumbnail for version as of 06:20, 26 August 2013612 × 792 (81 KB)IkamusumeFanUser created page with UploadWizard

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