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Summary

DescriptionMplwp Dickman function log.svg
English: Logarithmic plot of the Dickman function in the interval [0, 15], solving the delay differential equation
u ρ ( u ) + ρ ( u 1 ) = 0 {\displaystyle u\rho '(u)+\rho (u-1)=0,円} {\displaystyle u\rho '(u)+\rho (u-1)=0,円}
with initial conditions ρ ( u ) = 1 {\displaystyle \rho (u)=1} {\displaystyle \rho (u)=1} for 0 ≤ u ≤ 1.
Date
Source Own work
Author Geek3
Other versions
SVG development
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The source code of this SVG is invalid due to an error.
This W3C-invalid plot was created with mplwp, the Matplotlib extension for Wikipedia plots.
Source code
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Python code

Python Matplotlib mplwp source code
#!/usr/bin/python
# -*- coding: utf8 -*-
importmatplotlib.pyplotasplt
importmatplotlibasmpl
importnumpyasnp
frommathimport *
code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
 importmplwp
except ImportError, er:
 print 'ImportError:', er
 print 'You need to download mplwp.py from', code_website
 exit(1)
name = 'mplwp_Dickman_function_log.svg'
fig = mplwp.fig_standard(mpl)
xlim = 0, 15; fig.gca().set_xlim(xlim)
ylim = 1e-19, 1e1; fig.gca().set_ylim(ylim)
fig.gca().set_yscale('log')
fig.gca().yaxis.set_major_locator(mpl.ticker.FixedLocator(np.logspace(-18, 0, 10)))
mplwp.move_axes(fig, 8, 0)
n = 100 * 4 # multiple of 4
dx = 1. / n
x = np.arange(xlim[0], xlim[1] + dx/2., dx)
y = np.empty_like(x)
for i, xx in enumerate(x):
 if xx <= 1.0:
 y[i] = 1.0
 elif xx <= 2.0:
 y[i] = 1.0 - log(xx)
 else:
 # Simpson's rule to integrate x * y(x) = \int_{x-1}^x y(x) dx
 s = y[i-n]
 s += 2. * np.sum(y[i-n+2:i-1:2])
 s += 4. * np.sum(y[i-n+1:i:2])
 y[i] = s / (3. * xx / dx - 1.)
plt.plot(x, y, label='Dickman function')
plt.legend(loc='upper right').get_frame().set_alpha(0.9)
plt.savefig(name)
mplwp.postprocess(name)

Licensing

Geek3, the copyright holder of this work, hereby publishes it under the following licenses:
[画像:GNU head] Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License , Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License .http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
Attribution:
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.
https://creativecommons.org/licenses/by/3.0CC BY 3.0 Creative Commons Attribution 3.0 truetrue
You may select the license of your choice.

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29 June 2015

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File history

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Date/TimeThumbnailDimensionsUserComment
current14:19, 11 July 2015 Thumbnail for version as of 14:19, 11 July 2015 600 ×ばつ 400 (38 KB)Geek3 more accurate calculation
06:02, 29 June 2015 Thumbnail for version as of 06:02, 29 June 2015 600 ×ばつ 400 (38 KB)Geek3 Dickman_function_log plot by Geek3

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Short titlemplwp_Dickman_function_log.svg
Image titlehttp://commons.wikimedia.org/wiki/File:mplwp_Dickman_function_log.svg Plot created with mplwp, the Matplotlib extension for Wikipedia plots.
Width600px
Height400px

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