Image:NumInt-MC.png

From Wikipedia, the free encyclopedia

Wikimedia Commons logo This is a file from the Wikimedia Commons. The description on its description page there is shown below.
Commons is a freely licensed media file repository. You can help.
Description

numerical intergration with monte carlo. new points are dark blue (navy), old points are skyblue. points/nodes are uniform distributed over the integration interval. the value of the integral tends to 3,32.
Source

created with the help of GNU R, see source below
Date

13 Apr. 2006
Author

Thomas Steiner
Permission
(Reusing this image)

Thomas Steiner put it under the GFDL


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".

Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/-

R-source code:

a=0.5
b=2
cs=c("red","skyblue","navy","darkgrey")

f<-function(x) {
  return( 0.9*sin(9*x^0.6+0.3)+x+0.9 )
}

mc_plot<-function(n,new=1) {
  set.seed(6911)
  x=seq(a*0.6,b*1.05,length=700)
  if (n>0) {
    xi=sort((b-a)*runif(n)+a)
  } else {
    xi=NA
  }
  Xi=sort((b-a)*runif(new)+a)
  pts=sort(c(a,xi,Xi,b))
  plot(x,f(x),type="n",ylim=range(f(x),0),xlab="",ylab="")
  polygon(c(pts,b,a),c(f(pts),0,0),col=cs[4], border=cs[2],lwd=2)
  for (i in xi) {
    segments(i,0,i,f(i),col=cs[2],lwd=3)
  }
  for (i in Xi) {
    segments(i,0,i,f(i),col=cs[3],lwd=3)
  }
  lines(x,f(x),col=cs[1],lwd=3)
  ##calcualte area (integral)
  area=0
  for (p in 1:(length(pts)-1) ) {
    area <- area + (pts[p+1]-pts[p]) * (f(pts[p+1])+f(pts[p])) / 2
  }
  text(x=0.45,y=3.2, labels=substitute(integral(f(x)*dx, A, B)%~~% AREA,list(A=a,B=b,AREA=format(area,digits=3))),cex=1.5,col=cs[4],pos=4)
}


png(filename = "NumInt-MC.png", width=1200, height=900, pointsize = 12)
par(bg="grey90",mfrow=c(2,2), oma=c(0,0,3,0), cex.axis=0.85)
mc_plot(n=0)
mc_plot(n=1)
mc_plot(n=2)
mc_plot(n=3,new=5)
title(main="Numerische Integration mit Monte Carlo (Trapezmethode)", outer=TRUE,cex.main=1.9)
dev.off()

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current15:13, 13 April 20061,200×900 (16 KB)Thire ({{Information| |Description = numerical intergration with monte carlo. new points are dark blue (navy), old points are skyblue |Source = created with the help of GNU R, see source below |Date = 13 Apr. 2006 |Author = Thomas Steiner )
The following pages on the English Wikipedia link to this file (pages on other projects are not listed):