File:Convex Function.png

File:Convex Function.svg is a vector version of this file. It should be used in place of this PNG file. File:Convex Function.png → File:Convex Function.svg For more information, see Help:SVG. In other languages Alemannisch ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−

 

DescriptionConvex Function.png	graph of a convex function (which? see the source code)
Date	14 November 2006
Source	created with GNU R, see source below. I tried somehow to replicate the image mentioned in "other versions"
Author	Thomas Steiner
Permission (Reusing this file)	Thomas Steiner put it under the CC-by-SA 2.5.
Other versions	,

This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic 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.

https://creativecommons.org/licenses/by-sa/2.5CC BY-SA 2.5 Creative Commons Attribution-Share Alike 2.5 truetrue

 

This chart was created with R.

Read at User_talk:AtonX#SVG_of_convex_function, why I prefer the .png to the .svg

R-source code:

from=-0.9
to=2.05
a=seq(from,to,length=100)

con<-function(p) {
  p^2+0.1
}

png(filename="Convex_Function.png", width=1200, height=800, pointsize=12)

par(lwd=2,bg="whitesmoke",font=3)

plot(a,con(a),type="l",col="navy",lwd=3,xlab="",ylab="", axes=FALSE)

st=par("usr")[1]+0.06
ady=c(-0.2,-0.5)
adx=c(1.25,-0.75)
x=-0.7
y=1.98
t=0.3
z=x*t+y*(1-t)
m=((con(y)-con(x))/(y-x))*z + con(x)-((con(y)-con(x))/(y-x))*x
sz=3.2

##gerade
lines(c(x,y),c(con(x),con(y)),col="magenta",lwd=3)

## x
lines(c(x,x),c(0,con(x)),type="l",lty=2,col="grey")
text(x,0,labels="x",adj=adx,cex=sz)
lines(c(st,x),c(con(x),con(x)),col="darkgrey",lty=2)
text(st,con(x),labels="f(x)",adj=ady,cex=sz)
lines(x,con(x),type="p",lwd=3,col="red")

## y
lines(c(y,y),c(0,con(y)),type="l",lty=2,col="grey")
text(y,0,labels="y",adj=adx,cex=sz)
lines(c(st,y),c(con(y),con(y)),col="darkgrey",lty=2)
text(st,con(y),labels="f(y)",adj=ady,cex=sz)
lines(y,con(y),type="p",lwd=3,col="red")

## zwischenstelle z
lines(c(z,z),c(0,con(z)),type="l",lty=2,col="grey")
text(z+0.2,0,labels="tx+(1-t)y",adj=adx,cex=sz)
lines(c(st,z),c(con(z),con(z)),col="darkgrey",lty=2)
lines(c(z,z),c(0,m),type="l",lty=2,col="darkgrey")
lines(c(st,z),c(m,m),col="grey",lty=2)
text(st-0.13,con(z),labels="f( tx+(1-t)y )",adj=ady,cex=sz)
text(st-0.13,m,labels="t f(x) + (1-t) f(y)",adj=ady,cex=sz)
lines(z,con(z),type="p",lwd=3,col="red")
lines(z,m,type="p",lwd=3,col="red")

arrows(st-0.05,0.05,par("usr")[2]-0.05,0.05)
arrows(st,0,st,par("usr")[4])

dev.off()