Dosiero:Convex Function.png
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This file has been superseded by Image:Convex Function.svg. It is recommended that the other file be used. If you just added this tag and want to nominate this image for deletion, please add the following code to here: (Please review the discussion here.)
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Description |
graph of a convex function (which? see the source code) |
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Source |
created with GNU R, see source below. I tried somehow to replicate the image mentioned in "other versions" |
Date |
14 nov. 2006 |
Author | |
Permission |
Thomas Steiner put it under the CC-by-SA 2.5. |
Other versions |
,
![]()
by User:AtonX
|
![]() ![]() ![]() |
This file is licensed under the Creative Commons Attribution ShareAlike 2.5 License |
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()
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