Daily Archives: 03/05/2013

Computer, Graphics, LaTeX

LaTeX in R graphs

2 Comments

A nice post was recently published on the rsnippets blog, about the tikzDevice R package. This package is – indeed – awesome. Even if it has been removed from the CRAN website. Of course, it can be download from the archive folder, on http://cran.r-project.org/…, but also (for a more recent version)  on http://download.r-forge.r-project.org/…. But first, it is necessary to install the following package.

> install.packages("filehash")

Then, we download on of the tikzDevice.zip files, and load it, e.g. using (on Mac)

Then, we can load the library

> library("tikzDevice")

If we want to use nice LaTeX formulas, it might be necessary to upload some (LaTeX) libraries and to specify the encoding format

> "options(tikzMetricPackages = c("\\usepackage[utf8]{inputenc}",
+ "\\usepackage[T1]{fontenc}", "\\usetikzlibrary{calc}", "\\usepackage{amssymb}"))

(this is detailed, e.g. in  http://yihui.name/…), then, we write a code to plot a graph. The idea is to produce a tex file which contains the graph, or more precisely which will produce a pdf graph when we compile it. We start with

> tikz("normal-dist.tex", width = 8, height = 4, 
+ standAlone = TRUE,
+ packages = c("\\usepackage{tikz}",
+ "\\usepackage[active,tightpage,psfixbb]{preview}",
+ "\\PreviewEnvironment{pgfpicture}",
+ "\\setlength\\PreviewBorder{0pt}",
+ "\\usepackage{amssymb}"))

We will produce a 8×4 graph. The graph is the following,

> u=seq(-3,3,by=.01)
> plot(u,dnorm(u),type="l",axes=FALSE,xlab="",ylab="",col="white")
> axis(1)
> I=which((u>=0)&(u<=1))
> polygon(c(u[I],rev(u[I])),c(dnorm(u)[I],rep(0,length(I))),col="red",border=NA)
> lines(u,dnorm(u),lwd=2,col="blue")

We can add text (or TeX based text)

> text(-1.5, dnorm(-1.5)+.17, "$\\textcolor{blue}{X\\sim\\mathcal{N}(0,1)}$", cex = 1.5)
> text(1.75, dnorm(1.75)+.25, 
+ "$\\textcolor{red}{\\mathbb{P}(X\\in[0,1])=\\displaystyle{\\int_0^1 \\varphi(x)dx}}$", cex = 1.5)

And we end the file with a standard

> dev.off()

This will produce a .tex file. If we compile this file, we can generate a pdf file, that can be inserted in lecture notes, slides or articles,

Nice, isn’t it ?

LaTeX

Animation, from R to LaTeX

8 Comments

Just a short post, to share some codes used to generate animated graphs, with R. Assume that we would like to illustrate the law of large number, and the convergence of the average value from binomial sample. We can generate samples https://latex.codecogs.com/gif.latex?X_{i,j}\sim\mathcal{B}(1/2) using

> n=200
> k=1000
> set.seed(1)
> X=matrix(sample(0:1,size=n*k,replace=TRUE),n,k)

Each row https://latex.codecogs.com/gif.latex?\boldsymbol{X}_{i}=(X_{i,1},\cdots,X_{i,n},\cdots) will be a trajectory of heads and tails. For each trajectory, define the mean https://latex.codecogs.com/gif.latex?\bar{X}_{i,n}=n^{-1}(X_{i,1}+\cdots+X_{i,n}), which will denote the mean of the first https://latex.codecogs.com/gif.latex?n values. Such a matrix can be computed using

> cummean=function(M){
+ U=matrix(M[,1],nrow(M),1)
+ 	for(i in 2:ncol(M)){
+ 	U=cbind(U,(U[,i-1]*(i-1)+M[,i])/i)}
+ return(U)
+ }

Define then

> Xbar=cummean(X)

Now, to generate an animated gif, the way I usually do it is to generate graphs (png graphs) using a loop,

> S=trunc(10^seq(1,3,by=.05))
> for(j in 1:length(S)){
+ 	s=S[j]
+ 	Xhist=hist(Xbar[,s],breaks=seq(0,1,by=.05),plot=FALSE)
+ 	nfile=paste("LLN-",100+j,".png",sep="")
+ 	png(nfile,600,350)
+ 	layout(matrix(c(3,0,1,2),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
+ 	plot(1:s,Xbar[1,1:s],type="l",col="light blue",ylim=0:1,xlab="",ylab="",axes=FALSE,
+ 		 xlim=c(10,k),log="x")
+ 	axis(1)
+ 	axis(2)
+ 	for(i in 2:(n-1)) lines(1:s,Xbar[i,1:s],col="light blue")
+ 	lines(1:s,Xbar[n,1:s],col="red",lwd=2)
+ 	abline(v=s)
+ 	barplot(Xhist$counts, axes=TRUE,horiz=TRUE,col="light green",xlim=c(0,n/2*1.05))
+ 	dev.off()
+ }

I start at 100 because afterwards, when merging files, it is better to have (really) consecutive numbers, since sometimes, the lexical order is used, i.e. after 1 is 10, then 100, etc. Then I use Terminal commands

Here, the delay is in /100 seconds, and I use an infinite loop. The graph is here

It is possible to use

> library(animation)
> ani.options(interval=.15)
> saveGIF({      })

But the loop can be used also to generate several graphs, and to produce an animated graph in a pdf document (slides or lecture notes). The idea is to use the same code, but the output is here a pdf graph.

> S=trunc(10^seq(1,3,by=.1))
> for(j in 1:length(S)){
+ s=S[j]
+ Xhist=hist(Xbar[,s],breaks=seq(0,1,by=.05),plot=FALSE)
+ 	nfile=paste("LLN-",j,".pdf",sep="")
+ 	pdf(nfile,10,6)
+ layout(matrix(c(3,0,1,2),2,2,byrow=TRUE), c(3,1), c(1,3), TRUE)
+ plot(1:s,Xbar[1,1:s],type="l",col="light blue",ylim=0:1,xlab="",ylab="",axes=FALSE,
+ xlim=c(10,k),log="x")
+ axis(1)
+ axis(2)
+ for(i in 2:(n-1)) lines(1:s,Xbar[i,1:s],col="light blue")
+ lines(1:s,Xbar[n,1:s],col="red",lwd=2)
+ abline(v=s)
+ barplot(Xhist$counts, axes=TRUE,horiz=TRUE,col="light green",xlim=c(0,n/2*1.05))
+ 	dev.off()
+ }

We can then import them in LaTeX,

\documentclass[a4]{article}
\usepackage{graphicx}
\usepackage{animate}
\begin{document}
\begin{center}
\animategraphics[height=3.1in,palindrome]{1}{/Users/UQAM/LLN-}{1}{21}
\end{center}
\end{document}

This will generate the following pdf file. This animate package is described in several forums, e.g. http://www.geogebra.org/…