Beamer Adding Sweave - Biostatistics - Academic …yho/ph8400/HoExample4.pdf · Beamer Adding...
24
Beamer Adding Sweave Making Nice Slides using Beamer and Sweave Yen-Yi Ho Division of Biostatistics School of Public Health University of Minnesota 1/24
Transcript of Beamer Adding Sweave - Biostatistics - Academic …yho/ph8400/HoExample4.pdf · Beamer Adding...
BeamerAdding Sweave
Making Nice Slides using Beamer and Sweave
Yen-Yi Ho
Division of BiostatisticsSchool of Public HealthUniversity of Minnesota
1/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Syntax in Beamer
\documentclass{beamer}\usepackage{beamerthemeshadow}\title{Mytitle}
\begin{document}\begin{frame}\titlepage\end{frame}
\begin{frame}Content for Slide 1\end{frame}
\end{document}2/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
lists with pause
Introduction to LATEX
Course 2
Termpapers and presentations with LATEX
Beamer class
3/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
lists with pause
Introduction to LATEX
Course 2
Termpapers and presentations with LATEX
Beamer class
4/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
lists with pause
Introduction to LATEX
Course 2
Termpapers and presentations with LATEX
Beamer class
5/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
lists with pause
Introduction to LATEX
Course 2
Termpapers and presentations with LATEX
Beamer class
6/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Tables
Date Instructor TitleWS 04/05 John Mich First steps with LATEX
SS 05 Yen-Yi Ho LATEX Course serial
7/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
splitting screen
Beamer
Beamer Class
Beamer Class Latex
Instructor TitleJohn LATEX Course 1
Anding Course serial
8/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Animation
subject 1
subject 2
9/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Animation
subject 1
subject 2
150.
00
3.00
2.00
0.50
0.75
1.00
1.50
5.00
12.5
0
25.0
0
50.0
0
75.0
0
4161311812219141011151737208569
Relative Concentration
Pro
bese
t
SpikeIn.pm
−2 0 2Row Z−Score
060
140
Color Keyand Histogram
Cou
nt
10/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Animation
subject 1
subject 2
11/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Animation
subject 1
subject 2
1.00
1.50
2.00
0.50
0.75
3.00
12.5
0
5.00
25.0
0
50.0
0
75.0
0
150.
00
6852097153113141210216174111918
Relative Concentration
Pro
bese
t
FoldChange
−15 0 10Value
040
80
Color Keyand Histogram
Cou
nt
12/24
BeamerAdding Sweave
PauseTableSplitting ScreenAnimationLove Letter Too
Love Letter Too
If I speak in the tongues of menor of angels, but do not have love, I am
only a resounding gong or a clanging cymbal. IfI have the gift of prophecy and can fathom all mys-teries and all knowledge, and if I have a faith that canmove mountains, but do not have love, I am nothing.If I give all I possess to the poor and give over my bodyto hardship that I may boast, but do not have love, Igain nothing. Love is patient, love is kind. It doesnot envy, it does not boast, it is not proud. Itdoes not dishonor others, it is not self-seeking,it is not easily angered, it keeps no recordof wrongs. Love does not delight in evil
but rejoices with the truth. It al-ways protects, always trusts,
always hopes, alwaysperseveres.
♥
13/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Literate programming means that text, data, and computer codeare interwoven in a single self-contained document.
14/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
This is not literate programming
A research document involving multiple files with figures and tablescut and paste from various places. For instance,
a stata do-file
an excel spreadsheet with results
an excel spreadsheet with data
a directory with filenames like “old.doc” and “new.doc”
a word document with tables and figures cut and paste fromvarious places
*Changes to the stata do-file are not automatically propogated tothe excel spread-sheet or to the Word document.
15/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Why you should use literate programming
Reproducible research
Dynamic reports
R Package vignettes: R vignettes are usually developed usingSweave
16/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
This presentation
If you have beamer and tex installed, try reproducing this talk:
> Sweave("HoExample4.Rnw")
> Sys.setenv(PATH=paste(Sys.getenv("PATH"),"/usr/texbin",sep=":"))
> texi2pdf("HoExample4", quiet=F)
17/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Literate programming in R using Sweave
Essentially requires a single source document – a ’.Rnw’ file.
*.RnwSweave−−−−→ *.tex
latex−−−−→ *.dvixdvi−−−−→ view of document
see http://www.bias-project.org.uk/Rpackages_course/intro_Sweave.pdf
18/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Syntax using Beamer and Sweave
\documentclass{beamer}\usepackage{beamerthemeshadow}\usepackage{Sweave}\begin{document}\begin{frame}
Content for Slide 1\end{frame}� �=my R code chunk 1@\begin{frame}
Content for Slide 2� �=my R code chunk 2@\end{frame}
\end{document}
19/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Code chunk options
eval(TRUE, or FALSE)
Whether the R chunk is run
echo(TRUE, FALSE)
Whether the R chunk is shown in the LATEX file
results(verbatim, hide, tex)
Type of output used to show the printed results produced bythe R code.
fig(TRUE, FALSE)
Whether the output is a figure. By default, PDF files areproduced.
�figname, fig=TRUE, include=FALSE�
See the HoExample4.Rnw for examples.
20/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Extracting code chunks
To extract code chunks from a .Rnw file:
> Stangle("HoExample4.Rnw")
This command generates the file HoExample4.R containing thecode chunks used in this presentation.
21/24
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Dynamic reports
> require(geneplotter) || {
+ message("package not available. downloading from Bioconductor")
+ source("http://www.bioconductor.org/biocLite.R")
+ biocLite("geneplotter", type="source")
+ }
> x1 <- matrix(rnorm(1e4), ncol=2)
> x2 <- matrix(rnorm(1e4, mean=3, sd=1.5), ncol=2)
> x <- rbind(x1,x2)
> ##I use include=FALSE and then use latex to put the figure exactly where I want
> par(mfrow=c(2,2), las=1)
> par(mar=c(2,2,2,1))
> smoothScatter(x, nrpoints=0)
> smoothScatter(x)
> smoothScatter(x,nrpoints=Inf,colramp=colorRampPalette(RColorBrewer::brewer.pal(9, "YlOrRd")),bandwidth=1)
> colors <- densCols(x)
> plot(x, col=colors, pch=20)
22/24
Interweaving text, R code, and figures
Any changes to the preceding code will be propagated to this figure
automatically.
−4 −2 0 2 4 6 8
−2
0
2
4
6
8
x[,1]
−4 −2 0 2 4 6 8
−2
0
2
4
6
8
x[,1]
x[,2
]
−4 −2 0 2 4 6 8
−2
0
2
4
6
8
●●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
● ●
●
●
● ●
●
●
●
●●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●
● ●
●
●
●
●
●
● ●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●●●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
● ●
● ●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
● ●
●
●
●
●
● ●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●● ●
●
●
●
●
●●
● ●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●●
●●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●●
●● ●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●●
●●●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●●●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●● ●
●
●●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●●
●● ●
●
●●
●
●
●
●●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●●●
●
●●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●●
● ●●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●●
●
●
●●
●
●
●
●
●●
●
● ●
●
●
●
●● ●
●
●
●
●
● ●●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
● ●
●
●
●
●
●
●●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●
●
● ●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●●
●●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●●
●●
●
●●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●●●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
● ●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●●
●
●●●
●●
●●
●
●●●
●
●●
●
●
●
●●●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
● ●
●
●●
●●
●
● ●
●●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
● ●
●●
●
●
●
●
●● ●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
● ●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
● ●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
● ●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
● ●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●●
●
● ●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
● ●●
●●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
● ●
●
●
●● ● ●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
● ●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
● ●
●
●●●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●●
●
●
● ●●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●●
●
●●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●●
●
● ●●
●
●●
●●
●
●
●
●●
●
●
●●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ● ●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
● ●
●
●
●
●●
●●
●●
●●
●
●●
●●●●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●● ● ●
●
●
●
●
●●●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●●
●
●
●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●
●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●●●
●
● ●
●
●
●●
●
●
●●
●
●
●●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●●
●
●
●
● ●
●●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
● ●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
● ●
●
●
● ●
●●●
●
● ●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
● ●
●
●
● ●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
● ●
●
●
●
●●
●●●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●●●
●
●
●
●●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●●
●●
●
●
●
● ●
●
●
●
●●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
● ●
●●
●●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●● ●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
● ●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
● ●
●
●●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●●
●
● ●
●
● ●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●●
●
●
●
●●
●
●●
●
●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●
●
●
● ●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
● ●●
● ●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●●
●
●●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
● ●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
● ●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
● ●●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●●
●
●
●
● ●
●
●
●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
● ●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●●●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●●
●
●
● ●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
● ●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
● ●
● ●
●
●
●
● ●●
●
●
●
●●
●
●
●●
●●
●
●
●
●●
●● ●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●●
●
●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●● ●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
● ●
●
●
●●
●
●●
●
●
●
●
●
●
●●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
● ●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
●
●
●●
●
●
●●
●
●●
●●
● ●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●●
●
● ●
●
●
●●
●
●
●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●●
●
●
●
●
●
●
●
●
●
● ●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●●
●
●
● ●
●
●
●
●
●
●● ●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●
●
●●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
● ●
●
●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●
●
●●
●
●
●
●
●
●
●●
● ●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●●
●
●●
●
●●●
●
●
●
●
●
●●
●
● ●
●
●●
●●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●● ●
● ●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●●
●●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●
● ●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●● ●
●
●
●
● ●
●
●●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●● ●●
●
●
●
●
●●
●
●
●
●
●
● ●
●
●●
●
●
● ●
●●
●
●
●
●
●
●
●●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●
●
●
● ●
●
●
●
●●
● ●
●
−4 −2 0 2 4 6 8
−2
0
2
4
6
8
x[,2
]
BeamerAdding Sweave
Literate ProgrammingWhy SweaveHow Sweave worksMaking Nice Plots
Many public resources
Key words for google: reproducible research, Sweave
24/24
