%**************************************************************************
%
% # $Id: Venn.Rnw 80 2013-07-24 22:13:34Z js229 $
%\VignetteIndexEntry{Read this first: package overview}

<<defmakeme,echo=FALSE,eval=FALSE>>=
makeme <- function() {
	setwd("C:/Users/dad/Documents/vennerable/pkg/Vennerable/inst/doc")
	#library(weaver);	Sweave(driver="weaver","Venn.Rnw",stylepath=FALSE,use.cache=FALSE)
	Sweave("Venn.Rnw",stylepath=FALSE)
}
makeme()
@

% $Revision: 1.26 $
% $Author: js229 $
% $Date: 2013-07-24 23:13:34 +0100 (Wed, 24 Jul 2013) $
% $Log: Venn.Rnw,v $

\documentclass[a4paper]{article}


\title{
Venn diagrams in R\\with the \texttt{Vennerable} package
}
\author{Jonathan Swinton\\\texttt{jonathan@swintons.net}}

\usepackage{Sweave}
\SweaveOpts{prefix.string=Venn,debug=TRUE,eps=FALSE,echo=FALSE,pdf.version=1.4}
\usepackage{float}
\usepackage{natbib}
\usepackage{mathptmx}
\usepackage{rotating} 
\usepackage[nodayofweek]{datetime}\longdate
\usepackage{hyperref}
\begin{document}


\maketitle
<<loadstuff>>=
library(grid)
#library(Vennerable)
@
<<doremove,echo=FALSE>>=
if ("package:Vennerable" %in% search())detach("package:Vennerable")
remove(list=setdiff(ls(),"makeme"));library(Vennerable)
@

<<defmakevp>>=
options(width=80)
@
\begin{center}
<<front,fig=TRUE,cache=TRUE>>=
V4 <- Venn(n=4)
#plotVenn(V4,type="ellipses",doWeights=FALSE,
#	show=list(Universe=FALSE,FaceText="",SetLabels=FALSE,Faces=FALSE))
plot(V4,type="ellipses",doWeights=FALSE,
	show=list(Universe=FALSE,FaceText="",SetLabels=FALSE,Faces=FALSE))
@
\end{center}
\newpage
\tableofcontents
\newpage
\section{Overview}
The Vennerable package provides routines to compute and plot
Venn diagrams, including the classic two- and three-circle diagrams
but also a variety of others with different properties and
for up to seven sets. In addition it can plot diagrams in which the
area of each region is proportional to the corresponding number of set items or 
other weights. This includes Euler diagrams, which can be thought of as Venn diagrams where 
regions corresponding to empty intersections have been removed.


Figure \ref{fig:canonical} shows a three-circle Venn diagram of the sort
commonly found. To draw it, we use as an example the \texttt{StemCell} data
of Boyer et al.\cite{boyer2005} which lists the gene names associated with each of four transcription factors
<<loadsetm,echo=TRUE>>=
library(Vennerable)
data(StemCell)
str(StemCell)
@
First we construct an object of class \texttt{Venn}:
<<loadstem,echo=TRUE>>=
Vstem <- Venn(StemCell)
Vstem
@
Although Vennerable can cope with 4-set Venn diagrams, for now we reduce to a three-set object
<<to3,echo=TRUE>>=
Vstem3 <- Vstem[,c("OCT4","SOX2","NANOG")]
Vstem3
@
Note how the weights were appropriately updated.

@
Now a call to {\texttt plot} produces the diagram in Figure~\ref{fig:canonical} showing how many genes are common to each transcription factor.
\begin{figure}[H]\begin{center}
<<pVmonth3,echo=TRUE,fig=TRUE>>=
plot(Vstem3,doWeights=FALSE)
@
\caption{A three-circle Venn diagram} 
\label{fig:canonical}
\end{center}\end{figure}

Quite commonly, we may have sets whose intersections we only know by the number of elements. These
can be created as \texttt{Venn} objects by supplying a named
 vector of \texttt{Weight}s:
<<echo=TRUE>>=
Vdemo2 <- Venn(SetNames=c("foo","bar"),Weight= c("01"=7,"11"=8,"10"=12))
@
Whichever way the \texttt{Venn} object is created, we can plot Venn diagrams in which the area of each intersection is proportional to those weights as in Figure~\ref{fig:w2}.
\begin{figure}[H]\begin{center}
<<pVS23,echo=TRUE,fig=TRUE>>=
plot(Vdemo2,doWeights=TRUE,type="circles")
@
\caption{A two-set weighted Venn diagram} 
\label{fig:w2}
\end{center}\end{figure}
  

For these basic plots, use of the \texttt{Vennerable} package may sometimes be
overkill, but in more complex situations it has useful abilities.
First it allows the use of a variety of other shapes for
the set boundaries, and up to nine different sets.
Secondly it implements a number of published or novel
algorithms for generating diagrams in which the area
of each region is proportional to, for example, the number
of corresponding set elements. Finally it adds a number of
graphical control abilities, including the ability to colour individual
regions separately.
\section{Computation and Annotation}
\subsection{Computing Venn drawings}
The calls to \texttt{plot} are really convenience wrappers for two separate functions; the 
first computes the geometry of the drawing, returning an object of class \texttt{VennDrawing},
and the second renders that object.
For example
<<pnosho,echo=TRUE,eval=TRUE>>=
plot(Vstem3,doWeights=TRUE)
@
is equivalent to
\begin{figure}[H]\begin{center}
<<pwVmonth3,echo=TRUE,fig=TRUE>>=
C3 <- compute.Venn(Vstem3,doWeights=TRUE)
grid::grid.newpage()
plot(C3)
@
\caption{A weighted three-circle Venn diagram} 
\label{fig:canonicalw}
\end{center}\end{figure}
@
Note the use of a function from the \texttt{grid} graphics library package: 
all of the renderings are created using \texttt{grid} objects.
The \texttt{compute.Venn} function can take a variety of arguments such 
as \texttt{doWeights} controlling the geometry and topology of the drawing, while the \texttt{plot} method
has a number of arguments controlling annotation and display.
\subsection{Annotation parameters}
The text displayed in each face is controlled by the \texttt{FaceText} element of
the \texttt{show} parameter list to \texttt{plot}. 
Other elements of the parameter control whether, for example, set names are displayed or faces are individually coloured

\begin{figure}[H]\begin{center}
<<pwabVmonth3sig,echo=TRUE,fig=TRUE>>=
grid::grid.newpage()
plot(C3,show=list(FaceText="signature",SetLabels=FALSE,Faces=FALSE,DarkMatter=FALSE))
@
\caption{The same Venn diagram with different \texttt{show} parameters} 
\label{fig:canonicals}
\end{center}\end{figure}

\subsection{Graphical parameters}
The package makes its own decisions about how to colour lines and faces depending on the 
complexity of the diagram. This can be overridden with the \texttt{gpList} argument
to \texttt{plot}. The default choices are equivalent to 
<<eval=FALSE,echo=TRUE>>=
gpList <- VennThemes(C3)
plot(C3,gpList=gpList)
@
Low-level modifications can be using the \texttt{gpList} argument, typically by modifying the value of a call to \texttt{VennThemes}.
There is more detail on the \texttt{VennThemes} man page about the format of \texttt{gpList}.
More high-level modifications can be made by supplying the \texttt{ColourAlgorithm} or \texttt{increasingLineWidth} arguments to \texttt{VennThemes}.

\begin{figure}[H]\begin{center}
<<pwabVmonth3,echo=TRUE,fig=TRUE>>=
grid::grid.newpage()
gp <- VennThemes(C3,colourAlgorithm="binary")
plot(C3,gpList=gp,show=list(FaceText="sets",SetLabels=FALSE,Faces=TRUE))
@
\caption{The effect of setting \texttt{ColourAlgorithm="binary"} and \texttt{FaceText="sets"}} 
\label{fig:canonicalb}
\end{center}\end{figure}

The position and format of the set and face annotation are controlled by the data returned by \texttt{VennGetSetLabels} and \texttt{VennGetFaceLabels},
respectively, which can be modified and then reembedded in the \texttt{VennDrawing} object with \texttt{VennSetSetLabels} and \texttt{VennSetFaceLabels}.


\begin{figure}[H]\begin{center}
<<pwabVmonth3x2,echo=TRUE,fig=TRUE>>=
grid::grid.newpage()
SetLabels <- VennGetSetLabels(C3)
SetLabels[SetLabels$Label=="SOX2","y"] <- SetLabels[SetLabels$Label=="NANOG","y"]
C3 <- VennSetSetLabels(C3,SetLabels)
plot(C3)
@
\caption{Modifying the position of annotation} 
\label{fig:canonicald}
\end{center}\end{figure}

\newpage
\section{Unweighted Venn diagrams}

For another running example, we use sets named after months,
whose elements are the letters of their names.
<<mvn1,echo=TRUE>>=
setList <- strsplit(month.name,split="")
names(setList) <- month.name
Vmonth3 <- VennFromSets( setList[1:3])
Vmonth2 <- Vmonth3[,c("January","February"),]
@



\subsection{Unweighted 2-set Venn diagrams}


For two sets, a diagram can be drawn using either circles or squares, as controlled
by the \texttt{type} argument. This is shown in Figure~\ref{fig:Vmonth2cs}.\footnote{Here and in the rest of this vignette, much of the code to plot the Figures, which is mainly devoted to
layout,  is not shown. However all the cose used can be seen in  
\texttt{edit(vignette("Venn"),editor="internal")}.}


<<c19,echo=FALSE>>=
showe <- list(FaceText="elements",Faces=TRUE,DarkMatter=FALSE)

doAnnotatedVP <- function(TD,annotation,show) {
	anlay <- grid.layout(2,1,heights=unit(c(1,1),c("null","lines")))
	grid::pushViewport(viewport(layout=anlay))
	grid::pushViewport(viewport(layout.pos.row=2))
	grid.text(label=annotation)
	popViewport()
	grid::pushViewport(viewport(layout.pos.row=1))
	gp <- VennThemes(TD)
	gp <- lapply(gp,function(x){lapply(x,function(z){z$fontsize <- 10;z})})
	plot(TD,show=show,gpList=gp)
	popViewport()
	popViewport()
	}
doavp <- function(V,doWeights,doEuler,type) {
	TD <- compute.Venn(V,doWeights=doWeights,doEuler=doEuler,type=type)
	Vname <- deparse(substitute(V))
#	if (missing(doWeights)) dow <- "" else dow <- sprintf(",doWeights=%s",doWeights)
#	if (missing(doEuler)) dow <- "" else doe <- sprintf(",doEuler=%s",doEuler)
	txt <- sprintf("plot(%s,type=%s,...)",Vname,type)
	doAnnotatedVP(TD,annotation=txt,show=showe)
}
@
 
<<pVmonth2uw,echo=FALSE>>=
dopv2uw <- function(V) {
	grid::grid.newpage()
	grid::pushViewport(viewport(layout=grid.layout(1,2)))
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
	doavp(V,type="circles",doWeights=FALSE,doEuler=FALSE)
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
	doavp(V,"squares",doWeights=FALSE,doEuler=FALSE)
	popViewport()
}
@
\begin{figure}[H]\begin{center}

<<pv2uwwww,fig=TRUE,eval=TRUE>>=
dopv2uw(Vmonth2)
@
\caption{Unweighted 2-set Venn diagrams with \texttt{type=circles} or \texttt{type=squares}}
\label{fig:Vmonth2cs}
\end{center}\end{figure}

\newpage
\subsection{Unweighted 3-set Venn diagrams}
For three sets, the \texttt{type} argument
can be \texttt{circles}, \texttt{squares}, 
\texttt{ChowRuskey}, \texttt{triangles} or \texttt{AWFE}. We have already seen the circles plot.
The AWFE plot is an implementation of the elegant
ideas of  \cite{edwards:2004}. 
The Chow-Ruskey plot is from \cite{chowruskey:2005}, and is a redrawing of the AWFE plot in such a way that there is an algorithm which will
allow all of the faces to be adjusted in area without disrupting the topology of the diagram. 
The triangles plot is fairly obvious, for example to reference\cite{chow:2007}, but I have not seen it implemented elsewhere.

This example of the squares plot is not \emph{simple}, in the sense of \cite{ruskeyweston:2005}, because the set boundaries don't cross transversally.
Topologically, there is only one simple Venn diagram of order 3 (in a way that \cite{ruskeyweston:2005} makes precise).


\begin{figure}[H]\begin{center}
<<pV3uw,echo=FALSE>>=
plotV3uw <- function(V) {
	grid::grid.newpage()
	grid::pushViewport(viewport(layout=grid.layout(2,2)))
	anlay <- grid.layout(2,1,heights=unit(c(1,1),c("null","lines")))
	
	
	doavp <- function(type) {
		C2 <- compute.Venn(V,doWeights=FALSE,doEuler=FALSE,type=type)		
		grid::pushViewport(viewport(layout=anlay))
		txt <- sprintf("plot(Vmonth3,type=%s,...)",dQuote(type))
		grid::pushViewport(viewport(layout.pos.row=2))
		grid.text(label=txt)
		popViewport()
		grid::pushViewport(viewport(layout.pos.row=1))

		plot(C2,show=list(
			Sets=TRUE,FaceText="weight",
			SetLabels=FALSE,DarkMatter=FALSE,Faces=TRUE))
		popViewport()
		popViewport()
	}
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
	doavp("ChowRuskey")
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
	doavp("squares")
	popViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=1))
	doavp("triangles")
	popViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=2))
	doavp("AWFE")
	popViewport()
}
@
<<pv3uwww,fig=TRUE,eval=FALSE>>=
plotV3uw(Vmonth3)
@
\end{center}\end{figure}
\newpage
\subsection{Unweighted 4-set Venn diagrams}
For four sets, the \texttt{type} argument
can be  \texttt{ChowRuskey}, \texttt{AWFE},\texttt{squares} or \texttt{ellipses}.

The squares plot is said by Edwards \cite{edwards:2004} to have
been introduced by Lewis Carroll \cite{carroll:1896}.
The ellipse plot was suggested by Venn \cite{venn:1880}.

Note how the package makes an attempt to identify a point within each face where the annotation can be plotted,
but doesn't make a very good choice for very non-concave or elongated faces.

<<makeCrd1c,echo=FALSE>>=
V4 <-  Venn(n=4)
@

\begin{figure}[H]\begin{center}
<<pV4uw,fig=TRUE,cache=TRUE,eval=TRUE>>=
plotV4uw <- function(V) {
	grid::grid.newpage()
	grid::pushViewport(viewport(layout=grid.layout(2,2)))
	doavp <- function(type) {
		C2 <- compute.Venn(V,doWeights=FALSE,doEuler=FALSE,type=type)		
		plot(C2,show=list(
			Sets=TRUE,
			FaceText="signature",
			SetLabels=FALSE,DarkMatter=FALSE,Faces=TRUE))
	}
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
	doavp("ChowRuskey")
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
	doavp("squares")
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=1))
	doavp("ellipses")
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=2))
	doavp("AWFE")
	upViewport()
}
plotV4uw(V4)
@
\caption{Venn diagrams on four sets drawn with the \texttt{type} argument set to \texttt{ChowRuskey},
 \texttt{squares}, \texttt{ellipses}, and  \texttt{AWFE}.
}
\end{center}\end{figure}

A number of variants on the \texttt{squares} type are implemented. Currently they can only be accessed
by passing the parameters \texttt{s} or \texttt{likesquares} to the low level creation function \texttt{compute.S4} directly,
which is what is done in Figure~\ref{fig:4sq4}.


<<S4figdef,echo=FALSE>>=
dosans <- function(V4,s,likeSquares,showe) {
	S4  <- compute.S4(V4,s=s,likeSquares=likeSquares)
	gp <- VennThemes(S4,increasingLineWidth=TRUE)
	anlay <- grid.layout(2,1,heights=unit(c(1,1),c("null","lines")))
	grid::pushViewport(viewport(layout=anlay))
	txt <- sprintf("compute.S4(V4,s=%f,likeSquares=%f)",s,likeSquares)
	grid::pushViewport(viewport(layout.pos.row=2))
	popViewport()
	grid::pushViewport(viewport(layout.pos.row=1))
	plot(S4,gpList=gp,show=showe)
	popViewport()
	popViewport()
}

@
For more details on this see the help pages for \texttt{compute.S4}.

\begin{figure}[H]\begin{center}
<<S4fig,fig=TRUE,eval=TRUE>>=
shows4 <- list(SetLabels=FALSE,Faces=TRUE,FaceText="signature",DarkMatter=FALSE)
grid::grid.newpage()
grid::pushViewport( viewport(layout=grid.layout(2,2)))
grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
dosans(V4,s=0.2,likeSquares=FALSE,shows4 )
upViewport()
grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
dosans(V4,s=0,likeSquares=FALSE,shows4 )
upViewport()
grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=1))
dosans(V4,s=0.2,likeSquares=TRUE,shows4 )
upViewport()
grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=2))
dosans(V4,s=0,likeSquares=TRUE,shows4 )
upViewport()

@
\caption{Four variants on the four-squares}
\label{fig:4sq4}
\end{center}\end{figure}


\clearpage
\subsection{Unweighted Venn diagrams on more than four sets}

The package implements a variant of the Edwards construction\cite{edwards:2004}, which can in principle 
generate Venn diagrams on an arbitrary number of sets $n$. The currently implemented algorithm only 
computes up to 8 sets for the classic construction. 

\begin{figure}[H]\begin{center}
<<S47fig,fig=TRUE,cache=TRUE,eval=TRUE>>=
doans <- function(n) {
	S4  <- compute.AWFE(Venn(n=n),type="AWFE")
	if (n==1) { # borrow the universe from the larger picture
		S5 <- compute.AWFE(Venn(n=2),type="AWFE")
		S4 <- VennSetUniverseRange(S4,VennGetUniverseRange(S5))
	}
	gp <- VennThemes(drawing=S4,colourAlgorithm="binary")
	plot(S4,gpList=gp,show=list(FaceText="",Faces=TRUE,SetLabels=FALSE,Sets=FALSE))
}
grid::grid.newpage()
grid::pushViewport( viewport(layout=grid.layout(3,2)))
grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
doans(1)
upViewport()
grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
doans(2)
upViewport()
grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=1))
doans(3)
upViewport()
grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=2))
doans(4)
upViewport()
grid::pushViewport(viewport(layout.pos.row=3,layout.pos.col=1))
doans(5)
upViewport()
grid::pushViewport(viewport(layout.pos.row=3,layout.pos.col=2))
doans(6)
upViewport()
if (FALSE) {
grid::pushViewport(viewport(layout.pos.row=4,layout.pos.col=1))
doans(7)
upViewport()
grid::pushViewport(viewport(layout.pos.row=4,layout.pos.col=2))
doans(8)
upViewport()
}
@
\caption{Edwards constructions for five to eight sets}
\end{center}\end{figure}


A variant on the Edwards construction I developed as both quicker to compute with, because it is based on straight lines,
and slightly easier to visualise high-order intersections in, is shown in Figure \ref{fig:battle}.
It can be drawn by using \texttt{type="battle"} for up to 9 sets. 


\begin{figure}[H]\begin{center}
<<S47battle,fig=TRUE,echo=TRUE,eval=TRUE>>=
plot(Venn(n=9),type="battle",show=list(SetLabels=FALSE,FaceText=""))
@
\caption{The battlement variant of the Edwards construction on 9 sets with the \texttt{type=battle} argument}
\label{fig:battle}
\end{center}\end{figure}









\newpage
%########################################################
\section{Weighted Venn diagrams}
There are repeated requests to generate Venn diagrams in which the areas of the faces
themselves are meant to carry information, mainly by being proportional to the intersection weights.
Even when these diagrams can be drawn, 
they are not often a success in their information-bearing mission. But we can try anyway, through use
of the argument \texttt{doWeights=TRUE}. First of all we consider the case when all the visible intersection weights are nonzero. 


\subsection{Weighted 2-set Venn diagrams for 2 Sets}
\subsubsection{Circles}
It is always possible to get an exactly area-weighted solution for two circles 
as shown in Figure \ref{fig:pv2b2}.

\begin{figure}[H]
  \begin{center}
<<pv2b2,fig=TRUE,echo=TRUE>>=
V3.big <- Venn(SetNames=LETTERS[1:3],Weight=2^(1:8))
Vmonth2.big <- V3.big[,c(1:2)]
plot(Vmonth2.big)
@
\caption{Weighted 2d Venn}
\label{fig:pv2b2}
\end{center}\end{figure}


\subsubsection{Squares}
As for circles, square weight-proportional diagrams 
can be simply constructed.
\begin{figure}[H]
  \begin{center}
<<sqpv2b,fig=TRUE,echo=TRUE>>=
plot(Vmonth2.big,type="squares")
@
\caption{Weighted 2d Venn squares}
\end{center}\end{figure}

\newpage
\subsection{Weighted 3-set Venn diagrams}


\subsubsection{Circles}
There is no general way of creating area-proportional
3-circle diagrams. While these attempts at these diagrams are quite commonly seen, they must almost always be inexact.

The \texttt{Vennerable} package makes an attempt
at produce approximate ones. Figure~\ref{fig:combo}
shows a dataset taken from Chow and Ruskey \cite{chowruskey:2003}
\begin{figure}[H]
  \begin{center}
<<ccomboutransp,fig=TRUE,echo=TRUE>>= 
Vcombo <- Venn(SetNames=c("Female","Visible Minority","CS Major"),
	Weight= c(0,4148,409,604,543,67,183,146))
plot(Vcombo)
@
  \caption{ 3D Venn diagram }
\label{fig:combo}
  \end{center}
\end{figure}
The algorithm used is to compute the individual circles to have the exact area necessary
for proportionality, and then compute each of the three pairwise distances
between centres necessary for the correct pairwise areas. If these distances do not satisfy the triangle inequality
the largest is reduced until they do. Then the circles are arranged with their centres
separated by these (possibly modified) distances.


\newpage

\subsubsection{Squares}
There is are a number of possible algorithms to generate exact Venn diagrams based on polygons. 
With \texttt{type=squares} the package uses an algorithm almost identical to that suggested by \citet{chowruskey:2003},
which tries to generate rectangles as the set boundaries if possible

\begin{figure}[H]\begin{center}
<<S3ccpdemo1,fig=TRUE>>=
plot(Vstem3,type="squares")
@
\caption{Weighted 3-set Venn diagram based on the algorithm of \cite{chowruskey:2003}}
\end{center}\end{figure}

\begin{figure}[H]\begin{center}
<<S3ccpdemo2,fig=TRUE,echo=TRUE>>=
V3a <- Venn(SetNames=month.name[1:3],Weight=1:8)
plot(V3a,type="squares",show=list(FaceText="weight",SetLabels=FALSE))
@
\caption{Weighted 3-set Venn diagram based on the algorithm of \cite{chowruskey:2003}. This time the algorithm fails to find rectangles.}
\end{center}\end{figure}


\newpage

\subsubsection{Triangles}
The triangular Venn diagram on 3-sets lends itself nicely to
an area-proportional drawing under some contraints on the weights (detailed elsewhere).


\begin{figure}[H]\begin{center}
<<plotT3,echo=TRUE,fig=TRUE>>=
grid::grid.newpage()
C3t <- compute.Venn(V3a,type="triangles")
plot(C3t,show=list(SetLabels=FALSE,DarkMatter=FALSE))
@
\caption{Weighted Triangular Venn diagram}
\end{center}
\end{figure}

\newpage

\subsection{Chow-Ruskey diagrams for 3 or more sets}
The general Chow-Ruskey algorithm  \cite{chowruskey:2005} for area-proportional faces can be implemented
in principle for an arbitrary number of sets provided
the weight of the common intersection is nonzero. In practice the package is limited (to $n=9$) by the size of the largest AWFE diagram it can compute.


\begin{figure}[H]\begin{center}
<<plotCR3,echo=TRUE,fig=TRUE>>=
plot(V3a,type="ChowRuskey",show=list(SetLabels=FALSE,DarkMatter=FALSE))
@
\caption{Chow-Ruskey weighted 3-set diagram}
\end{center}
\end{figure}

\begin{figure}[H]\begin{center}
<<>>=
@
<<plotCR4,echo=TRUE,fig=TRUE,cache=TRUE>>=
V4a <- Venn(SetNames=LETTERS[1:4],Weight=16:1)
plot(V4a,type="ChowRuskey",show=list(SetLabels=FALSE,DarkMatter=FALSE))
@
\caption{Chow-Ruskey weighted 4-set diagram}
\end{center}
\end{figure}


\begin{figure}[H]\begin{center}
<<plotCR4stem,echo=FALSE,fig=TRUE,cache=TRUE>>=
Tstem <- compute.Venn(Vstem,type="ChowRuskey")
gp <- VennThemes(Tstem,colourAlgorithm="sequential",increasingLineWidth=TRUE)
plot(Tstem,show=list(SetLabels=TRUE),gp=gp)
@
\caption{Chow-Ruskey weighted 4-set diagram for the stem cell data}
\end{center}
\end{figure}


\newpage
%########################################################
\section{Euler diagrams}

A  \emph{Euler diagram} is one in which regions of zero-weight are not displayed at all (but those which are displayed are not necessarily area-proportional).
This can be achieved, for some geometries, by use of the \texttt{doEuler=TRUE} argument.

As we have seen, for some geometries it is not possible
to enforce exact area-proportionality when requested by the \texttt{doWeight=TRUE} argument,
and an attempt is made to produce an approximately area-proportional diagram. In
particular, regions whose weight is zero may appear with nonzero areas.
These two flags can interact in weird and uncomfortable ways depending on
exactly which intersection weights are zero.

\subsection{2-set Euler diagrams}

\subsubsection{Circles}
<<p2three,echo=FALSE>>=
p2four <- function(V,type="circles",doFaces=TRUE) {
	grid::grid.newpage()
	anlay <- grid.layout(2,1,heights=unit(c(1,1),c("null","lines")))
	
	doavp <- function(doWeights,doEuler,type) {
		C2 <- compute.Venn(V,doWeights=doWeights,doEuler=doEuler,type=type)
		grid::pushViewport(viewport(layout=anlay))
		grid::pushViewport(viewport(layout.pos.row=2))
		txt <- paste(if(doWeights){"Weighted"}else{"Unweighted"},
				 if (doEuler){"Euler"}else{"Venn"})
		grid.text(label=txt)
		popViewport()
		grid::pushViewport(viewport(layout.pos.row=1))
	plot(C2,show=list(
			Sets=!doFaces,
			SetLabels=FALSE,DarkMatter=FALSE,Faces=doFaces))
			
			popViewport()
		popViewport()
	}

	grid::pushViewport(viewport(layout=grid.layout(2,2)))
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
	doavp(FALSE,FALSE,type)
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
	doavp(TRUE,FALSE,type)
	popViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=1))
	doavp(FALSE,TRUE,type)
	popViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=2))
	doavp(TRUE,TRUE,type)
	popViewport()

}
p2two <- function(V,type="circles",doFaces=TRUE,doEuler=FALSE,gp,show) {
	grid::grid.newpage()
	anlay <- grid.layout(2,1,heights=unit(c(1,1),c("null","lines")))
	
	doavp <- function(doWeights,doEuler,type,gp,show) {
		C2 <- compute.Venn(V,doWeights=doWeights,doEuler=doEuler,type=type)
		if (missing(gp)) gp <- VennThemes(C2)
		grid::pushViewport(viewport(layout=anlay))
		grid::pushViewport(viewport(layout.pos.row=2))
		txt <- paste(if(doWeights){"Weighted"}else{"Unweighted"},
				 if (doEuler){"Euler"}else{"Venn"})
		grid.text(label=txt)
		popViewport()
		grid::pushViewport(viewport(layout.pos.row=1))
		if (missing(show)) show <- list(Sets=TRUE,SetLabels=FALSE,DarkMatter=FALSE,Faces=doFaces)
		plot(C2,gp=gp,show=show)		
		popViewport()
		popViewport()
	}

	grid::pushViewport(viewport(layout=grid.layout(1,2)))
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
	doavp(doWeights=FALSE,doEuler=doEuler,type,gp=gp)
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
	doavp(doWeights=TRUE,doEuler=doEuler,type,gp=gp)
	popViewport()
}

@

<<setv2,echo=FALSE>>=
Vmonth2.no01 <- Vmonth2
Weights(Vmonth2.no01)["01"] <- 0
Vmonth2.no10 <- Vmonth2
Weights(Vmonth2.no10)["10"] <- 0

Vmonth2.no11 <- Vmonth2
Weights(Vmonth2.no11)["11"] <- 0

@

\begin{figure}[H]\begin{center}
<<p2threef01,fig=TRUE,eval=TRUE>>=
p2four (Vmonth2.no01,doFaces=TRUE)
@
\caption{Effect of the \texttt{doEuler} and \texttt{doWeights} flags for a \texttt{Venn} object with \texttt{Weights(V)["01"]=0}}
\end{center}\end{figure}


\begin{figure}[H]\begin{center}
<<p2no11threef,fig=TRUE,eval=TRUE>>=
p2four (Vmonth2.no11,doFaces=TRUE)
@
\caption{As before for when the intersection set has zero weight}
\end{center}\end{figure}

\subsubsection{Squares}
As for circles, the idea of a weighted Venn diagram when some of the weights
are zero doesn't make much sense in theory but might be useful for making visual 
points. 
\begin{figure}[H]\begin{center}
<<p2s01threef,fig=TRUE,eval=TRUE>>=
p2four (Vmonth2.no01,type="squares")
@
\end{center}\end{figure}


\begin{figure}[H]\begin{center}
<<p2sthreef,fig=TRUE,eval=TRUE>>=
p2four (Vmonth2.no11,type="squares")
@
\end{center}\end{figure}

\newpage
\subsection{3-set Euler diagrams}


\subsubsection{Circles}
There is currently no effect of setting \texttt{doEuler=TRUE} for three circles,
but the \texttt{doWeights=TRUE} flag does an approximate job. There are about
 40 distinct ways in which intersection regions can have zeroes can occur, but here are some examples.


<<otherV,echo=FALSE>>=


Vempty <- VennFromSets( setList[c(4,5,7)])
Vempty2 <- VennFromSets( setList[c(4,5,11)])
Vempty3 <- VennFromSets( setList[c(4,5,6)])
Vempty4 <- VennFromSets( setList[c(9,5,6)])

@


\begin{figure}[H]\begin{center}
<<pv3wempty,fig=TRUE>>=
showe <- list(FaceText="elements",Faces=FALSE,DarkMatter=FALSE,Universe=FALSE)
grid::grid.newpage()
	grid::pushViewport(viewport(layout=grid.layout(2,2)))
	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=1))
	plot(Vempty,add=TRUE,show=showe)
	upViewport()
	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=1))
	plot(Vempty2,add=TRUE,show=showe)
	upViewport()

	grid::pushViewport(viewport(layout.pos.row=1,layout.pos.col=2))
	plot(Vempty3,add=TRUE,show=showe)
	upViewport()

	grid::pushViewport(viewport(layout.pos.row=2,layout.pos.col=2))
	plot(Vempty4,add=TRUE,show=showe)


@
\caption{Weighted 3d Venn  empty intersections.}
\end{center}\end{figure}

\begin{figure}[H]
  \begin{center}
<<pv3winn,fig=TRUE,cache=TRUE>>=
plot(Vmonth3,doWeights=TRUE,show=showe)
@
\caption{Approximate weighted 3d Venn showing element set membership}
\end{center}\end{figure}


\clearpage
\subsubsection{Triangles}


The \texttt{doEuler} flag has no effect for triangles; all
the weighted diagrams produced are Euler diagrams.
\begin{figure}[H]\begin{center}
<<pv3wempty1t,fig=TRUE,eval=TRUE>>=
	p2two (Vempty,type="triangles",doEuler=TRUE)
@
\caption{3d Venn triangular with two zero weights plotted with the \texttt{doWeights} flag FALSE and TRUE}
\end{center}\end{figure}

\begin{figure}[H]\begin{center}
<<pv3wempty2t,fig=TRUE,eval=TRUE>>=
	p2two (Vempty2,type="triangles",doEuler=TRUE)
@
\caption{3d Venn triangular with three zero weights plotted with the \texttt{doWeights} flag FALSE and TRUE}
\end{center}\end{figure}

\newpage
\subsection{4-set Euler diagrams}
\subsubsection{Chow-Ruskey diagrams}


The \texttt{doEuler} flag has no effect for Chow-Ruskey because all
the weighted diagrams produced are already Euler diagrams.

\begin{figure}[H]\begin{center}
<<CR4fig,fig=TRUE>>=
V4z <-  VennFromSets( setList[1:4])
CK4z <- compute.Venn(V4z,type="ChowRuskey")
grid::grid.newpage()
gp <- VennThemes(CK4z,increasingLineWidth=TRUE)
plot(CK4z,show=list(SetLabels=FALSE,FaceText="elements",Faces=TRUE),gpList=gp)
@
\caption{Chow-Ruskey diagram with some zero weights}
\end{center}\end{figure}

\newpage
\section{Some loose definitions}
Figure \ref{fig:canonical} illustrates membership of three sets,
in order OCT4, SOX2 , NANOG. 
Genes which are members of the SOX2 set but not the OCT4 or NANOG sets
are members of an \emph{intersection subset} with \emph{indicator string} or \emph{signature}
\texttt{010}.

Given $n$ subsets of a universe,
 there are $2^n$ {intersection subsets}. Each of these is 
a subset of the universe and there
is one corresponding to each of the binary strings of length $n$.
If one of these indicator strings has a 1 in the $i$-th position, all of members of the 
corresponding intersection subset must be members of the $i$-th subset. Depending on the application, the 
universe of elements from which members of the sets are drawn 
may be important. 
Elements in intersection set \texttt{00\ldots}, which are in 
the universe but not in any known set, are called (by me) \emph{dark matter},
and we tend to display these differently.

A diagram which produces a visualisation of each of the sets
as a connected curve in the plane whose regions of intersection
are connected and correspond to each of the $2^n$ intersection subsets
is an \emph{unweighted Venn diagram}.
Weights can be assigned to each of the intersections,
most naturally being proportional to the number of elements each one contains.
\emph{Weighted Venn diagrams} have the same topology as unweighted ones, but 
(attempt to) make the area of each region proportional to the weights. 
This may not be possible, if any of the weights are zero for example, or because 
of the geometric constraints of the diagram. Venn diagrams based on 3 circles
are unable in general to represent even nonzero weights exactly, and cannot be constructed
at all for $n>3$.

Diagrams in which only those intersections with non-zero weight appear are \emph{Euler diagrams},
and diagrams which go further and make the area of every intersection proportional to its weight are weighted Euler diagrams.
For more details and rather more rigour see first the online review of Ruskey and Weston~\cite{ruskeyweston:2005} and then the references it contains.

\newpage


\section{This document}

\begin{tabular}{|l|l|}
\hline
Author & Jonathan Swinton
\\
Generated on & \today
\\
R version & 
<<echo=FALSE,results=tex>>=
cat(R.version.string)
@
\\
\hline
\end{tabular}

\bibliographystyle{plain}

<<echo=FALSE,results=tex,eval=TRUE>>= 
# tilde from shortened windows pathname really upsets latex....
#bib <- system.file( "doc", "Venn.bib", package = "Vennerable" )
#bib <- gsub("~","\\~",bib,fixed=TRUE)
bib <- "Venn"
cat( "\\bibliography{",bib,"}\n",sep='')
@
%\bibliography{Venn}

\end{document}