[Robast-commits] r26 - pkg/RandVar/inst/doc
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Feb 18 06:08:59 CET 2008
Author: stamats
Date: 2008-02-18 06:08:59 +0100 (Mon, 18 Feb 2008)
New Revision: 26
Modified:
pkg/RandVar/inst/doc/RandVar.aux
pkg/RandVar/inst/doc/RandVar.brf
pkg/RandVar/inst/doc/RandVar.log
pkg/RandVar/inst/doc/RandVar.out
pkg/RandVar/inst/doc/RandVar.pdf
pkg/RandVar/inst/doc/RandVar.tex
pkg/RandVar/inst/doc/RandVar.toc
Log:
checks and installs without any errors on R version 2.6.2 Patched (2008-02-10 r44423)
Modified: pkg/RandVar/inst/doc/RandVar.aux
===================================================================
--- pkg/RandVar/inst/doc/RandVar.aux 2008-02-16 03:32:41 UTC (rev 25)
+++ pkg/RandVar/inst/doc/RandVar.aux 2008-02-18 05:08:59 UTC (rev 26)
@@ -1,42 +1,42 @@
-\relax
-\ifx\hyper at anchor\@undefined
-\global \let \oldcontentsline\contentsline
-\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
-\global \let \oldnewlabel\newlabel
-\gdef \newlabel#1#2{\newlabelxx{#1}#2}
-\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
-\AtEndDocument{\let \contentsline\oldcontentsline
-\let \newlabel\oldnewlabel}
-\else
-\global \let \hyper at last\relax
-\fi
-
-\citation{MK:05}
-\@writefile{brf}{\backcite{MK:05}{{1}{(document)}{Doc-Start}}}
-\citation{distr}
-\@writefile{toc}{\contentsline {section}{\numberline {1}{\tt S4} Classes}{2}{section.1}}
-\@writefile{brf}{\backcite{distr}{{2}{1}{section.1}}}
-\citation{distr}
-\citation{Cham:98}
-\citation{Gent:03}
-\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Class {\tt RandVariable} and Subclasses}}{3}{figure.1}}
-\newlabel{ap.Rpack.RandVar.dia1}{{1}{3}{Class {\tt RandVariable} and Subclasses\relax }{figure.1}{}}
-\@writefile{toc}{\contentsline {section}{\numberline {2}Functions and Methods}{3}{section.2}}
-\@writefile{brf}{\backcite{distr}{{3}{2}{section.2}}}
-\@writefile{brf}{\backcite{Cham:98}{{3}{2}{section.2}}}
-\@writefile{brf}{\backcite{Gent:03}{{3}{2}{section.2}}}
-\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Generating Functions of Package {\tt RandVar}}}{4}{table.1}}
-\newlabel{ap.Rpack.RandVar.tab.gen}{{1}{4}{Generating Functions of Package {\tt RandVar}\relax }{table.1}{}}
-\citation{distr}
-\@writefile{brf}{\backcite{distr}{{8}{2}{table.1}}}
-\citation{distr}
-\citation{MK:05}
-\bibcite{Cham:98}{1}
-\@writefile{brf}{\backcite{distr}{{9}{2}{table.1}}}
-\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces New Generic Functions of Package {\tt RandVar}}}{9}{table.2}}
-\newlabel{ap.Rpack.RandVar.tab}{{2}{9}{New Generic Functions of Package {\tt RandVar}\relax }{table.2}{}}
-\@writefile{toc}{\contentsline {section}{\numberline {3}Odds and Ends}{9}{section.3}}
-\@writefile{brf}{\backcite{MK:05}{{9}{3}{section.3}}}
-\bibcite{Gent:03}{2}
-\bibcite{MK:05}{3}
-\bibcite{distr}{4}
+\relax
+\ifx\hyper at anchor\@undefined
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+\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\let \contentsline\oldcontentsline
+\let \newlabel\oldnewlabel}
+\else
+\global \let \hyper at last\relax
+\fi
+
+\citation{MK:05}
+\@writefile{brf}{\backcite{MK:05}{{1}{(document)}{Doc-Start}}}
+\citation{distr}
+\@writefile{toc}{\contentsline {section}{\numberline {1}{\tt S4} Classes}{2}{section.1}}
+\@writefile{brf}{\backcite{distr}{{2}{1}{section.1}}}
+\citation{distr}
+\citation{Cham:98}
+\citation{Gent:03}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Class {\tt RandVariable} and Subclasses}}{3}{figure.1}}
+\newlabel{ap.Rpack.RandVar.dia1}{{1}{3}{Class {\tt RandVariable} and Subclasses\relax }{figure.1}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {2}Functions and Methods}{3}{section.2}}
+\@writefile{brf}{\backcite{distr}{{3}{2}{section.2}}}
+\@writefile{brf}{\backcite{Cham:98}{{3}{2}{section.2}}}
+\@writefile{brf}{\backcite{Gent:03}{{3}{2}{section.2}}}
+\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Generating Functions of Package {\tt RandVar}}}{4}{table.1}}
+\newlabel{ap.Rpack.RandVar.tab.gen}{{1}{4}{Generating Functions of Package {\tt RandVar}\relax }{table.1}{}}
+\citation{distr}
+\@writefile{brf}{\backcite{distr}{{8}{2}{table.1}}}
+\citation{distr}
+\citation{MK:05}
+\bibcite{Cham:98}{1}
+\@writefile{brf}{\backcite{distr}{{9}{2}{table.1}}}
+\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces New Generic Functions of Package {\tt RandVar}}}{9}{table.2}}
+\newlabel{ap.Rpack.RandVar.tab}{{2}{9}{New Generic Functions of Package {\tt RandVar}\relax }{table.2}{}}
+\@writefile{toc}{\contentsline {section}{\numberline {3}Odds and Ends}{9}{section.3}}
+\@writefile{brf}{\backcite{MK:05}{{9}{3}{section.3}}}
+\bibcite{Gent:03}{2}
+\bibcite{MK:05}{3}
+\bibcite{distr}{4}
Modified: pkg/RandVar/inst/doc/RandVar.brf
===================================================================
--- pkg/RandVar/inst/doc/RandVar.brf 2008-02-16 03:32:41 UTC (rev 25)
+++ pkg/RandVar/inst/doc/RandVar.brf 2008-02-18 05:08:59 UTC (rev 26)
@@ -1,8 +1,8 @@
-\backcite {MK:05}{{1}{(document)}{Doc-Start}}
-\backcite {distr}{{2}{1}{section.1}}
-\backcite {distr}{{3}{2}{section.2}}
-\backcite {Cham:98}{{3}{2}{section.2}}
-\backcite {Gent:03}{{3}{2}{section.2}}
-\backcite {distr}{{8}{2}{table.1}}
-\backcite {distr}{{9}{2}{table.1}}
-\backcite {MK:05}{{9}{3}{section.3}}
+\backcite {MK:05}{{1}{(document)}{Doc-Start}}
+\backcite {distr}{{2}{1}{section.1}}
+\backcite {distr}{{3}{2}{section.2}}
+\backcite {Cham:98}{{3}{2}{section.2}}
+\backcite {Gent:03}{{3}{2}{section.2}}
+\backcite {distr}{{8}{2}{table.1}}
+\backcite {distr}{{9}{2}{table.1}}
+\backcite {MK:05}{{9}{3}{section.3}}
Modified: pkg/RandVar/inst/doc/RandVar.log
===================================================================
--- pkg/RandVar/inst/doc/RandVar.log 2008-02-16 03:32:41 UTC (rev 25)
+++ pkg/RandVar/inst/doc/RandVar.log 2008-02-18 05:08:59 UTC (rev 26)
@@ -1,443 +1,459 @@
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+
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+
+
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+
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+Underfull \hbox (badness 10000) in paragraph at lines 462--462
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Modified: pkg/RandVar/inst/doc/RandVar.out
===================================================================
--- pkg/RandVar/inst/doc/RandVar.out 2008-02-16 03:32:41 UTC (rev 25)
+++ pkg/RandVar/inst/doc/RandVar.out 2008-02-18 05:08:59 UTC (rev 26)
@@ -1,3 +1,3 @@
-\BOOKMARK [1][-]{section.1}{S4 Classes}{}
-\BOOKMARK [1][-]{section.2}{Functions and Methods}{}
-\BOOKMARK [1][-]{section.3}{Odds and Ends}{}
+\BOOKMARK [1][-]{section.1}{S4 Classes}{}
+\BOOKMARK [1][-]{section.2}{Functions and Methods}{}
+\BOOKMARK [1][-]{section.3}{Odds and Ends}{}
Modified: pkg/RandVar/inst/doc/RandVar.pdf
===================================================================
(Binary files differ)
Modified: pkg/RandVar/inst/doc/RandVar.tex
===================================================================
--- pkg/RandVar/inst/doc/RandVar.tex 2008-02-16 03:32:41 UTC (rev 25)
+++ pkg/RandVar/inst/doc/RandVar.tex 2008-02-18 05:08:59 UTC (rev 26)
@@ -1,466 +1,466 @@
-%\VignetteIndexEntry{RandVar}
-%\VignetteDepends{distr,distrEx}
-%\VignetteKeywords{random variable, S4 classes, S4 methods}
-%\VignettePackage{RandVar}
-%
-\documentclass[11pt]{article}
-\usepackage{geometry}\usepackage{color}
-\usepackage{ifpdf}
-\definecolor{darkblue}{rgb}{0.0,0.0,0.75}
-\usepackage[%
-baseurl={http://www.stamats.de},%
-pdftitle={RandVar: Implementation of random variables by means of S4 classes and methods},%
-pdfauthor={Matthias Kohl},%
-pdfsubject={RandVar},%
-pdfkeywords={random variable, S4 classes, S4 methods},%
-pagebackref,bookmarks,colorlinks,linkcolor=darkblue,citecolor=darkblue,%
-pagecolor=darkblue,raiselinks,plainpages,pdftex]{hyperref}
-%
-\markboth{\sl Packages ``{\tt RandVar}''}{\sl Packages ``{\tt RandVar}''}
-%
-% -------------------------------------------------------------------------------
-\newcommand{\code}[1]{{\tt #1}}
-\newcommand{\pkg}[1]{{\tt "#1"}}
-\newcommand{\pkgversion}{{\tt 1.8}}
-\newcommand{\pkgExversion}{{\tt 0.4-4}}
-% -------------------------------------------------------------------------------
-%
-% -------------------------------------------------------------------------------
-\usepackage{c:/Programme/R/R-2.6.0rc/share/texmf/Sweave}
-\begin{document}
-% -------------------------------------------------------------------------------
-\title{RandVar: Implementation of random variables by means
- of {\tt S4} classes and methods}
-\author{Matthias Kohl\\
-e-Mail: {\tt matthias.kohl at stamats.de}\\
-}
-\maketitle
-% -------------------------------------------------------------------------------
-\begin{abstract}
-% -------------------------------------------------------------------------------
-In this package we implement random variables by means of {\tt S4} classes
-and methods. This vignette corresponds to Appendix D.2 in Kohl~(2005)~\cite{MK:05}.
-% -------------------------------------------------------------------------------
-\end{abstract}
-% -------------------------------------------------------------------------------
-\tableofcontents
-% -------------------------------------------------------------------------------
-\clearpage
-% -----------------------------------------------------------------------
-\section{{\tt S4} Classes}
-% -----------------------------------------------------------------------
-The {\tt S4} class {\tt RandVariable} (cf.\ Figure~\ref{ap.Rpack.RandVar.dia1})
-has the slots {\tt Map}, {\tt Domain} and {\tt Range} where {\tt Map}
-contains a list of functions which are measurable maps from {\tt Domain}
-to {\tt Range}. The elements contained in the list {\tt Map} must be functions in
-one argument named {\tt x}. We do not allow further parameters for these
-functions as this would lead to inconsistent objects. Strictly speaking, an object of
-class {\tt RandVariable} would represent not only one random variable but a whole
-set of random variables depending on these parameters.
-% -----------------------------------------------------------------------
-\par
-The slots {\tt Domain} and {\tt Range} are filled with an object of
-class {\tt OptionalrSpace}; i.e., they contain {\tt NULL} or an object of class
-{\tt rSpace} (see package {\tt distr}~\cite{distr}). In case of
-{\tt EuclRandVariable} and {\tt RealRandVariable} the slot {\tt Range} is filled
-with an object of class {\tt Euclideanspace} and {\tt Reals}, respectively. The
-class {\tt EuclRandMatrix} additionally has the slot {\tt Dim} which is a vector
-of integers and contains the dimensions of the Euclidean random matrix.
-% -----------------------------------------------------------------------
-\par
-Using these {\tt S4} classes there are two possibilities to implement a ${\rm R}^k$
-valued random variable. First, we could define a {\tt EuclRandVariable}
-whose slot {\tt Map} contains a list with one function which maps to ${\rm R}^k$;
-i.e., the slot {\tt Range} is a $k$-dimensional Euclidean space. Second, we could
-define a {\tt EuclRandVariable} whose slot {\tt Map} contains a list with $n$
-functions (projections) which map to ${\rm R}^m$ where $k = m*n$. Now, the slot
-{\tt Range} is an $m$-dimensional Euclidean space.
-Since it is sometimes convenient to regard a ${\rm R}^k$ valued random variable
-as measurable map consisting of ${\rm R}^{k_i}$ valued maps where $\sum k_i = k$,
-we introduce a further class called {\tt EuclRandVarList}.
-With this class we can now define ${\rm R}^k$ valued random variables as a list
-of ${\rm R}^{k_i}$ valued random variables with compatible domains. More precisely,
-the elements of a {\tt EuclRandVarList} may even have very different ranges
-(not necessarily Euclidean spaces) they only need to have compatible
-domains which is checked via the generic function {\tt compatibleDomains}.
-% -----------------------------------------------------------------------
-\begin{figure}[!ht]
-\begin{center}
- \ifpdf
- \includegraphics[scale=1.0, viewport = 14 15 244 275]{RandVariable.pdf}
- \else
- \includegraphics[scale=1.0]{RandVariable.eps}
- \fi
- \caption[Class {\tt RandVariable} and Subclasses]{Class
- {\tt RandVariable} and subclasses.}
- \label{ap.Rpack.RandVar.dia1}
-\end{center}
-\end{figure}
-% -----------------------------------------------------------------------
-\newpage
-\section{Functions and Methods}
-% -----------------------------------------------------------------------
-As in case of package {\tt distrEx}~\cite{distr}, we follow the advices of
-Section~7.3 of \cite{Cham:98} and \cite{Gent:03}. That is, we introduce
-generating functions as well as accessor and replacement functions. A short
-description of the implemented generating functions is given in
-Table~\ref{ap.Rpack.RandVar.tab.gen}.
-% -----------------------------------------------------------------------
-\begin{table}[!ht]
-\begin{center}
-\begin{tabular}{p{4cm}|p{7.5cm}}
- \textbf{Generating Function} & \textbf{Description} \\ \hline\hline
- {\tt EuclRandMatrix} & Generates an object of class {\tt EuclRandMatrix}\\ \hline
- {\tt EuclRandVariable} & Generates an object of class {\tt EuclRandVariable}\\ \hline
- {\tt EuclRandVarList} & Generates an object of class {\tt EuclRandVarList}\\ \hline
- {\tt RandVariable} & Generates an object of class {\tt RandVariable}\\ \hline
- {\tt RealRandVariable} & Generates an object of class {\tt RealRandVariable}
-\end{tabular}
-\caption[Generating Functions of Package {\tt RandVar}]{Generating
-functions of package {\tt RandVar}.}\label{ap.Rpack.RandVar.tab.gen}%
-\end{center}
-\end{table}
-% -----------------------------------------------------------------------
-\par\noindent
-While there are accessor functions for all slots of the newly defined
-{\tt S4} classes, replacement functions are only implemented for those
-slots a user should modify.
-% -----------------------------------------------------------------------
-\par
-Our next goal was that one can use these classes of random variables like
-ordinary numeric vectors or matrices. Hence, we overloaded the {\tt S4}
-group generic functions {\tt Arith} and {\tt Math} as well as matrix
-multiplication {\tt \%*\%}. For the matrix multiplication of {\tt EuclRandVarList}s
-we additionally introduced the operator {\tt \%m\%}.
-Now, if we have random variables {\tt X} and {\tt Y}, a numerical
-vector {\tt v} and a numerical matrix {\tt M} (with compatible dimensions)
-we can for instance generate
-\begin{Schunk}
-\begin{Sinput}
-> library(RandVar)
-> (X <- RealRandVariable(Map = list(function(x) {
-+ x
-+ }, function(x) {
-+ x^2
-+ }), Domain = Reals(), Range = Reals()))
-\end{Sinput}
-\begin{Soutput}
-An object of class "RealRandVariable"
-length of Map: 2
-Domain: Real Space with dimension 1
-Range: Real Space with dimension 1
-\end{Soutput}
-\begin{Sinput}
-> Map(X)
-\end{Sinput}
-\begin{Soutput}
-[[1]]
-function (x)
-{
- x
-}
-
-[[2]]
-function (x)
-{
- x^2
-}
-\end{Soutput}
-\begin{Sinput}
-> evalRandVar(X, 2)
-\end{Sinput}
-\begin{Soutput}
- [,1]
-[1,] 2
-[2,] 4
-\end{Soutput}
-\begin{Sinput}
-> evalRandVar(X, as.matrix(seq(2, 10, 2)))
-\end{Sinput}
-\begin{Soutput}
-, , 1
-
- [,1] [,2] [,3] [,4] [,5]
-[1,] 2 4 6 8 10
-[2,] 4 16 36 64 100
-\end{Soutput}
-\begin{Sinput}
-> R1 <- exp(X - 1)
-> Map(R1)
-\end{Sinput}
-\begin{Soutput}
-[[1]]
-function (x)
-{
- f1 <- function (x)
- {
- f1 <- function (x)
- {
- x
- }
- f1(x) - 1
- }
- exp(f1(x))
-}
-<environment: 0x02e7816c>
-
-[[2]]
-function (x)
-{
- f1 <- function (x)
- {
- f1 <- function (x)
- {
- x^2
- }
- f1(x) - 1
- }
- exp(f1(x))
-}
-<environment: 0x02e7816c>
-\end{Soutput}
-\begin{Sinput}
-> R2 <- exp(X - 1:2)
-> Map(R2)
-\end{Sinput}
-\begin{Soutput}
-[[1]]
-function (x)
-{
- f1 <- function (x)
- {
- f1 <- function (x)
- {
- x
- }
- f1(x) - 1L
- }
- exp(f1(x))
-}
-<environment: 0x02fc2db4>
-
-[[2]]
-function (x)
-{
- f1 <- function (x)
- {
- f1 <- function (x)
- {
- x^2
- }
- f1(x) - 2L
- }
- exp(f1(x))
-}
-<environment: 0x02fc2db4>
-\end{Soutput}
-\begin{Sinput}
-> (Y <- RealRandVariable(Map = list(function(x) {
-+ sin(x)
-+ }, function(x) {
-+ cos(x)
-+ }), Domain = Reals(), Range = Reals()))
-\end{Sinput}
-\begin{Soutput}
-An object of class "RealRandVariable"
-length of Map: 2
-Domain: Real Space with dimension 1
-Range: Real Space with dimension 1
-\end{Soutput}
-\begin{Sinput}
-> Map(Y)
-\end{Sinput}
-\begin{Soutput}
-[[1]]
-function (x)
-{
- sin(x)
-}
-
-[[2]]
-function (x)
-{
- cos(x)
-}
-\end{Soutput}
-\begin{Sinput}
-> R3 <- X %*% Y
-> dimension(R3)
-\end{Sinput}
-\begin{Soutput}
-[1] 1
-\end{Soutput}
-\begin{Sinput}
-> 2 * sin(2) + 2^2 * cos(2)
-\end{Sinput}
-\begin{Soutput}
-[1] 0.1540075
-\end{Soutput}
-\begin{Sinput}
-> (R4 <- X %*% t(Y))
-\end{Sinput}
-\begin{Soutput}
-An object of class "EuclRandMatrix"
-Dim of Map: 2 2
-Domain: Real Space with dimension 1
-Range: Euclidean Space with dimension 1
-\end{Soutput}
-\begin{Sinput}
-> dimension(R4)
-\end{Sinput}
-\begin{Soutput}
-[1] 4
-\end{Soutput}
-\begin{Sinput}
-> (M <- matrix(c(2 * sin(2), 2^2 * sin(2), 2 * cos(2), 2^2 * cos(2)),
-+ ncol = 2))
-\end{Sinput}
-\begin{Soutput}
- [,1] [,2]
-[1,] 1.818595 -0.8322937
-[2,] 3.637190 -1.6645873
-\end{Soutput}
-\begin{Sinput}
-> (R5 <- M %*% R4)
-\end{Sinput}
-\begin{Soutput}
-An object of class "EuclRandMatrix"
-Dim of Map: 2 2
-Domain: Real Space with dimension 1
-Range: Real Space with dimension 1
-\end{Soutput}
-\end{Schunk}
-We also implemented {\tt S4} methods for the generic function {\tt E} of
-package {\tt distrEx}~\cite{distr}. That is, given some distribution {\tt D},
-respectively some conditional distribution {\tt CD} and some random variable {\tt X}
-we can compute the (conditional) expectation of {\tt X} under {\tt D}, respectively
-{\tt CD} simply by
-\begin{Schunk}
-\begin{Sinput}
-> D <- Norm()
-> E(object = D, fun = X)
-\end{Sinput}
-\begin{Soutput}
-[1] 2.792788e-16 9.999942e-01
-\end{Soutput}
-\begin{Sinput}
-> E(D)
-\end{Sinput}
-\begin{Soutput}
-[1] 0
-\end{Soutput}
-\begin{Sinput}
-> var(D)
-\end{Sinput}
-\begin{Soutput}
-[1] 1
-\end{Soutput}
-\begin{Sinput}
-> (CD <- LMCondDistribution(theta = 1))
-\end{Sinput}
-\begin{Soutput}
-Distribution object of class: AbscontCondDistribution
-theta : 1
-intercept : 0
-scale : 1
-## cond:
-name: conditioning by an Euclidean space
-Range: Euclidean Space with dimension 1
-\end{Soutput}
-\begin{Sinput}
-> E(object = CD, fun = X, cond = 2)
-\end{Sinput}
-\begin{Soutput}
-[1] 2.000000 4.999993
-\end{Soutput}
-\begin{Sinput}
-> E(Norm(mean = 2))
-\end{Sinput}
-\begin{Soutput}
-[1] 2
-\end{Soutput}
-\begin{Sinput}
-> E(Norm(mean = 2), fun = function(x) {
-+ x^2
-+ })
-\end{Sinput}
-\begin{Soutput}
-[1] 4.999993
-\end{Soutput}
-\end{Schunk}
-for some given condition {\tt cond}.
-% -----------------------------------------------------------------------
-\par
-In addition, we define methods for the generic function {\tt show} for the classes
-{\tt RandVariable}, {\tt EuclRandMatrix} and {\tt EuclRandVarList}. There are
-also methods for the generic functions {\tt dimension} (see package
-{\tt distr}~\cite{distr}), {\tt length}, {\tt ncol}, {\tt nrow}, {\tt t} and
-{\tt [} (cf.\ package {\tt base}). For more details we refer to the corresponding
-help pages.
-% -----------------------------------------------------------------------
-\par
-Finally, we introduce several new generic functions. A brief description
-of these functions is given in Table~\ref{ap.Rpack.RandVar.tab}.
-% -----------------------------------------------------------------------
-\begin{table}[!ht]
-\begin{center}
-\begin{tabular}{p{3.5cm}|p{8cm}}
- \textbf{Generic Function} & \textbf{Description} \\ \hline\hline
- \texttt{\%m\%} & matrix multiplication for {\tt EuclRandVarList}s \\ \hline
- \texttt{compatibleDomains} & test if the domains of two random variables
- are compatible \\ \hline
- \texttt{evalRandVar} & evaluation of random variables\\ \hline
- \texttt{imageDistr} & image distribution of some distribution under some
- random variable \\ \hline
- \texttt{numberOfMaps} & number of functions contained in the slots {\tt Map}
- of the members of a {\tt EuclRandVarList}
-\end{tabular}
-\caption[New Generic Functions of Package {\tt RandVar}]
-{New generic functions of package {\tt RandVar} (without accessor
-and replacement functions).}\label{ap.Rpack.RandVar.tab}%
-\end{center}
-\end{table}
-% -----------------------------------------------------------------------
-\par\noindent
-For more details about the full functionality of package {\tt RandVar}
-we refer to the source code and the corresponding help pages, respectively.
-% -----------------------------------------------------------------------
-\section{Odds and Ends}
-% -----------------------------------------------------------------------
-The main issue is to reduce the computation time for methods using
-objects of class {\tt RandVariable} and its subclasses as these classes
-play an important role in the computation of optimally robust
-estimators; confer Kohl~(2005)~\cite{MK:05}.
-In particular, we are looking for ways to increase the computation speed
-of {\tt evalRandVar} and {\tt E}.
-%-------------------------------------------------------------------------------
-\begin{thebibliography}{8}
-
-\bibitem{Cham:98}
-Chambers J.M.
-\newblock {\em {Programming with data. A guide to the S language}\/}.
-\newblock {Springer}.
-\newblock http://cm.bell-labs.com/stat/Sbook/index.html
-
-\bibitem{Gent:03}
-Gentleman R.
-\newblock {\em Object Orientated Programming. Slides of a Short Course held in Auckland\/}.
-\newblock http://www.stat.auckland.ac.nz/S-Workshop/Gentleman/Methods.pdf
-
-\bibitem{MK:05}
-Kohl M.
-\newblock {\em Numerical Contributions to the Asymptotic Theory of Robustness\/}.
-\newblock {Dissertation}, Universit\"at Bayreuth.
-\newblock See also http://stamats.de/ThesisMKohl.pdf
-
-\bibitem{distr}
-Ruckdeschel P., Kohl M., Stabla T., and Camphausen F.
-\newblock {S4 Classes for Distributions.}
-\newblock {\em R-News\/}, {\bf 6}(2): 10--13.
-\newblock http://CRAN.R-project.org/doc/Rnews/Rnews\_2006-2.pdf
-\newblock See also {http://www.uni-bayreuth.de/departments/math/org/mathe7/RUCKDESCHEL/pubs/distr.pdf}
-
-\end{thebibliography}
-% -------------------------------------------------------------------------------
-\end{document}
-% -------------------------------------------------------------------------------
+%\VignetteIndexEntry{RandVar}
+%\VignetteDepends{distr,distrEx}
+%\VignetteKeywords{random variable, S4 classes, S4 methods}
+%\VignettePackage{RandVar}
+%
+\documentclass[11pt]{article}
+\usepackage{geometry}\usepackage{color}
+\usepackage{ifpdf}
+\definecolor{darkblue}{rgb}{0.0,0.0,0.75}
+\usepackage[%
+baseurl={http://www.stamats.de},%
+pdftitle={RandVar: Implementation of random variables by means of S4 classes and methods},%
+pdfauthor={Matthias Kohl},%
+pdfsubject={RandVar},%
+pdfkeywords={random variable, S4 classes, S4 methods},%
+pagebackref,bookmarks,colorlinks,linkcolor=darkblue,citecolor=darkblue,%
+pagecolor=darkblue,raiselinks,plainpages,pdftex]{hyperref}
+%
+\markboth{\sl Packages ``{\tt RandVar}''}{\sl Packages ``{\tt RandVar}''}
+%
+% -------------------------------------------------------------------------------
+\newcommand{\code}[1]{{\tt #1}}
+\newcommand{\pkg}[1]{{\tt "#1"}}
+\newcommand{\pkgversion}{{\tt 1.8}}
+\newcommand{\pkgExversion}{{\tt 0.4-4}}
+% -------------------------------------------------------------------------------
+%
+% -------------------------------------------------------------------------------
+\usepackage{/home/btm722/RTOP/R-2-6-branch/share/texmf/Sweave}
+\begin{document}
+% -------------------------------------------------------------------------------
+\title{RandVar: Implementation of random variables by means
+ of {\tt S4} classes and methods}
+\author{Matthias Kohl\\
+e-Mail: {\tt matthias.kohl at stamats.de}\\
+}
+\maketitle
+% -------------------------------------------------------------------------------
+\begin{abstract}
+% -------------------------------------------------------------------------------
+In this package we implement random variables by means of {\tt S4} classes
+and methods. This vignette corresponds to Appendix D.2 in Kohl~(2005)~\cite{MK:05}.
+% -------------------------------------------------------------------------------
+\end{abstract}
+% -------------------------------------------------------------------------------
+\tableofcontents
+% -------------------------------------------------------------------------------
+\clearpage
+% -----------------------------------------------------------------------
+\section{{\tt S4} Classes}
+% -----------------------------------------------------------------------
+The {\tt S4} class {\tt RandVariable} (cf.\ Figure~\ref{ap.Rpack.RandVar.dia1})
+has the slots {\tt Map}, {\tt Domain} and {\tt Range} where {\tt Map}
+contains a list of functions which are measurable maps from {\tt Domain}
+to {\tt Range}. The elements contained in the list {\tt Map} must be functions in
+one argument named {\tt x}. We do not allow further parameters for these
+functions as this would lead to inconsistent objects. Strictly speaking, an object of
+class {\tt RandVariable} would represent not only one random variable but a whole
+set of random variables depending on these parameters.
+% -----------------------------------------------------------------------
+\par
+The slots {\tt Domain} and {\tt Range} are filled with an object of
+class {\tt OptionalrSpace}; i.e., they contain {\tt NULL} or an object of class
+{\tt rSpace} (see package {\tt distr}~\cite{distr}). In case of
+{\tt EuclRandVariable} and {\tt RealRandVariable} the slot {\tt Range} is filled
+with an object of class {\tt Euclideanspace} and {\tt Reals}, respectively. The
+class {\tt EuclRandMatrix} additionally has the slot {\tt Dim} which is a vector
+of integers and contains the dimensions of the Euclidean random matrix.
+% -----------------------------------------------------------------------
+\par
+Using these {\tt S4} classes there are two possibilities to implement a ${\rm R}^k$
+valued random variable. First, we could define a {\tt EuclRandVariable}
+whose slot {\tt Map} contains a list with one function which maps to ${\rm R}^k$;
+i.e., the slot {\tt Range} is a $k$-dimensional Euclidean space. Second, we could
+define a {\tt EuclRandVariable} whose slot {\tt Map} contains a list with $n$
+functions (projections) which map to ${\rm R}^m$ where $k = m*n$. Now, the slot
+{\tt Range} is an $m$-dimensional Euclidean space.
+Since it is sometimes convenient to regard a ${\rm R}^k$ valued random variable
+as measurable map consisting of ${\rm R}^{k_i}$ valued maps where $\sum k_i = k$,
+we introduce a further class called {\tt EuclRandVarList}.
+With this class we can now define ${\rm R}^k$ valued random variables as a list
+of ${\rm R}^{k_i}$ valued random variables with compatible domains. More precisely,
+the elements of a {\tt EuclRandVarList} may even have very different ranges
+(not necessarily Euclidean spaces) they only need to have compatible
+domains which is checked via the generic function {\tt compatibleDomains}.
+% -----------------------------------------------------------------------
+\begin{figure}[!ht]
+\begin{center}
+ \ifpdf
+ \includegraphics[scale=1.0, viewport = 14 15 244 275]{RandVariable.pdf}
+ \else
+ \includegraphics[scale=1.0]{RandVariable.eps}
+ \fi
+ \caption[Class {\tt RandVariable} and Subclasses]{Class
+ {\tt RandVariable} and subclasses.}
+ \label{ap.Rpack.RandVar.dia1}
+\end{center}
+\end{figure}
+% -----------------------------------------------------------------------
+\newpage
+\section{Functions and Methods}
+% -----------------------------------------------------------------------
+As in case of package {\tt distrEx}~\cite{distr}, we follow the advices of
+Section~7.3 of \cite{Cham:98} and \cite{Gent:03}. That is, we introduce
+generating functions as well as accessor and replacement functions. A short
+description of the implemented generating functions is given in
+Table~\ref{ap.Rpack.RandVar.tab.gen}.
+% -----------------------------------------------------------------------
+\begin{table}[!ht]
+\begin{center}
+\begin{tabular}{p{4cm}|p{7.5cm}}
+ \textbf{Generating Function} & \textbf{Description} \\ \hline\hline
+ {\tt EuclRandMatrix} & Generates an object of class {\tt EuclRandMatrix}\\ \hline
+ {\tt EuclRandVariable} & Generates an object of class {\tt EuclRandVariable}\\ \hline
+ {\tt EuclRandVarList} & Generates an object of class {\tt EuclRandVarList}\\ \hline
+ {\tt RandVariable} & Generates an object of class {\tt RandVariable}\\ \hline
+ {\tt RealRandVariable} & Generates an object of class {\tt RealRandVariable}
+\end{tabular}
+\caption[Generating Functions of Package {\tt RandVar}]{Generating
+functions of package {\tt RandVar}.}\label{ap.Rpack.RandVar.tab.gen}%
+\end{center}
+\end{table}
+% -----------------------------------------------------------------------
+\par\noindent
+While there are accessor functions for all slots of the newly defined
+{\tt S4} classes, replacement functions are only implemented for those
+slots a user should modify.
+% -----------------------------------------------------------------------
+\par
+Our next goal was that one can use these classes of random variables like
+ordinary numeric vectors or matrices. Hence, we overloaded the {\tt S4}
+group generic functions {\tt Arith} and {\tt Math} as well as matrix
+multiplication {\tt \%*\%}. For the matrix multiplication of {\tt EuclRandVarList}s
+we additionally introduced the operator {\tt \%m\%}.
+Now, if we have random variables {\tt X} and {\tt Y}, a numerical
+vector {\tt v} and a numerical matrix {\tt M} (with compatible dimensions)
+we can for instance generate
+\begin{Schunk}
+\begin{Sinput}
+> library(RandVar)
+> (X <- RealRandVariable(Map = list(function(x) {
++ x
++ }, function(x) {
++ x^2
++ }), Domain = Reals(), Range = Reals()))
+\end{Sinput}
+\begin{Soutput}
+An object of class “RealRandVariable”
+length of Map: 2
+Domain: Real Space with dimension 1
+Range: Real Space with dimension 1
+\end{Soutput}
+\begin{Sinput}
+> Map(X)
+\end{Sinput}
+\begin{Soutput}
+[[1]]
+function (x)
+{
+ x
+}
+
+[[2]]
+function (x)
+{
+ x^2
+}
+\end{Soutput}
+\begin{Sinput}
+> evalRandVar(X, 2)
+\end{Sinput}
+\begin{Soutput}
+ [,1]
+[1,] 2
+[2,] 4
+\end{Soutput}
+\begin{Sinput}
+> evalRandVar(X, as.matrix(seq(2, 10, 2)))
+\end{Sinput}
+\begin{Soutput}
+, , 1
+
+ [,1] [,2] [,3] [,4] [,5]
+[1,] 2 4 6 8 10
+[2,] 4 16 36 64 100
+\end{Soutput}
+\begin{Sinput}
+> R1 <- exp(X - 1)
+> Map(R1)
+\end{Sinput}
+\begin{Soutput}
+[[1]]
+function (x)
+{
+ f1 <- function (x)
+ {
+ f1 <- function (x)
+ {
+ x
+ }
+ f1(x) - 1
+ }
+ exp(f1(x))
+}
+<environment: 0x9da0aec>
+
+[[2]]
+function (x)
+{
+ f1 <- function (x)
+ {
+ f1 <- function (x)
+ {
+ x^2
+ }
+ f1(x) - 1
+ }
+ exp(f1(x))
+}
+<environment: 0x9da0aec>
+\end{Soutput}
+\begin{Sinput}
+> R2 <- exp(X - 1:2)
+> Map(R2)
+\end{Sinput}
+\begin{Soutput}
+[[1]]
+function (x)
+{
+ f1 <- function (x)
+ {
+ f1 <- function (x)
+ {
+ x
+ }
+ f1(x) - 1L
+ }
+ exp(f1(x))
+}
+<environment: 0x9e94594>
+
+[[2]]
+function (x)
+{
+ f1 <- function (x)
+ {
+ f1 <- function (x)
+ {
+ x^2
+ }
+ f1(x) - 2L
+ }
+ exp(f1(x))
+}
+<environment: 0x9e94594>
+\end{Soutput}
+\begin{Sinput}
+> (Y <- RealRandVariable(Map = list(function(x) {
++ sin(x)
++ }, function(x) {
++ cos(x)
++ }), Domain = Reals(), Range = Reals()))
+\end{Sinput}
+\begin{Soutput}
+An object of class “RealRandVariable”
+length of Map: 2
+Domain: Real Space with dimension 1
+Range: Real Space with dimension 1
+\end{Soutput}
+\begin{Sinput}
+> Map(Y)
+\end{Sinput}
+\begin{Soutput}
+[[1]]
+function (x)
+{
+ sin(x)
+}
+
+[[2]]
+function (x)
+{
+ cos(x)
+}
+\end{Soutput}
+\begin{Sinput}
+> R3 <- X %*% Y
+> dimension(R3)
+\end{Sinput}
+\begin{Soutput}
+[1] 1
+\end{Soutput}
+\begin{Sinput}
+> 2 * sin(2) + 2^2 * cos(2)
+\end{Sinput}
+\begin{Soutput}
+[1] 0.1540075
+\end{Soutput}
+\begin{Sinput}
+> (R4 <- X %*% t(Y))
+\end{Sinput}
+\begin{Soutput}
+An object of class “EuclRandMatrix”
+Dim of Map: 2 2
+Domain: Real Space with dimension 1
+Range: Euclidean Space with dimension 1
+\end{Soutput}
+\begin{Sinput}
+> dimension(R4)
+\end{Sinput}
+\begin{Soutput}
+[1] 4
+\end{Soutput}
+\begin{Sinput}
+> (M <- matrix(c(2 * sin(2), 2^2 * sin(2), 2 * cos(2), 2^2 * cos(2)),
++ ncol = 2))
+\end{Sinput}
+\begin{Soutput}
+ [,1] [,2]
+[1,] 1.818595 -0.8322937
+[2,] 3.637190 -1.6645873
+\end{Soutput}
+\begin{Sinput}
+> (R5 <- M %*% R4)
+\end{Sinput}
+\begin{Soutput}
+An object of class “EuclRandMatrix”
+Dim of Map: 2 2
+Domain: Real Space with dimension 1
+Range: Real Space with dimension 1
+\end{Soutput}
+\end{Schunk}
+We also implemented {\tt S4} methods for the generic function {\tt E} of
+package {\tt distrEx}~\cite{distr}. That is, given some distribution {\tt D},
+respectively some conditional distribution {\tt CD} and some random variable {\tt X}
+we can compute the (conditional) expectation of {\tt X} under {\tt D}, respectively
+{\tt CD} simply by
+\begin{Schunk}
+\begin{Sinput}
+> D <- Norm()
+> E(object = D, fun = X)
+\end{Sinput}
+\begin{Soutput}
+[1] 2.587378e-16 9.999942e-01
+\end{Soutput}
+\begin{Sinput}
+> E(D)
+\end{Sinput}
+\begin{Soutput}
+[1] 0
+\end{Soutput}
+\begin{Sinput}
+> var(D)
+\end{Sinput}
+\begin{Soutput}
+[1] 1
+\end{Soutput}
+\begin{Sinput}
+> (CD <- LMCondDistribution(theta = 1))
+\end{Sinput}
+\begin{Soutput}
+Distribution object of class: AbscontCondDistribution
+theta : 1
+intercept : 0
+scale : 1
+## cond:
+name: conditioning by an Euclidean space
+Range: Euclidean Space with dimension 1
+\end{Soutput}
+\begin{Sinput}
+> E(object = CD, fun = X, cond = 2)
+\end{Sinput}
+\begin{Soutput}
+[1] 2.000000 4.999993
+\end{Soutput}
+\begin{Sinput}
+> E(Norm(mean = 2))
+\end{Sinput}
+\begin{Soutput}
+[1] 2
+\end{Soutput}
+\begin{Sinput}
+> E(Norm(mean = 2), fun = function(x) {
++ x^2
++ })
+\end{Sinput}
+\begin{Soutput}
+[1] 4.999993
+\end{Soutput}
+\end{Schunk}
+for some given condition {\tt cond}.
+% -----------------------------------------------------------------------
+\par
+In addition, we define methods for the generic function {\tt show} for the classes
+{\tt RandVariable}, {\tt EuclRandMatrix} and {\tt EuclRandVarList}. There are
+also methods for the generic functions {\tt dimension} (see package
+{\tt distr}~\cite{distr}), {\tt length}, {\tt ncol}, {\tt nrow}, {\tt t} and
+{\tt [} (cf.\ package {\tt base}). For more details we refer to the corresponding
+help pages.
+% -----------------------------------------------------------------------
+\par
+Finally, we introduce several new generic functions. A brief description
+of these functions is given in Table~\ref{ap.Rpack.RandVar.tab}.
+% -----------------------------------------------------------------------
+\begin{table}[!ht]
+\begin{center}
+\begin{tabular}{p{3.5cm}|p{8cm}}
+ \textbf{Generic Function} & \textbf{Description} \\ \hline\hline
+ \texttt{\%m\%} & matrix multiplication for {\tt EuclRandVarList}s \\ \hline
+ \texttt{compatibleDomains} & test if the domains of two random variables
+ are compatible \\ \hline
+ \texttt{evalRandVar} & evaluation of random variables\\ \hline
+ \texttt{imageDistr} & image distribution of some distribution under some
+ random variable \\ \hline
+ \texttt{numberOfMaps} & number of functions contained in the slots {\tt Map}
+ of the members of a {\tt EuclRandVarList}
+\end{tabular}
+\caption[New Generic Functions of Package {\tt RandVar}]
+{New generic functions of package {\tt RandVar} (without accessor
+and replacement functions).}\label{ap.Rpack.RandVar.tab}%
+\end{center}
+\end{table}
+% -----------------------------------------------------------------------
+\par\noindent
+For more details about the full functionality of package {\tt RandVar}
+we refer to the source code and the corresponding help pages, respectively.
+% -----------------------------------------------------------------------
+\section{Odds and Ends}
+% -----------------------------------------------------------------------
+The main issue is to reduce the computation time for methods using
+objects of class {\tt RandVariable} and its subclasses as these classes
+play an important role in the computation of optimally robust
+estimators; confer Kohl~(2005)~\cite{MK:05}.
+In particular, we are looking for ways to increase the computation speed
+of {\tt evalRandVar} and {\tt E}.
+%-------------------------------------------------------------------------------
+\begin{thebibliography}{8}
+
+\bibitem{Cham:98}
+Chambers J.M.
+\newblock {\em {Programming with data. A guide to the S language}\/}.
+\newblock {Springer}.
+\newblock http://cm.bell-labs.com/stat/Sbook/index.html
+
+\bibitem{Gent:03}
+Gentleman R.
+\newblock {\em Object Orientated Programming. Slides of a Short Course held in Auckland\/}.
+\newblock http://www.stat.auckland.ac.nz/S-Workshop/Gentleman/Methods.pdf
+
+\bibitem{MK:05}
+Kohl M.
+\newblock {\em Numerical Contributions to the Asymptotic Theory of Robustness\/}.
+\newblock {Dissertation}, Universit\"at Bayreuth.
+\newblock See also http://stamats.de/ThesisMKohl.pdf
+
+\bibitem{distr}
+Ruckdeschel P., Kohl M., Stabla T., and Camphausen F.
+\newblock {S4 Classes for Distributions.}
+\newblock {\em R-News\/}, {\bf 6}(2): 10--13.
+\newblock http://CRAN.R-project.org/doc/Rnews/Rnews\_2006-2.pdf
+\newblock See also {http://www.uni-bayreuth.de/departments/math/org/mathe7/RUCKDESCHEL/pubs/distr.pdf}
+
+\end{thebibliography}
+% -------------------------------------------------------------------------------
+\end{document}
+% -------------------------------------------------------------------------------
Modified: pkg/RandVar/inst/doc/RandVar.toc
===================================================================
--- pkg/RandVar/inst/doc/RandVar.toc 2008-02-16 03:32:41 UTC (rev 25)
+++ pkg/RandVar/inst/doc/RandVar.toc 2008-02-18 05:08:59 UTC (rev 26)
@@ -1,3 +1,3 @@
-\contentsline {section}{\numberline {1}{\tt S4} Classes}{2}{section.1}
-\contentsline {section}{\numberline {2}Functions and Methods}{3}{section.2}
-\contentsline {section}{\numberline {3}Odds and Ends}{9}{section.3}
+\contentsline {section}{\numberline {1}{\tt S4} Classes}{2}{section.1}
+\contentsline {section}{\numberline {2}Functions and Methods}{3}{section.2}
+\contentsline {section}{\numberline {3}Odds and Ends}{9}{section.3}
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