|
|
APPENDIX D Matrix algebra in R |
543 |
|
Table D.1 R functions and operators for matrix algebra |
|
|
||
|
|
|
|
|
Operator or function |
|
Description |
|
|
|
|
|
|
|
ginv(A) |
Moore-Penrose Generalized Inverse of A. (Requires the MASS package.) |
|
|
|
qr(A) |
QR decomposition of A. If y <- qr(A), then |
|
|
|
|
■ |
y$qr has an upper triangle that contains the decomposition and a lower |
|
|
|
|
triangle that contains information on the decomposition. |
|
|
|
■ |
y$rank is the rank of A. |
|
|
|
■ |
y$qraux is a vector which contains additional information on Q. |
|
|
|
■ |
y$pivot contains information on the pivoting strategy used. |
|
|
rbind(A, B, …) |
Combines matrices or vectors vertically. Returns a matrix. |
|
|
|
rowMeans(A) |
Returns a vector containing the row means of A. |
|
|
|
rowSums(A) |
Returns a vector containing the row sums of A. |
|
|
|
solve(A) |
Inverse of A where A is a square matrix. |
|
|
|
solve(A, b) |
Solves for vector x in the equation b = Ax. |
|
|
|
svd(A) |
Single-value decomposition of A. If y <- svd(A), then |
|
|
|
|
■ |
y$d is a vector containing the singular values of A. |
|
|
|
■ |
y$u is a matrix with columns containing the left singular vectors of A. |
|
|
|
■ |
y$v is a matrix with columns containing the right singular vectors of A. |
|
|
t(A) |
Transpose of A. |
|
|
|
|
|
|
|
|
Several user-contributed packages are particularly useful for matrix algebra. The matlab package contains wrapper functions and variables used to replicate MATLAB function calls as closely as possible. These functions can help you port MATLAB applications and code to R. There’s also a useful cheat sheet for converting MATLAB statements to R statements at http://mathesaurus.sourceforge.net/octave-r.html.
The Matrix package contains functions that extend R in order to support highly dense or sparse matrices. It provides efficient access to BLAS (Basic Linear Algebra Subroutines), Lapack (dense matrix), TAUCS (sparse matrix), and UMFPACK (sparse matrix) routines.
Finally, the matrixStats package provides methods for operating on the rows and columns of matrices, including functions that calculate counts, sums, products, central tendency, dispersion, and more. Each is optimized for speed and efficient memory use.
APPENDIX E Packages used in this book |
545 |
Table E.1 Contributed packages used in this book (continued)
Package |
Authors |
Description |
Chapter(s) |
|
|
|
|
coin |
Torsten Hothorn, Kurt Hornik, |
Conditional inference procedures in |
12 |
|
Mark A. van de Wiel, and |
a permutation test framework |
|
|
Achim Zeileis |
|
|
corrgram |
Kevin Wright |
Plots a corrgram |
11 |
corrperm |
Douglas M. Potter |
Permutation tests of correlation |
12 |
|
|
with repeated measurements |
|
doBy |
Søren Højsgaard with contribu- |
Group-wise computations of sum- |
7 |
|
tions from Kevin Wright and Ales- |
mary statistics, general linear con- |
|
|
sandro A. Leidi |
trasts and other utilities |
|
doParallel |
Revolution Analytics, Steve |
foreach parallel adaptor for the |
20 |
|
Weston |
parallel package |
|
effects |
John Fox and Jangman Hong |
Effect displays for linear, general- |
8, 9 |
|
|
ized linear, multinomial-logit, and |
|
|
|
proportional-odds logit models |
|
FactoMineR |
Francois Husson, Julie Josse, |
Multivariate exploratory data analy- |
14 |
|
Sebastien Le, and Jeremy Mazet |
sis and data mining with R |
|
FAiR |
Ben Goodrich |
Factor analysis using a genetic |
14 |
|
|
algorithm |
|
fCalendar |
Diethelm Wuertz and Yohan |
Functions for chronological and |
4 |
|
Chalabi |
calendrical objects |
|
flexclust |
Friedrich Leish and Evgenia |
Flexible cluster algorithms |
16 |
|
Dimnitriadou |
|
|
forecast |
Rob J. Hyndman with contribu- |
Methods and tools for displaying |
15 |
|
tions from George Athanasopou- |
and analyzing univariate time series |
|
|
los, Slava Razbash, Drew Schmidt, |
forecasts, including exponential |
|
|
Zhenyu Zhou, Yousaf Khan, Chris- |
smoothing via state space models |
|
|
toph Bergmeir, and Earo Wang |
and automatic ARIMA modeling |
|
foreach |
Revolution Analytics, Steve |
foreach looping construct for R |
20 |
|
Weston |
|
|
foreign |
R Core members Saikat DebRoy, |
Reads data stored by Minitab, S, |
2 |
|
Roger Bivand, and others |
SAS, SPSS, Stata, Systat, dBase, |
|
|
|
and others |
|
gclus |
Catherine Hurley |
Clustering graphics |
1, 11 |
ggplot2 |
Hadley Wickam |
An implementation of the Grammar |
19, 20 |
|
|
of Graphics |
|
glmPerm |
Wiebke Werft and Douglas M. |
Permutation test for inference in |
12 |
|
Potter |
generalized linear models |
|
|
|
|
|
546 |
APPENDIX E Packages used in this book |
Table E.1 Contributed packages used in this book (continued)
Package |
Authors |
Description |
Chapter(s) |
|
|
|
|
gmodels |
Gregory R. Warnes. Includes R |
Various R programming tools for |
7 |
|
source code and/or documenta- |
model fitting |
|
|
tion contributed by Ben Bolker, |
|
|
|
Thomas Lumley, and Randall C. |
|
|
|
Johnson. Contributions from Ran- |
|
|
|
dall C. Johnson are copyright |
|
|
|
(2005) SAIC-Frederick, Inc. |
|
|
gplots |
Gregory R. Warnes. Includes R |
Various R programming tools for |
6, 9 |
|
source code and/or documenta- |
plotting data |
|
|
tion contributed by Ben Bolker, |
|
|
|
Lodewijk Bonebakker, Robert |
|
|
|
Gentleman, Wolfgang Huber, Andy |
|
|
|
Liaw, Thomas Lumley, Martin |
|
|
|
Maechler, Arni Magnusson, |
|
|
|
Steffen Moeller, Marc Schwartz, |
|
|
|
and Bill Venables. |
|
|
grid |
Paul Murrell |
A rewrite of the graphics layout |
19 |
|
|
capabilities, plus some support for |
|
|
|
interaction |
|
gridExtra |
Baptiste Auguie |
Functions for grid graphics |
19 |
gvlma |
Edsel A. Pena and Elizabeth H. |
Global validation of linear models |
8 |
|
Slate |
assumptions |
|
rhdf5 |
Bernd Fisher and Gregoire Paue |
Interface to the NCSA HDF5 library |
2 |
roxygen2 |
Hadley Wickham |
A Doxygen-like in-source documen- |
21 |
|
|
tation system |
|
hexbin |
Dan Carr, ported by Nicholas |
Hexagonal binning routines |
11 |
|
Lewin-Koh and Martin Maechler |
|
|
HH |
Richard M. Heiberger |
Support software for Statistical |
9 |
|
|
Analysis and Data Display by Hei- |
|
|
|
berger and Holland (Springer, 2004) |
|
kernlab |
Alexandros Karatzoglou, Alex |
Kernel-based machine learning lab |
17 |
|
Smola, and Kurt Hornik |
|
|
knitr |
Yihui Xie |
A general-purpose package for |
22 |
|
|
dynamic report generation in R |
|
Hmisc |
Frank E. Harrell Jr., with contribu- |
Harrell miscellaneous functions for |
2, 3, 7 |
|
tions from many other users |
data analysis, high-level graphics, |
|
|
|
utility operations, and more |
|
kmi |
Arthur Allignol |
Kaplan-Meier multiple imputation |
18 |
|
|
for the analysis of cumulative inci- |
|
|
|
dence functions in the competing |
|
|
|
risks setting |
|
|
|
|
|
APPENDIX E Packages used in this book |
547 |
Table E.1 Contributed packages used in this book (continued)
Package |
Authors |
Description |
Chapter(s) |
|
|
|
|
lattice |
Deepayan Sarkar |
Lattice graphics |
19 |
lavaan |
Yves Rosseel |
Functions for latent variable mod- |
14 |
|
|
els, including confirmatory factor |
|
|
|
analysis, structural equation model- |
|
|
|
ing, and latent growth-curve models |
|
lcda |
Michael Buecker |
Latent class-discriminant |
14 |
|
|
analysis |
|
leaps |
Thomas Lumley, using Fortran |
Regression subset selection, |
8 |
|
code by Alan Miller |
including exhaustive search |
|
lmPerm |
Bob Wheeler |
Permutation tests for linear models |
12 |
logregperm |
Douglas M. Potter |
Permutation test for inference in |
12 |
|
|
logistic regression |
|
longitudinal- |
Christophe Genolini |
Tools for longitudinal data |
18 |
Data |
|
|
|
lsa |
Fridolin Wild |
Latent semantic analysis |
14 |
ltm |
Dimitris Rizopoulos |
Latent trait models under item |
14 |
|
|
response theory |
|
lubridate |
Garrett Grolemund and Hadley |
Functions to identify and parse |
4 |
|
Wickham |
date-time data, extract and modify |
|
|
|
components of a date-time, per- |
|
|
|
form accurate math on date-times, |
|
|
|
and handle time zones and Daylight |
|
|
|
Savings Time |
|
MASS |
S original by Venables and |
Functions and datasets to support |
4, 5, 7, 8, |
|
Ripley. R port by Brian Ripley, |
Venables’ and Ripley’s Modern |
9, 12 |
|
following earlier work by Kurt |
Applied Statistics with S, 4th edition |
|
|
Hornik and Albrecht Gebhardt. |
(Springer, 2003) |
|
mlogit |
Yves Croissant |
Estimation of the multinomial logit |
13 |
|
|
model |
|
multcomp |
Torsten Hothorn, Frank Bretz, |
Simultaneous tests and confi- |
9, 12 |
|
Peter Westfall, Richard M. |
dence intervals for general linear |
|
|
Heiberger, and Andre Schuetzen- |
hypotheses in parametric models, |
|
|
meister |
including linear, generalized linear, |
|
|
|
linear mixed effects, and survival |
|
|
|
models |
|
mvnmle |
Kevin Gross, with help from |
ML estimation for multivariate nor- |
18 |
|
Douglas Bates |
mal data with missing values |
|
mvoutlier |
Moritz Gschwandtner and Peter |
Multivariate outlier detection based |
9 |
|
Filzmoser |
on robust methods |
|
|
|
|
|
548 |
APPENDIX E Packages used in this book |
Table E.1 Contributed packages used in this book (continued)
Package |
Authors |
Description |
Chapter(s) |
|
|
|
|
NbClustv |
Malika Charrad, Nadia Ghazzali, |
An examination of indices for deter- |
16 |
|
Veronique Boiteau, and Azam |
mining the number of clusters |
|
|
Niknafs |
|
|
ncdf, ncdf4 |
David Pierce |
Interface to Unidata netCDF data |
2 |
|
|
files |
|
nFactors |
Gilles Raiche |
Parallel analysis and non- |
14 |
|
|
graphical solutions to the Cattell |
|
|
|
scree test |
|
OpenMx |
Steven Boker, Michael Neale, |
Advanced structural equation |
14 |
|
Hermine Maes, Michael Wilde, |
modeling. |
|
|
Michael Spiegel, Timothy R. Brick, |
|
|
|
Jeffrey Spies, Ryne Estabrook, |
|
|
|
Sarah Kenny, Timothy Bates, |
|
|
|
Paras Mehta, and John Fox |
|
|
odfWeave |
Max Kuhn, with contributions from |
Sweave processing of Open |
22 |
|
Steve Weston, Nathan Coulter, |
Document Format (ODF) files |
|
|
Patrick Lenon, Zekai Otles, and |
|
|
|
the R Core Team |
|
|
pastecs |
Frederic Ibanez, Philippe Gros- |
Package for the analysis of |
7 |
|
jean, and Michele Etienne |
space-time ecological series |
|
party |
Torsten Hothorn, Kurt Hornik, |
A laboratory for recursive |
17 |
|
Carolin Strobl, and Achim Zeileis |
partitioning |
|
poLCA |
Drew Linzer and Jeffrey Lewis |
Polytomous variable latent-class |
14 |
|
|
analysis |
|
psych |
William Revelle |
Procedures for psychological, psy- |
7, 14 |
|
|
chometric, and personality research |
|
pwr |
Stephane Champely |
Basic functions for power analysis |
10 |
qcc |
Luca Scrucca |
Quality-control charts |
13 |
randomLCA |
Ken Beath |
Random effects latent-class |
14 |
|
|
analysis |
|
randomForest |
Fortran original by Leo Breiman |
Breiman and Cutler's random |
17 |
|
and Adele Cutler, R port by Andy |
forests for classification and |
|
|
Liaw and Matthew Wiener |
regression |
|
R2wd |
Christian Ritter |
Writes MS-Word documents from R |
22 |
rattle |
Graham Williams, Mark Vere Culp, |
Graphical user interface for data |
16, 17 |
|
Ed Cox, Anthony Nolan, Denis |
mining in R |
|
|
White, Daniele Medri, Akbar |
|
|
|
Waljee (OOB AUC for Random |
|
|
|
Forest), and Brian Ripley (original |
|
|
|
author of print.summary.nnet) |
|
|
|
|
|
|
APPENDIX E Packages used in this book |
549 |
Table E.1 Contributed packages used in this book (continued)
Package |
Authors |
Description |
Chapter(s) |
|
|
|
|
Rcmdr |
John Fox, with contributions from |
R Commander, a platform- |
Appendix A |
|
Liviu Andronic, Michael Ash, |
independent, basic-statistics |
|
|
Theophilius Boye, Stefano Calza, |
graphical user interface for R, |
|
|
Andy Chang, Philippe Grosjean, |
based on the tcltk package |
|
|
Richard Heiberger, G. Jay Kerns, |
|
|
|
Renaud Lancelot, Matthieu |
|
|
|
Lesnoff, Uwe Ligges, Samir |
|
|
|
Messad, Martin Maechler, |
|
|
|
Robert Muenchen, Duncan |
|
|
|
Murdoch, Erich Neuwirth, Dan |
|
|
|
Putler, Brian Ripley, Miroslav |
|
|
|
Ristic, and Peter Wolf |
|
|
reshape2 |
Hadley Wickham |
Flexibly reshape data |
4, 5, 7, 20 |
rgl |
Daniel Adler and Duncan Murdoch |
3D visualization device system |
11 |
|
|
(OpenGL) |
|
RJDBC |
Simon Urbanek |
Provides access to databases |
2 |
|
|
through the JDBC interface |
|
rms |
Frank E. Harrell, Jr. |
Regression modeling strategies: |
13 |
|
|
about 225 functions that assist |
|
|
|
with and streamline regression |
|
|
|
modeling, testing, estimations, |
|
|
|
validation, graphics, prediction, |
|
|
|
and typesetting |
|
robust |
Jiahui Wang, Ruben Zamar, Alfio |
A package of robust methods |
13 |
|
Marazzi, Victor Yohai, Matias |
|
|
|
Salibian-Barrera, Ricardo |
|
|
|
Maronna, Eric Zivot, David Rocke, |
|
|
|
Doug Martin, Martin Maechler, |
|
|
|
and Kjell Konis |
|
|
RODBC |
Brian Ripley and Michael Lapsley |
ODBC database access |
2 |
rpart |
Terry Therneau, Beth Atkinson, |
Recursive partitioning and regres- |
17 |
|
and Brian Ripley (author of the |
sion trees |
|
|
initial R port) |
|
|
ROracle |
David A. James and Jake Luciani |
Oracle database interface for R |
2 |
rrcov |
Valentin Todorov |
Robust location and scatter |
9 |
|
|
estimation, and robust multi- |
|
|
|
variate analysis with a high |
|
|
|
breakdown point |
|
sampling |
Yves Tillé and Alina Matei |
Functions for drawing and calibrat- |
4 |
|
|
ing samples |
|
scatterplot3d |
Uwe Ligges |
Plots a three-dimensional (3D) |
11 |
|
|
point cloud |
|
|
|
|
|
550 |
APPENDIX E Packages used in this book |
Table E.1 Contributed packages used in this book (continued)
Package |
Authors |
Description |
Chapter(s) |
|
|
|
|
sem |
John Fox, with contributions from |
Structural equation models |
14 |
|
Adam Kramer and Michael |
|
|
|
Friendly |
|
|
SeqKnn |
Ki-Yeol Kim and Gwan-Su Yi, |
Sequential KNN imputation method |
18 |
|
CSBio lab, Information and |
|
|
|
Communications University |
|
|
sm |
Adrian Bowman and Adelchi |
Smoothing methods for nonpara- |
6, 9 |
|
Azzalini. Ported to R by B. D. |
metric regression and density |
|
|
Ripley up to version 2.0, version |
estimation |
|
|
2.1 by Adrian Bowman and |
|
|
|
Adelchi Azzalini, version 2.2 by |
|
|
|
Adrian Bowman. |
|
|
vcd |
David Meyer, Achim Zeileis, and |
Functions for visualizing categori- |
1, 6, 7, |
|
Kurt Hornik |
cal data |
11, 12 |
vegan |
Jari Oksanen, F. Guillaume |
Ordination methods, diversity |
9 |
|
Blanchet, Roeland Kindt, Pierre |
analysis, and other functions for |
|
|
Legendre, R. B. O’Hara, Gavin L. |
community and vegetation |
|
|
Simpson, Peter Solymos, |
ecologists |
|
|
M. Henry, H. Stevens, and |
|
|
|
Helene Wagner |
|
|
VIM |
Matthias Templ, Andreas Alfons, |
Visualization and imputation of |
18 |
|
and Alexander Kowarik |
missing values |
|
xlsx |
Adrian A. Dragulescu |
Reads, writes, and formats Excel |
2 |
|
|
2007 (.xlsx) files |
|
XML |
Duncan Temple Lang |
Tools for parsing and generating |
2 |
|
|
XML in R and S-Plus |
|
|
|
|
|