fdarm-ch02.R
In fda: Functional Data Analysis

###
### Ramsay, Hooker & Graves (2009)
### Functional Data Analysis with R and Matlab (Springer)
###

#  Remarks and disclaimers

#  These R commands are either those in this book, or designed to
#  otherwise illustrate how R can be used in the analysis of functional
#  data.
#  We do not claim to reproduce the results in the book exactly by these
#  commands for various reasons, including:
#    -- the analyses used to produce the book may not have been
#       entirely correct, possibly due to coding and accuracy issues
#       in the functions themselves
#    -- we may have changed our minds about how these analyses should be
#       done since, and we want to suggest better ways
#    -- the R language changes with each release of the base system, and
#       certainly the functional data analysis functions change as well
#    -- we might choose to offer new analyses from time to time by
#       augmenting those in the book
#    -- many illustrations in the book were produced using Matlab, which
#       inevitably can imply slightly different results and graphical
#       displays
#    -- we may have changed our minds about variable names.  For example,
#       we now prefer "yearRng" to "yearRng" for the weather data.
#    -- three of us wrote the book, and the person preparing these scripts
#       might not be the person who wrote the text
#  Moreover, we expect to augment and modify these command scripts from time
#  to time as we get new data illustrating new things, add functionality
#  to the package, or just for fun.

###
### ch. 2.  Essential Comparisons of the Matlab and R Languages
###

#  load the fda package

library(fda)

#  display the data files associated with the fda package

data(package='fda')

#  start the HTML help system if you are connected to the Internet, in
#  order to open the R-Project documentation index page in order to obtain
#  information about R or the fda package.

help.start()

##
## Section 2.1 A Quick Comparison of Matlab and R Syntax
##

# Names with periods:

min.fourier.basis = create.fourier.basis()

# structure of this fourier basis object:

str(min.fourier.basis)

# One component of this list of class 'basisfd'

min.fourier.basis$type

# create a vector

rng = c(0, 1)

# Access a component of a vector

rng[2]

# Logical values:

TRUE
FALSE

# T and F are variables
# by default are TRUE and FALSE, respectively,

T
F

# but can be redefined:

F = TRUE
if(F)cat('TRUE')

# alternative

F = c('Do', 'not', 'use', 'F', 'as', 'a', 'logical.')

# The following will now throw an error, and illustrates why only
# TRUE and FALSE ought to be used as logical constants:

# if (F) cat('TRUE')

# addition?

1 + TRUE # = 2

# Any line that is not syntactically complete
# is assumed to continue to the next line

c("like",
  'This')

"line can end in ';'";
"but not required."

# Section 2.1.2.  Using Functions

b3.4    = create.bspline.basis(norder=3, breaks=c(0, .5, 1))
fdPar3  = fdPar(b3.4, lambda=1)
fd3.4s0 = smooth.basis(0:1, 0:1, fdPar3)

class(fd3.4s0) # fdSmooth

# its 'fd' component

myfdobj. = fd3.4s0$fd

# or directly with the function call in one line

myfdobj = smooth.basis(0:1, 0:1, fdPar3)$fd

all.equal(myfdobj., myfdobj)

fd3.4s0$gcv

# specifying arguments by name not in the standard order

myfdobj = smooth.basis(y=c(1,1,2), argvals=seq(0, 1, .5), fdPar3)$fd

##
## Section 2.2 Singleton Index Issues
##

temp = matrix(c(1,2,3,4),2,2)
class(temp)
class(temp[,1])
temp[,1] # not a matrix
temp[,1, drop=FALSE] # still a matrix

index = 1:2
temp[, index] # matrix
index = 1
temp[, index] # not a matrix

index = 1:2
temp[, index][, 1] # OK
index = 1
# temp[, index][, 1] # Error

# 3-d array

A      = array(1:2, dim=c(1, 2, 1))
a1     = A[, 1, ] # scalar
dim(a1)= dim(A)[-2]
a1 # 1 x 1 matrix

##
## Section 2.3 Classes and Objects in R and Matlab
##

default.fd = fd()
is.list(default.fd)

class(default.fd$basis)

plot(default.fd)

# same as

plot.fd(default.fd)

attributes(default.fd)

coef(default.fd)

# same as

default.fd$coefs

# fdPar example

rangeval  = c(-3,3)
x         =  rnorm(50)
x[x < -3] = -2.99
x[x >  3] =  2.99
basisobj  = create.bspline.basis(rangeval, 11)
Wfd0      = fd(matrix(0,11,1), basisobj)
WfdParobj = fdPar(Wfd0)

coef(WfdParobj)
WfdParobj$coefs # NULL
WfdParobj$fd$coefs # OK

# str = structure

str(WfdParobj)

# All methods for the generic function 'coef' in attached packages

methods(coef)
library('nlme')

# add 'coef' methods for objects defined in the 'nlme' package

methods(coef)

methods(class='fd') # methods for objects of class 'fd'

##
## Section 2.4 More to Read
##