create.fourier.basis  R Documentation 
Create an Fourier basis object defining a set of Fourier functions with specified period.
create.fourier.basis(rangeval=c(0, 1), nbasis=3,
period=diff(rangeval), dropind=NULL, quadvals=NULL,
values=NULL, basisvalues=NULL, names=NULL,
axes=NULL)
rangeval 
a vector of length 2 containing the initial and final values of the interval over which the functional data object can be evaluated. 
nbasis 
positive odd integer: If an even number is specified, it is rounded
up to the nearest odd integer to preserve the pairing of sine and
cosine functions. An even number of basis functions only makes
sense when there are always only an even number of observations at
equally spaced points; that case can be accommodated using dropind =
nbasis1 (because the bases are 
period 
the width of any interval over which the Fourier functions repeat themselves or are periodic. 
dropind 
an optional vector of integers specifiying basis functions to be dropped. 
quadvals 
an optional matrix with two columns and a number of rows equal to
the number of quadrature points for numerical evaluation of the
penalty integral. The first column of 
values 
an optional list of matrices with one row for each row of

basisvalues 
an optional list of lists, allocated by code such as
vector("list",1). This field is designed to avoid evaluation of a
basis system repeatedly at a set of argument values. Each sublist
corresponds to a specific set of argument values, and must have at
least two components: a vector of argument values and a matrix of
the values the basis functions evaluated at the arguments in the
first component. Third and subsequent components, if present,
contain matrices of values their derivatives. Whenever function
getbasismatrix is called, it checks the first list in each row to
see, first, if the number of argument values corresponds to the size
of the first dimension, and if this test succeeds, checks that all
of the argument values match. This takes time, of course, but is
much faster than reevaluation of the basis system. Even this time
can be avoided by direct retrieval of the desired array. For
example, you might set up a vector of argument values called
"evalargs" along with a matrix of basis function values for these
argument values called "basismat". You might want too use tags like
"args" and "values", respectively for these. You would then assign
them to basisobj$basisvalues < vector("list",1) basisobj$basisvalues[[1]] < list(args=evalargs, values=basismat) 
names 
either a character vector of the same length as the number of basis functions or a simple stem used to construct such a vector. If If names = NA, no names are used. 
axes 
an optional list used by selected 
Functional data objects are constructed by specifying a set of basis functions and a set of coefficients defining a linear combination of these basis functions. The Fourier basis is a system that is usually used for periodic functions. It has the advantages of very fast computation and great flexibility. If the data are considered to be nonperiod, the Fourier basis is usually preferred. The first Fourier basis function is the constant function. The remainder are sine and cosine pairs with integer multiples of the base period. The number of basis functions generated is always odd.
a basis object with the type fourier
.
Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.
basisfd
,
create.bspline.basis
,
create.constant.basis
,
create.exponential.basis
,
create.monomial.basis
,
create.polygonal.basis
,
create.power.basis
# Create a minimal Fourier basis for annual data
# using 3 basis functions
yearbasis3 < create.fourier.basis(c(0,365),
axes=list("axesIntervals") )
# plot the basis
oldpar < par(no.readonly=TRUE)
plot(yearbasis3)
# Identify the months with letters
plot(yearbasis3, axes=list('axesIntervals', labels=monthLetters))
# The same labels as part of the basis object
yearbasis3. < create.fourier.basis(c(0,365),
axes=list("axesIntervals", labels=monthLetters) )
plot(yearbasis3.)
# set up the Fourier basis for the monthly temperature data,
# using 9 basis functions with period 12 months.
monthbasis < create.fourier.basis(c(0,12), 9, 12.0)
# plot the basis
plot(monthbasis)
# Create a false Fourier basis using 1 basis function.
falseFourierBasis < create.fourier.basis(nbasis=1)
# plot the basis: constant
plot(falseFourierBasis)
par(oldpar)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.