This is the constructor function for objects of the fd class.
Each function that sets up an object of this class must call this
function. This includes functions Data2fd,
smooth.basis, density.fd, and so forth
that estimate functional data objects that smooth or otherwise
represent data. Ordinarily, users of the functional data analysis
software will not need to call this function directly, but these notes
are valuable to understanding the components of a list of class
fd.
Usage
fd(coef=NULL, basisobj=NULL, fdnames=NULL)
Arguments
coef
a vector, matrix, or three-dimensional array of coefficients.
The first dimension (or elements of a vector) corresponds to basis
functions.
A second dimension corresponds to the number of functional
observations, curves or replicates. If coef is a vector, it
represents only a single functional observation.
If coef is an array, the third dimension corresponds to
variables for multivariate functional data objects.
A functional data object is "univariate" if coef is a vector
or matrix and "multivariate" if it is a three-dimensional array.
A list of length 3, each member being a string vector containing
labels for the levels of the corresponding dimension of the discrete
data. The first dimension is for argument values, and is given the
default name "time", the second is for replications, and is given
the default name "reps", and the third is for functions, and is
given the default name "values".
Details
To check that an object is of this class, use function
is.fd.
Normally only developers of new functional data analysis
functions will actually need to use this function.
Value
A functional data object (i.e., having class fd), which is a
list with components named coefs, basis, and
fdnames.
Source
Ramsay, James O., and Silverman, Bernard W. (2006), Functional
Data Analysis, 2nd ed., Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2002), Applied
Functional Data Analysis, Springer, New York
##
## default
##
fd()
##
## The simplest b-spline basis: order 1, degree 0, zero interior knots:
## a single step function
##
bspl1.1 <- create.bspline.basis(norder=1, breaks=0:1)
fd.bspl1.1 <- fd(0, basisobj=bspl1.1)
fd.bspl1.1a <- fd(basisobj=bspl1.1)
all.equal(fd.bspl1.1, fd.bspl1.1a)
# TRUE
## Not run:
fd.bspl1.1b <- fd(0)
Error in fd(0) :
Number of coefficients does not match number of basis functions.
... because fd by default wants to create a cubic spline
## End(Not run)
##
## Cubic spline: 4 basis functions
##
bspl4 <- create.bspline.basis(nbasis=4)
plot(bspl4)
parab4.5 <- fd(c(3, -1, -1, 3)/3, bspl4)
# = 4*(x-.5)^2
plot(parab4.5)
##
## Fourier basis
##
f3 <- fd(c(0,0,1), create.fourier.basis())
plot(f3)
# range over +/-sqrt(2), because
# integral from 0 to 1 of cos^2 = 1/2
# so multiply by sqrt(2) to get
# its square to integrate to 1.
##
## subset of an fd object
##
gaitbasis3 <- create.fourier.basis(nbasis=5)
gaitfd3 <- Data2fd(gait, basisobj=gaitbasis3)
gaitfd3[1]