# fd

##### Define a Functional Data Object

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 `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.if(is.null(coef)) coef <- rep(0, basisobj[['nbasis']])

- basisobj
a functional basis object defining the basis

`if(is.null(basisobj)){ if(is.null(coef)) basisobj <- basisfd() else { rc <- range(coef) if(diff(rc)==0) rc <- rc+0:1 nb <- max(4, nrow(coef)) basisobj <- create.bspline.basis(rc, nbasis = nb) } }`

- fdnames
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`

.

##### See Also

`smooth.basis`

`smooth.fdPar`

`smooth.basisPar`

`density.fd`

`create.bspline.basis`

`arithmetic.fd`

##### Examples

```
# NOT RUN {
##
## 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)
# }
# NOT RUN {
all.equal(fd.bspl1.1, fd.bspl1.1a)
# }
# NOT RUN {
# 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
# }
# 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)
gaittime = (1:20)/21
gaitfd3 <- smooth.basis(gaittime, gait, gaitbasis3)$fd
gaitfd3[1]
# }
```

*Documentation reproduced from package fda, version 5.1.9, License: GPL (>= 2)*