a vector of length 2 containing the initial and final values of the interval over which the functional data object can be evaluated.

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 = nbasis-1 (because the bases are const, sin, cos, ...).

the width of any interval over which the Fourier functions repeat themselves or are periodic.

an optional vector of integers specifiying basis functions to be dropped.

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 quadvals contains the quadrature points, and the second column the quadrature weights. A minimum of 5 values are required for each inter-knot interval, and that is often enough. For Simpson's rule, these points are equally spaced, and the weights are proportional to 1, 4, 2, 4, ..., 2, 4, 1.

an optional list of matrices with one row for each row of quadvals and one column for each basis function. The elements of the list correspond to the basis functions and their derivatives evaluated at the quadrature points contained in the first column of quadvals.

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 re-evaluation 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 basisvalues with code such as the following:

basisobj\$basisvalues <- vector("list",1)

basisobj\$basisvalues[[1]] <- list(args=evalargs, values=basismat)

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 nbasis = 3, names defaults to c('const', 'cos', 'sin'). If nbasis > 3, names defaults to c('const', outer(c('cos', 'sin'), 1:((nbasis-1)/2), paste, sep=”)).

If names = NA, no names are used.

an optional list used by selected plot functions to create custom axes. If this axes argument is not NULL, functions plot.basisfd, plot.fd, plot.fdSmooth plotfit.fd, plotfit.fdSmooth, and plot.Lfd will create axes via x$axes[[1]] and x$axes[-1]. The primary example of this is to create CanadianWeather plots using list("axesIntervals")