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fda (version 1.2.3)

basisfd: Define a Functional Basis Object

Description

This is the constructor function for objects of the basisfd class. Each function that sets up an object of this class must call this function. This includes functions create.bspline.basis, create.constant.basis, create.fourier.basis, and so forth that set up basis objects of a specific type. Ordinarily, user of the functional data analysis software will not need to call this function directly, but these notes are valuable to understanding what the "slots" or "members" of the basisfd class are.

Usage

basisfd(type, rangeval, nbasis, params,
        dropind=NULL, quadvals=NULL,
        values=vector("list", 0))

Arguments

type
a character string indicating the type of basis. Currently, there are eight possible types:

  1. bspline
  2. const
  3. expon
  4. fourier
  5. monom
  6. polyg
  7. polynom
  8. power

rangeval
a vector of length 2 containing the lower and upper boundaries of the range over which the basis is defined
nbasis
the number of basis functions
params
a vector of parameter values defining the basis
dropind
a vector of integers specifiying the basis functions to be dropped, if any. For example, if it is required that a function be zero at the left boundary, this is achieved by dropping the first basis function, the only one that is nonzero at that p
quadvals
a matrix with two columns and a number of rows equal to the number of argument values used to approximate an integral using Simpson's rule. The first column contains these argument values. A minimum of 5 values are required for each inter-knot int
values
a list containing the basis functions and their derivatives evaluated at the quadrature points contained in the first column of quadvals.

Value

  • an object of class basisfd

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

Details

Previous versions of the 'fda' software used the name basis for this class, and the code in Matlab still does. However, this class name was already used elsewhere in the S languages, and there was a potential for a clash that might produce mysterious and perhaps disastrous consequences.

To check that an object is of this class, use function is.basis.

It is comparatively simple to add new basis types. The code in the following functions needs to be estended to allow for the new type: basisfd, use.proper.basis, getbasismatrix and getbasispenalty. In addition, a new "create" function should be written for the new type, as well as functions analogous to fourier and fourierpen for evaluating basis functions for basis penalty matrices.

The "create" function names are rather long, and users who mind all that typing might be advised to modify these to versions with shorter names, such as "splbas", "conbas", and etc. However, a principle of good programming practice is to keep the code readable, preferably by somebody other than the programmer. Normally only developers of new basis types will actually need to use this function, so no examples are provided.

See Also

is.basis, is.eqbasis, plot.basisfd, getbasismatrix, getbasispenalty, create.bspline.basis, create.constant.basis, create.exponential.basis, create.fourier.basis, create.monomial.basis, create.polygonal.basis, create.polynomial.basis, create.power.basis