basisfd {fda} | R Documentation |
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.
basisfd(type, rangeval, nbasis, params, dropind=NULL, quadvals=NULL, values=vector("list", 0))
type |
a character string indicating the type of basis. Currently,
there are eight possible types:
|
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 point. Default value NULL. |
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 interval, and that is often enough. These are equally spaced between two adjacent knots. The second column contains the weights used for Simpson's rule. These are proportional to 1, 4, 2, 4, ..., 2, 4, 1. |
values |
a list containing the basis functions and their derivatives
evaluated at the quadrature points contained in the first
column of quadvals .
|
Older versions of the 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.
an object of class basisfd
is.basis, is.eqbasis, plot.basis, 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