This function creates a bivariate functional data object, which consists of two bases for expanding a functional data object of two variables, s and t, and a set of coefficients defining this expansion. The bases are contained in "basisfd" objects.
bifd (coef=matrix(0,2,1), sbasisobj=create.bspline.basis(),
tbasisobj=create.bspline.basis(), fdnames=defaultnames)A bivariate functional data object = a list of class 'bifd' with the following components:
the input 'coefs' possible with dimnames from dfnames if provided or from sbasisobj$names and tbasisobsj$names
a functional data basis object for the first argument s of the bivariate function.
a functional data basis object for the second argument t of the bivariate function.
a list of length 4 giving names for the dimensions of coefs, with one or two unused lists of names if length(dim(coefs)) is only two or one, respectively.
a two-, three-, or four-dimensional array containing coefficient values for the expansion of each set of bivariate function values=terms of a set of basis function values
If 'coef' is two dimensional, this implies that there is only one variable and only one replication. In that case, the first and second dimensions correspond to the basis functions for the first and second argument, respectively.
If 'coef' is three dimensional, this implies that there are multiple replicates on only one variable. In that case, the first and second dimensions correspond to the basis functions for the first and second argument, respectively, and the third dimension corresponds to replications.
If 'coef' has four dimensions, the fourth dimension corresponds to variables.
a functional data basis object for the first argument s of the bivariate function.
a functional data basis object for the second argument t of the bivariate function.
A list of length 4 containing dimnames for 'coefs' if it is a 4-dimensional array. If it is only 2- or 3-dimensional, the later components of fdnames are not applied to 'coefs'. In any event, the components of fdnames describe the following:
(1) The row of 'coefs' corresponding to the bases in sbasisobj. Defaults to sbasisobj[["names"]] if non-null and of the proper length, or to existing dimnames(coefs)[[1]] if non-null and of the proper length, and to 's1', 's2', ..., otherwise.
(2) The columns of 'coefs' corresponding to the bases in tbasisobj. Defaults to tbasisobj[["names"]] if non-null and of the proper length, or to existing dimnames(coefs)[[2]] if non-null and of the proper length, and to 't1', 't2', ..., otherwise.
(3) The replicates. Defaults to dimnames(coefs)[[3]] if non-null and of the proper length, and to 'rep1', ..., otherwise.
(4) Variable names. Defaults to dimnames(coefs)[[4]] if non-null and of the proper length, and to 'var1', ..., otherwise.
Spencer Graves
Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.
basisfd
objAndNames
Bspl2 <- create.bspline.basis(nbasis=2, norder=1)
Bspl3 <- create.bspline.basis(nbasis=3, norder=2)
(bBspl2.3 <- bifd(array(1:6, dim=2:3), Bspl2, Bspl3))
str(bBspl2.3)
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