goffda (version 0.1.2)

fda.usc_efic: Auxiliary functions for the goffda package

Description

Auxiliary functions required for the methods implemented in the goffda package, as enhancements of the auxiliary functions fdata.cen and func.mean from the fda.usc-package.

Usage

fdata_cen(X_fdata, mean_X = func_mean(X_fdata))
func_mean(X_fdata)
inprod_fdata(X_fdata1, X_fdata2 = NULL, int_rule = "trapezoid",
  as_matrix = TRUE, verbose = FALSE)

Arguments

X_fdata

sample of functional data as an fdata object of length n.

mean_X

functional mean of X_fdata.

X_fdata1, X_fdata2

samples of functional data as fdata objects of lengths \(n_1\) and \(n_2\), respectively. Sample sizes can be different.

int_rule

quadrature rule for approximating the definite unidimensional integral: trapezoidal rule (int_rule = "trapezoid") and extended Simpson rule (int_rule = "Simpson") are available. Defaults to "trapezoid".

as_matrix

flag to indicate if inprod_fdata returns a matrix or the vector of its lower triangular part in column-major order. Defaults to TRUE.

verbose

whether to show or not information about the inprod_fdata procedure.

Author

Code iterated by Eduardo García-Portugués, Gonzalo Álvarez-Pérez, and Javier Álvarez-Liébana from the fda.usc-package originals.

Details

• func_mean: computes the functional mean of X_fdata.

• fdata_cen: centers the functional data X_fdata.

• inprod_fdata(X_fdata1): computes as a row vector the elements of the lower triangular part of the inner products matrix (X_fdata vs X_fdata). If as_matrix = TRUE, the matrix of inner products is given.

• inprod_fdata(X_fdata1, X_fdata2): computes the matrix of inner products (as_matrix = TRUE is forced) between X_fdata1 and X_fdata2.

Examples

## fdata_cen() vs fda.usc::fdata_cen()

data(phoneme, package = "fda.usc")
mlearn <- phoneme$learn[1:10, ]
plot(fda.usc::fdata.cen(mlearn)$Xcen)
plot(fdata_cen(mlearn))

## inprod_fdata() vs fda.usc::inprod.fdata()

# inprod_fdata between mlearn and mlearn: as a row vector

A <- fda.usc::inprod.fdata(fdata1 = mlearn)
A[upper.tri(A, diag = TRUE)]
inprod_fdata(X_fdata1 = mlearn, int_rule = "trapezoid", as_matrix = FALSE)

# inprod_fdata between mlearn and mlearn: as a matrix

A <- fda.usc::inprod.fdata(fdata1 = mlearn)
A
inprod_fdata(X_fdata1 = mlearn, int_rule = "trapezoid", as_matrix = TRUE)

# inprod_fdata between mlearn and mlearn2: as a matrix

mlearn2 <- phoneme$learn[11:30, ]
A <- fda.usc::inprod.fdata(fdata1 = mlearn, fdata2 = mlearn2)
A
B <- inprod_fdata(X_fdata1 = mlearn, X_fdata2 = mlearn2,
int_rule = "trapezoid", as_matrix = TRUE)
B
# \donttest{
## Efficiency comparisons

microbenchmark::microbenchmark(fda.usc::fdata.cen(mlearn), fdata_cen(mlearn),
                               times = 1e3, control = list(warmup = 20))

microbenchmark::microbenchmark(fda.usc::inprod.fdata(fdata1 = mlearn),
                               inprod_fdata(X_fdata1 = mlearn,
                               as_matrix = FALSE), times = 1e3,
                               control = list(warmup = 20))
# }