This function implements a constructor for elements of S3 class
fData, aimed at implementing a representation of a functional
dataset.
fData(grid, values)the evenly spaced grid over which the functional observations are
measured. It must be a numeric vector of length P.
the values of the observations in the functional dataset,
provided in form of a 2D data structure (e.g. matrix or array) having as
rows the observations and as columns their measurements over the 1D grid of
length P specified in grid.
The function returns a S3 object of class fData, containing
the following elements:
"N": the number of elements in the dataset;
"P": the number of points in the 1D grid over which elements
are measured;
"t0": the starting point of the 1D grid;
"tP": the ending point of the 1D grid;
"values": the matrix of measurements of the functional
observations on the 1D grid provided with grid.
The functional dataset is represented as a collection of measurement of the observations on an evenly spaced, 1D grid of discrete points (representing, e.g. time), namely, for functional data defined over a grid \([t_0, t_1, \ldots, t_{P-1}]\):
$$ f_{i,j} = f_i( t_0 + j h ), \quad h = \frac{t_P - t_0}{N}, \quad \forall j = 1, \ldots, P, \quad \forall i = 1, \ldots N.$$
# Defining parameters
N = 20
P = 1e2
# One dimensional grid
grid = seq( 0, 1, length.out = P )
# Generating an exponential covariance function (see related help for more
# information )
C = exp_cov_function( grid, alpha = 0.3, beta = 0.4 )
# Generating a synthetic dataset with a gaussian distribution and
# required mean and covariance function:
values = generate_gauss_fdata( N,
centerline = sin( 2 * pi * grid ),
Cov = C )
fD = fData( grid, values )