# fData: 'S3' Class for univariate functional datasets. In roahd: Robust Analysis of High Dimensional Data

## Description

This function implements a constructor for elements of S3 class fData, aimed at implementing a representation of a functional dataset.

## Usage

 1 fData(grid, values) 

## Arguments

 grid the evenly spaced grid over which the functional observations are measured. It must be a numeric vector of length P. values the values of the observations in the functional dataset, prodived 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.

## Details

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, …, t_{P-1}]:

f_{i,j} = f_i( t_0 + j h ), \quad h = \frac{t_P - t_0}{N}, \quad \forall j = 1, …, P, \quad \forall i = 1, … N.

## Value

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.

generate_gauss_fdata, sub-.fData
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 # 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 )