# area_under_curve: Area under curve of elements of univariate functional data In roahd: Robust Analysis of High Dimensional Data

## Description

This method computes the (signed) area under the curve of elements of a univariate functional dataset, namely, their integral.

## Usage

 1 area_under_curve(fData) 

## Arguments

 fData the functional dataset containing elements whose areas under the curve have to be computed, in form of fData object.

## Details

Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t), defined over a compact interval I=[a,b] and observed on an evenly spaced 1D grid [a = t_0, t_1, …, t_{P-1} = b] \subset I, the function computes:

∑_{i=1}^{P-2} \frac{X(t_{i+1}) - X(t_{i-1})}{2} h \approx \int_a^b X(t) dt,

where h = t_1 - t_0.

## Value

The function returns a numeric vector containing the values of areas under the curve for all the elements of the functional dataset fData.

area_ordered, fData
  1 2 3 4 5 6 7 8 9 10 11 P = 1e3 grid = seq( 0, 1, length.out = P ) fD = fData( grid, matrix( c( sin( 2 * pi * grid ), cos( 2 * pi * grid ), 4 * grid * ( 1 - grid ) ), nrow = 3, ncol = P, byrow = TRUE ) ) plot( fD ) area_under_curve( fD )