This function implements an order relation between univariate functional data based on the area-under-curve relation, that is to say a pre-order relation obtained by comparing the area-under-curve of two different functional data.
the first univariate functional dataset containing elements to
be compared, in form of
the second univariate functional dataset containing elements to
be compared , in form of
Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t) and another functional dataset Y_1(t), Y_2(t), …, Y_M(t) defined over the same compact interval I=[a,b], the function computes the area-under-curve (namely, the integral) in both the datasets, and checks whether the first ones are lower or equal than the second ones.
By default the function tries to compare each X_i(t) with the corresponding Y_i(t), thus assuming N=M, but when either N=1 or M=1, the comparison is carried out cycling over the dataset with fewer elements. In all the other cases (N\neq M, and either N \neq 1 or M \neq 1) the function stops.
The function returns a logical vector of length \max(N,M) containing the value of the predicate for all the corresponding elements.
Valencia, D., Romo, J. and Lillo, R. (2015). A Kendall correlation
coefficient for functional dependence, Universidad Carlos III de Madrid
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P = 1e3 grid = seq( 0, 1, length.out = P ) Data_1 = matrix( c( 1 * grid, 2 * grid ), nrow = 2, ncol = P, byrow = TRUE ) Data_2 = matrix( 3 * ( 0.5 - abs( grid - 0.5 ) ), nrow = 1, byrow = TRUE ) Data_3 = rbind( Data_1, Data_1 ) fD_1 = fData( grid, Data_1 ) fD_2 = fData( grid, Data_2 ) fD_3 = fData( grid, Data_3 ) area_ordered( fD_1, fD_2 ) area_ordered( fD_2, fD_3 )
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