This is a convenience function that simplifies the task of appending univariate functional observations of two datasets to a unique univariate functional dataset.
append_fData(fD1, fD2)is the first functional dataset, stored into an fData object.
is the second functional dataset, stored into an fData object.
The function returns an fData object containing the union of fD1 and fD2
The two original datasets must be compatible, i.e. must be defined on the same grid. If we denote with \(X_1, \ldots, X_n\) the first dataset, defined over the grid \(I = t_1, \ldots, t_P\), and with \(Y_1, \ldots, Y_m\) the second functional dataset, defined on the same grid, the method returns the union dataset obtained by taking all the \(n + m\) observations together.
# Creating two simple univariate datasets
grid = seq(0, 2 * pi, length.out = 100)
values1 = matrix( c(sin(grid),
sin(2 * grid)), nrow = 2, ncol = length(grid),
byrow=TRUE)
values2 = matrix( c(cos(grid),
cos(2 * grid)), nrow = 2, ncol = length(grid),
byrow=TRUE)
fD1 = fData( grid, values1 )
fD2 = fData( grid, values2 )
# Appending them to a unique dataset
append_fData(fD1, fD2)
#> $t0
#> [1] 0
#>
#> $tP
#> [1] 6.283185
#>
#> $h
#> [1] 0.06346652
#>
#> $P
#> [1] 100
#>
#> $N
#> [1] 4
#>
#> $values
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] 0 0.06342392 0.1265925 0.1892512 0.2511480 0.3120334 0.3716625
#> [2,] 0 0.12659245 0.2511480 0.3716625 0.4861967 0.5929079 0.6900790
#> [3,] 1 0.99798668 0.9919548 0.9819287 0.9679487 0.9500711 0.9283679
#> [4,] 1 0.99195481 0.9679487 0.9283679 0.8738494 0.8052703 0.7237340
#> [,8] [,9] [,10] [,11] [,12] [,13] [,14]
#> [1,] 0.4297949 0.4861967 0.5406408 0.5929079 0.6427876 0.69007901 0.73459171
#> [2,] 0.7761465 0.8497254 0.9096320 0.9549022 0.9848078 0.99886734 0.99685478
#> [3,] 0.9029265 0.8738494 0.8412535 0.8052703 0.7660444 0.72373404 0.67850941
#> [4,] 0.6305527 0.5272255 0.4154150 0.2969204 0.1736482 0.04758192 -0.07924996
#> [,15] [,16] [,17] [,18] [,19] [,20]
#> [1,] 0.7761465 0.8145760 0.8497254 0.8814534 0.9096320 0.9341479
#> [2,] 0.9788024 0.9450008 0.8959938 0.8325699 0.7557496 0.6667690
#> [3,] 0.6305527 0.5800569 0.5272255 0.4722711 0.4154150 0.3568862
#> [4,] -0.2048067 -0.3270680 -0.4440666 -0.5539201 -0.6548607 -0.7452644
#> [,21] [,22] [,23] [,24] [,25] [,26]
#> [1,] 0.9549022 0.9718116 0.9848078 0.9938385 0.99886734 0.99987413
#> [2,] 0.5670599 0.4582265 0.3420201 0.2203105 0.09505604 -0.03172793
#> [3,] 0.2969204 0.2357589 0.1736482 0.1108382 0.04758192 -0.01586596
#> [4,] -0.8236766 -0.8888354 -0.9396926 -0.9754298 -0.99547192 -0.99949654
#> [,27] [,28] [,29] [,30] [,31] [,32]
#> [1,] 0.99685478 0.9898214 0.9788024 0.9638422 0.9450008 0.9223543
#> [2,] -0.15800140 -0.2817326 -0.4009305 -0.5136774 -0.6181590 -0.7126942
#> [3,] -0.07924996 -0.1423148 -0.2048067 -0.2664738 -0.3270680 -0.3863451
#> [4,] -0.98743889 -0.9594930 -0.9161085 -0.8579834 -0.7860531 -0.7014749
#> [,33] [,34] [,35] [,36] [,37] [,38]
#> [1,] 0.8959938 0.8660254 0.8325699 0.7957618 0.7557496 0.71269417
#> [2,] -0.7957618 -0.8660254 -0.9223543 -0.9638422 -0.9898214 -0.99987413
#> [3,] -0.4440666 -0.5000000 -0.5539201 -0.6056097 -0.6548607 -0.70147489
#> [4,] -0.6056097 -0.5000000 -0.3863451 -0.2664738 -0.1423148 -0.01586596
#> [,39] [,40] [,41] [,42] [,43] [,44]
#> [1,] 0.6667690 0.6181590 0.5670599 0.5136774 0.4582265 0.4009305
#> [2,] -0.9938385 -0.9718116 -0.9341479 -0.8814534 -0.8145760 -0.7345917
#> [3,] -0.7452644 -0.7860531 -0.8236766 -0.8579834 -0.8888354 -0.9161085
#> [4,] 0.1108382 0.2357589 0.3568862 0.4722711 0.5800569 0.6785094
#> [,45] [,46] [,47] [,48] [,49] [,50]
#> [1,] 0.3420201 0.2817326 0.2203105 0.1580014 0.09505604 0.03172793
#> [2,] -0.6427876 -0.5406408 -0.4297949 -0.3120334 -0.18925124 -0.06342392
#> [3,] -0.9396926 -0.9594930 -0.9754298 -0.9874389 -0.99547192 -0.99949654
#> [4,] 0.7660444 0.8412535 0.9029265 0.9500711 0.98192870 0.99798668
#> [,51] [,52] [,53] [,54] [,55] [,56]
#> [1,] -0.03172793 -0.09505604 -0.1580014 -0.2203105 -0.2817326 -0.3420201
#> [2,] 0.06342392 0.18925124 0.3120334 0.4297949 0.5406408 0.6427876
#> [3,] -0.99949654 -0.99547192 -0.9874389 -0.9754298 -0.9594930 -0.9396926
#> [4,] 0.99798668 0.98192870 0.9500711 0.9029265 0.8412535 0.7660444
#> [,57] [,58] [,59] [,60] [,61] [,62]
#> [1,] -0.4009305 -0.4582265 -0.5136774 -0.5670599 -0.6181590 -0.6667690
#> [2,] 0.7345917 0.8145760 0.8814534 0.9341479 0.9718116 0.9938385
#> [3,] -0.9161085 -0.8888354 -0.8579834 -0.8236766 -0.7860531 -0.7452644
#> [4,] 0.6785094 0.5800569 0.4722711 0.3568862 0.2357589 0.1108382
#> [,63] [,64] [,65] [,66] [,67] [,68]
#> [1,] -0.71269417 -0.7557496 -0.7957618 -0.8325699 -0.8660254 -0.8959938
#> [2,] 0.99987413 0.9898214 0.9638422 0.9223543 0.8660254 0.7957618
#> [3,] -0.70147489 -0.6548607 -0.6056097 -0.5539201 -0.5000000 -0.4440666
#> [4,] -0.01586596 -0.1423148 -0.2664738 -0.3863451 -0.5000000 -0.6056097
#> [,69] [,70] [,71] [,72] [,73] [,74]
#> [1,] -0.9223543 -0.9450008 -0.9638422 -0.9788024 -0.9898214 -0.99685478
#> [2,] 0.7126942 0.6181590 0.5136774 0.4009305 0.2817326 0.15800140
#> [3,] -0.3863451 -0.3270680 -0.2664738 -0.2048067 -0.1423148 -0.07924996
#> [4,] -0.7014749 -0.7860531 -0.8579834 -0.9161085 -0.9594930 -0.98743889
#> [,75] [,76] [,77] [,78] [,79] [,80]
#> [1,] -0.99987413 -0.99886734 -0.9938385 -0.9848078 -0.9718116 -0.9549022
#> [2,] 0.03172793 -0.09505604 -0.2203105 -0.3420201 -0.4582265 -0.5670599
#> [3,] -0.01586596 0.04758192 0.1108382 0.1736482 0.2357589 0.2969204
#> [4,] -0.99949654 -0.99547192 -0.9754298 -0.9396926 -0.8888354 -0.8236766
#> [,81] [,82] [,83] [,84] [,85] [,86]
#> [1,] -0.9341479 -0.9096320 -0.8814534 -0.8497254 -0.8145760 -0.7761465
#> [2,] -0.6667690 -0.7557496 -0.8325699 -0.8959938 -0.9450008 -0.9788024
#> [3,] 0.3568862 0.4154150 0.4722711 0.5272255 0.5800569 0.6305527
#> [4,] -0.7452644 -0.6548607 -0.5539201 -0.4440666 -0.3270680 -0.2048067
#> [,87] [,88] [,89] [,90] [,91] [,92]
#> [1,] -0.73459171 -0.69007901 -0.6427876 -0.5929079 -0.5406408 -0.4861967
#> [2,] -0.99685478 -0.99886734 -0.9848078 -0.9549022 -0.9096320 -0.8497254
#> [3,] 0.67850941 0.72373404 0.7660444 0.8052703 0.8412535 0.8738494
#> [4,] -0.07924996 0.04758192 0.1736482 0.2969204 0.4154150 0.5272255
#> [,93] [,94] [,95] [,96] [,97] [,98]
#> [1,] -0.4297949 -0.3716625 -0.3120334 -0.2511480 -0.1892512 -0.1265925
#> [2,] -0.7761465 -0.6900790 -0.5929079 -0.4861967 -0.3716625 -0.2511480
#> [3,] 0.9029265 0.9283679 0.9500711 0.9679487 0.9819287 0.9919548
#> [4,] 0.6305527 0.7237340 0.8052703 0.8738494 0.9283679 0.9679487
#> [,99] [,100]
#> [1,] -0.06342392 -2.449294e-16
#> [2,] -0.12659245 -4.898587e-16
#> [3,] 0.99798668 1.000000e+00
#> [4,] 0.99195481 1.000000e+00
#>
#> attr(,"class")
#> [1] "fData"