Distance Between Functional Objects

Calculate the distance between functional objects over the defined range.

fdistmatrix(fd, subrange, distmethod)

Arguments

fd	A functional data object fd of fda package.
subrange	A vector of two values indicating the value range of functional object to calculate on.
distmethod	The method for calculating the distance matrix. Choose between "usc" and "manual". "usc" uses fda.usc::metric.lp() function while "manual" uses squared distance between functions. See Details.

Value

A distance matrix with diagonal value and the upper half.

Details

If choosing distmethod = "manual", the L2 distance between all pairs of functions \(y_i(t)\) and \(y_j(t)\) is given by: $$d_R(y_i, y_j) = \sqrt{\int_{a_r}^{b_r} [y_i(t) - y_j(t)]^2 dt}.$$

Examples

library(fda)
# Examples taken from fda::Data2fd()
data(gait)
# Function only works on two dimensional data
gait <- gait[, 1:5, 1]
gaitbasis3 <- create.fourier.basis(nbasis = 5)
gaitfd3 <- Data2fd(gait, basisobj = gaitbasis3)
#> 'y' is missing, using 'argvals'
#> 'argvals' is missing;  using seq( 0 ,  1 , length= 20 )

fdistmatrix(gaitfd3, c(0.2, 0.4), "usc")
#>          boy1     boy2     boy3     boy4     boy5
#> boy1 0.000000 1.508725 2.702666 2.959672 6.555149
#> boy2 1.508725 0.000000 2.089777 3.740105 7.326595
#> boy3 2.702666 2.089777 0.000000 5.570693 9.180862
#> boy4 2.959672 3.740105 5.570693 0.000000 3.643998
#> boy5 6.555149 7.326595 9.180862 3.643998 0.000000