This function carries out the warping of elements of a univariate functional dataset by using a set of pre-computed warping functions.
warp(fData, warpings)the functional dataset whose observations must be warped in
form of fData object.
the warping functions \(H_1, \ldots, H_N\), in form of
fData object, defined over the registered/warped grid.
The function returns the univariate functional dataset of warped
functions, in form of fData object.
Given a univariate functional dataset \(X_1(t), \ldots, X_N(t)\) and a set of warping functions \(H_1(t), \ldots, H_N(t)\), such that: $$ H_i : s \longrightarrow t = H_i(s), \quad \forall i = 1, \ldots, N,$$ where \(s\) spans the warped (or registered) grid and \(t\) spans the original grid, the function computes the warping given by the following composition: $$ X_1 \circ H_1(t), \ldots, X_N \circ H_N(t).$$
set.seed( 1618033 )
N = 30
t0 = 0
t1 = 1
P = 1e3 + 1
time_grid = seq( t0, t1, length.out = P )
means = round( runif( N,
t0 + (t1 - t0) / 8,
t1 - (t1 - t0) / 8 ), 3 )
Data = matrix( sapply( means,
function( m )( dnorm( time_grid, mean = m, sd = 0.05 ) ) ),
ncol = P, nrow = N, byrow = TRUE )
fD = fData( time_grid, Data )
# Piecewise linear warpings
template_warping = function( m )( c( time_grid[ time_grid <= 0.5 ] * m / 0.5,
( time_grid[ time_grid > 0.5 ]
- 0.5 ) * (1 - m ) / 0.5 + m ) )
warpings = matrix( sapply( means, template_warping ),
ncol = P,
nrow = N, byrow = TRUE )
wfD = fData( time_grid, warpings )
fD_warped = warp( fD, wfD )
dev.new()
oldpar <- par(mfrow = c(1, 1))
par(mfrow = c(1, 3))
plot( fD,
main = 'Unregistered functions', xlab = 'actual grid', ylab = 'values' )
plot( wfD,
main = 'Warping functions', xlab = 'registered grid',
ylab = 'actual grid' )
plot( fD_warped,
main = 'Warped functions', xlab = 'registered grid',
ylab = 'values' )
par(oldpar)