# Flip functional data objects This function flips an object `newObject` of class `funData`, `irregFunData` or `multiFunData` with respect to a reference object `refObject` of the same class (or of class `funData`, if `newObject` is irregular). This is particularly useful when dealing with functional principal components, as they are only defined up to a sign change. For details, see below. ```r flipFuns(refObject, newObject, ...) ``` ## Arguments - `refObject`: An object of class `funData`, `irregFunData` or `multiFunData` that serves as reference. It must have the same number of observations as `newObject` or have only one observation. In this case, all observations in `newObject` are flipped with respect to this single observation. - `newObject`: An object of class `funData`, `irregFunData` or `multiFunData` that is to be flipped with respect to `refObject`. - `...`: Further parameters passed to `norm`. ## Returns An object of the same class as `newData` with flipped observations. ## Details Functional principal component analysis is an important tool in functional data analysis. Just as eigenvectors, eigenfunctions (or functional principal components) are only defined up to a sign change. This may lead to difficulties in simulation studies or when bootstrapping pointwise confidence bands, as in these cases one wants the estimates to have the same "orientation" as the true function (in simulation settings) or the non-bootstrapped estimate (when calculating bootstrap confidence bands). This function allows to flip (i.e. multiply by $-1$) all observations in `newObject` that have a different orientation than their counterparts in `refData`. Technically, the function compares the distance between `newObject` and `refObject` $$ |||f_\mathrm{new} - f_\mathrm{ref}|||||| f_{new} -f_{ref}||| $$ and the distance between `newObject` and `-1 * refObject` $$ |||f_\mathrm{new} + f_\mathrm{ref}|||.||| f_{new} +f_{ref}|||. $$ If `newObject` is closer to `-1 * refObject`, it is flipped, i.e. multiplied by -1. ## Warning The function is currently implemented only for functional data with one- and two-dimensional domains. ## Examples ```r ### Univariate argvals <- seq(0,2*pi,0.01) refData <- funData(argvals, rbind(sin(argvals))) # one observation as reference newData <- funData(argvals, outer(sample(c(-1,1), 11, replace = TRUE) * seq(0.75, 1.25, by = 0.05), sin(argvals))) oldpar <- par(no.readonly = TRUE) par(mfrow = c(1,2)) plot(newData, col = "grey", main = "Original data") plot(refData, col = "red", lwd = 2, add = TRUE) plot(flipFuns(refData, newData), col = "grey", main = "Flipped data") plot(refData, col = "red", lwd = 2, add = TRUE) ### Univariate (irregular) ind <- replicate(11, sort(sample(1:length(argvals), sample(5:10,1)))) # sample observation points argvalsIrreg <- lapply(ind, function(i){argvals[i]}) argvalsIrregAll <- unique(sort(unlist(argvalsIrreg))) # one observation as reference (fully observed) refDataFull <- funData(argvals, rbind(sin(argvals))) # one observation as reference (irregularly observed) refDataIrreg <- irregFunData(argvals = list(argvalsIrregAll), X = list(sin(argvalsIrregAll))) newData <- irregFunData(argvals = argvalsIrreg, X = mapply(function(x, a, s){s * a * sin(x)}, x = argvalsIrreg, a = seq(0.75, 1.25, by = 0.05), s = sample(c(-1,1), 11, replace = TRUE))) plot(newData, col = "grey", main = "Original data (regular reference)") plot(refDataFull, col = "red", lwd = 2, add = TRUE) plot(flipFuns(refDataFull, newData), col = "grey", main = "Flipped data") plot(refDataFull, col = "red", lwd = 2, add = TRUE) plot(newData, col = "grey", main = "Original data (irregular reference)") plot(refDataIrreg, col = "red", lwd = 2, add = TRUE) plot(flipFuns(refDataIrreg, newData), col = "grey", main = "Flipped data") plot(refDataIrreg, col = "red", lwd = 2, add = TRUE) ### Multivariate refData <- multiFunData(funData(argvals, rbind(sin(argvals))), # one observation as reference funData(argvals, rbind(cos(argvals)))) sig <- sample(c(-1,1), 11, replace = TRUE) newData <- multiFunData(funData(argvals, outer(sig * seq(0.75, 1.25, by = 0.05), sin(argvals))), funData(argvals, outer(sig * seq(0.75, 1.25, by = 0.05), cos(argvals)))) par(mfrow = c(2,2)) plot(newData[[1]], col = topo.colors(11), main = "Original data") plot(refData[[1]], col = "red", lwd = 2, add = TRUE) plot(newData[[2]], col = topo.colors(11), main = "Original data") plot(refData[[2]], col = "red", lwd = 2, add = TRUE) plot(flipFuns(refData, newData)[[1]], col = topo.colors(11), main = "Flipped data") plot(refData[[1]], col = "red", lwd = 2, add = TRUE) plot(flipFuns(refData, newData)[[2]], col = topo.colors(11), main = "Flipped data") plot(refData[[2]], col = "red", lwd = 2, add = TRUE) par(oldpar) ``` ## See Also `funData`, `irregFunData`, `multiFunData`, `Arith.funData`

flipFuns function