f_to_srvf {fdasrvf}

Transformation to SRVF Space

Description

This function transforms functions in R^1 from their original functional space to the SRVF space.

Usage

f_to_srvf(f, time)

Arguments

f

Either a numeric vector of a numeric matrix or a numeric array specifying the functions that need to be transformed.

• If a vector, it must be of shape M and it is interpreted as a single 1-dimensional curve observed on a grid of size M.

• If a matrix, it must be of shape M \times N. In this case, it is interpreted as a sample of N curves observed on a grid of size M, unless M = 1 in which case it is interpreted as a single 1-dimensional curve observed on a grid of size M.

time

A numeric vector of length M specifying the grid on which the functions are evaluated.

Value

A numeric array of the same shape as the input array f storing the SRVFs of the original curves.

References

Srivastava, A., Wu, W., Kurtek, S., Klassen, E., Marron, J. S., May 2011. Registration of functional data using Fisher-Rao metric, arXiv:1103.3817v2.

Tucker, J. D., Wu, W., Srivastava, A., Generative models for functional data using phase and amplitude Separation, Computational Statistics and Data Analysis (2012), 10.1016/j.csda.2012.12.001.

Examples

q <- f_to_srvf(simu_data$f, simu_data$time)