This function transforms SRVFs back to the original functional space.
srvf_to_f(q, time, f0 = 0, multidimensional = FALSE)A numeric array of the same shape as the input q storing the
transformation of the SRSFs q back to the original functional space.
Either a numeric vector of a numeric matrix or a numeric array specifying the SRSFs 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 and multidimensional == FALSE, 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 \(M\).
If a matrix and multidimensional == TRUE,it must be of shape
\(L \times M\) and it is interpreted as a single \(L\)-dimensional
curve observed on a grid of size \(M\).
If a 3D array, it must be of shape \(L \times M \times N\) and it is interpreted as a sample of \(N\) \(L\)-dimensional curves observed on a grid of size \(M\).
A numeric vector of length \(M\) specifying the grid on which SRSFs are evaluated.
Either a numeric value or a numeric vector of or a numeric matrix specifying the initial value of the curves in the original functional space. It must be:
a value if q represents a single \(1\)-dimensional SRSF.
a vector of length \(L\) if q represents a single
\(L\)-dimensional SRSF.
a vector of length \(N\) if q represents a sample of \(N\)
\(1\)-dimensional SRSFs.
a matrix of shape \(L \times M\) if q represents a sample of \(N\)
\(L\)-dimensional SRSFs.
A boolean specifying if the curves are
multi-dimensional. This is useful when q is provided as a matrix to
determine whether it is a single multi-dimensional curve or a collection of
uni-dimensional curves. Defaults to FALSE.
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 amplitude and phase separation, Computational Statistics and Data Analysis (2012), 10.1016/j.csda.2012.12.001.
q <- f_to_srvf(simu_data$f, simu_data$time)
f <- srvf_to_f(q, simu_data$time, simu_data$f[1, ])
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