Functional Frobenius norm
Computes the functional Frobenius norm.
frobenius_norm_funct(m, PM)
m |
Data matrix with the residuals. This matrix has the same dimensions as the original data matrix. |
PM |
Penalty matrix obtained with |
Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.
Real number.
Irene Epifanio
Epifanio, I., Functional archetype and archetypoid analysis, 2016. Computational Statistics and Data Analysis 104, 24-34, https://doi.org/10.1016/j.csda.2016.06.007
library(fda) mat <- matrix(1:9, nrow = 3) fbasis <- create.fourier.basis(rangeval = c(1, 32), nbasis = 3) PM <- eval.penalty(fbasis) frobenius_norm_funct(mat, PM)
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