adamethods (version 1.2.1)

frobenius_norm_funct: Functional Frobenius norm

Description

Computes the functional Frobenius norm.

Usage

frobenius_norm_funct(m, PM)

Arguments

m

Data matrix with the residuals. This matrix has the same dimensions as the original data matrix.

PM

Penalty matrix obtained with eval.penalty.

Value

Real number.

Details

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.

References

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

Examples

# NOT RUN {
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)
                 
# }