frobenius_norm_funct {adamethods}

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.

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.

Value

Real number.

Author(s)

Irene Epifanio

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

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)