Unexplained behaviour with prinComp and grid2PCs

[matteodefelice]

Hi,
I was planning to use prinComp and grid2PCs to implement a sort of cross-validation for the use of PCA with seasonal forecasts.
Here the grid test file I have used: https://www.dropbox.com/s/a699e6wq4zae0vm/monthly-erain.rda?dl=0

Here a reproducible example:

rm(list = ls())
library(transformeR)
load(file = 'monthly-erain.rda')
orig_princomp <- prinComp(obs, 4)
get_pc <- PC2grid(orig_princomp)

# reapply on the same grid
reapplied_princomp = grid2PCs(orig_princomp, obs)
# compare PCs
plot(reapplied_princomp[[1]][,1] ~ get_pc$Data[1,,1,1])

If I use grid2PCs on the same grid file used to compute the prinComp I would expect to have the same identical PCs, am I wrong? Instead they are similar but not identical, what happens here?

[jbedia]

Because you are retaining the first 4 EOFs, you are not capturing the whole variance, but just a large proportion of it. Therefore, when you recover the original field from the PCs, the recovered field is not identical to the original one (it is very similar though...). Try to set the explained variance to 100% and you should obtain exactly the same grid (setting aside minor rounding errors...):

orig_princomp <- prinComp(obs, v.exp = 1)