getarrvec(nlevels, sort=T)
TRUE
then compute permutation for indexing a
wst object. If FALSE
then
compute permutation for indexing a wd
object.
nlevels-1
columns.
Column 1 corresponds to scale level nlevels-1
in the
wst object, and column nlevels-1
corresponds to scale level 1
in the
wst object. Replace wst
by wd if sort=FALSE
.
getarrvec
function to compute the
permutation which maps coefficients from one ordering to the other.
This function returns a matrix which gives the necessary permutations
for scale levels 1 to nlevels-1
.
If you want to get the permutation for the level 0 coefficients of
the wst object you will have to call
the levarr function directly.
This permutation is described in Nason, Sapatinas and Sawczenko, 1998.
The function that actually computes the permutations is levarr. This function just combines the results from levarr.
# # What would the permutation be for a wst # object with 4 levels? # arrvec <- getarrvec(4) arrvec # [,1] [,2] [,3] # [1,] 1 1 1 # [2,] 9 9 9 # [3,] 2 5 5 # [4,] 10 13 13 # [5,] 3 2 3 # [6,] 11 10 11 # [7,] 4 6 7 # [8,] 12 14 15 # [9,] 5 3 2 #[10,] 13 11 10 #[11,] 6 7 6 #[12,] 14 15 14 #[13,] 7 4 4 #[14,] 15 12 12 #[15,] 8 8 8 #[16,] 16 16 16 # # The permutation for level 3 is in column 1 # The permutation for level 2 is in column 2 # The permutation for level 1 is in column 3. # # The following shows that the above is the right permutation (for level 2 # at least. # # Start off with some random normal data! # myrand <- rnorm(1:16) # # Now take both the time ordered non-decimated wavelet # transform and the packet ordered non-decimated wavelet # transform. # myrwdS <- wd(myrand, type="station") myrwst <- wst(myrand) # # Let's look at the level 2 coefficients of myrwdS # accessD(myrwdS, level=2) # [1] -0.73280829 -0.97892279 1.33305777 1.46320165 -0.94790098 # [6] -1.39276215 0.40023757 0.82517249 -0.56317955 -0.89408713 #[11] 0.77166463 1.56204870 -0.34342230 -1.64133182 0.08235115 #[16] 1.05668106 # # Let's look at the level 2 coefficients of myrwst # accessD(myrwst, level=2) # [1] -0.73280829 -0.94790098 -0.56317955 -0.34342230 1.33305777 # [6] 0.40023757 0.77166463 0.08235115 -0.97892279 -1.39276215 #[11] -0.89408713 -1.64133182 1.46320165 0.82517249 1.56204870 #[16] 1.05668106 # # O.k. So the coefficients are the same, but they are not in the # same order as in myrwdS. So let's use the permutation in the # second column of arrvec to reorder the myrwst coefficients # to have the same order as the myrwdS ones # accessD(myrwst, level=2)[arrvec[,2]] # [1] -0.73280829 -0.97892279 1.33305777 1.46320165 -0.94790098 # [6] -1.39276215 0.40023757 0.82517249 -0.56317955 -0.89408713 #[11] 0.77166463 1.56204870 -0.34342230 -1.64133182 0.08235115 #[16] 1.05668106 # # These coefficients have the correct ordering.