Compute and return weaving permutation for conversion from wst objects to wd class objects.
getarrvec(nlevels, sort=TRUE)
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Conversion of wst objects into wd objects and vice versa can be carried out using the convert.wst and convert.wd functions. These latter functions depend on this getarrvec function to compute the permutation which maps coefficients from one ordering to the other.
This permutation is described in Nason, Sapatinas and Sawczenko, 1998.
Version 3.6 Copyright Guy Nason 1997
G P Nason
convert, convert.wd, convert.wst, levarr, wst, wst.object, wpst.
# # 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.
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