getarrvec: Compute and return weaving permutation for conversion from...

In wavethresh: Wavelets Statistics and Transforms

Compute and return weaving permutation for conversion from wst objects to wd class objects.

Description

Computes weaving permutation for conversion from wst objects to wd

Usage

getarrvec(nlevels, sort=TRUE)

Arguments

nlevels	The number of levels in the non-decimated transform for which the permutation is to be computed.
sort	If TRUE then compute permutation for indexing a wst object. If FALSE then compute permutation for indexing a wd object.

Details

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 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.

Value

A matrix with 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.

RELEASE

Version 3.6 Copyright Guy Nason 1997

Author(s)

G P Nason

See Also

convert, convert.wd, convert.wst, levarr, wst, wst.object, wpst.

Examples

#
# 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.

wavethresh documentation built on Sept. 11, 2024, 9:33 p.m.