findadds {adlift}

Finds minimum number of inversion steps

Description

This function finds the minimum inversion steps to perform to fully reconstruct (a subset of) data

Usage

findadds(rem, neighbrs, po, index = 1:(length(rem) + length(po)))

Arguments

rem

the removelist variable from a lifting decomposition. See fwtnp.

neighbrs

A list of neighbour indices corresponding to lifting steps in a decomposition. See fwtnp.

po

The pointsin variable in a lifting decomposition (the index into the unlifted datapoints). See fwtnp.

index

a vector of indices into the original data, indicating which points should be fully reconstructed during inversion.

Details

This function gives a computational shortcut to get datapoint information in certain inversion cases. In some circumstances,when inverting, you might only be interested in the inverted coefficients for a subset of timepoints. In this case, it is not necessary to do a full inversion to look at the desired coefficients; the function uses the neighbourhood and removal order of the forward transform information and notes: 1) when the desired points were lifted (if at all) and 2) when the desired points were used as neighbours in prediction (if applicable). The number of inversion steps needed for each index individually is then taken as the maximum for these two conditions to be met. Inverting the transform with this number will yield the correct inverted coefficient. Note that to get the correct coefficients for all index, the number of inversion steps is max(adds).

Value

adds: a vector corresponding to index, each element of which is the number of inversion steps needed for that datapoint to be fully reconstructed.

Author(s)

Matt Nunes ([e-mail])

See Also

invtnp

Examples

#create data:
x<-runif(256)

f<-make.signal2("bumps",x=x)

#do forward transform:
fwd<-fwtnp(x,f)

#I want to invert enough so that points 1:3 are reconstructed.

adds<-findadds(fwd$removelist,fwd$neighbrs,fwd$pointsin,1:3)
adds

#now reconstruct...
fhat<-invtnp(fwd,f,nadd=max(adds))

#...and check that the desired points are the same:
f[1:3]
fhat[1:3]