transmatdual: transmatdual
In nunesmatt/adlift: An Adaptive Lifting Scheme Algorithm

Description Usage Arguments Details Value Note Author(s) See Also Examples

Works out the transform matrix for a particular prediction scheme and neighbourhood structure.

1 2	transmatdual(x, f, Pred = AdaptNeigh, neigh = 1, int = TRUE, clo = TRUE, keep = 2,varonly=FALSE)

`x`	A vector of grid values. Can be of any length, not necessarily equally spaced.
`f`	A vector of function values corresponding to x. Must be of the same length as x.
`Pred`	The type of regression to be performed. Possible options are `LinearPred`, `QuadPred`, `CubicPred`, `AdaptPred` and `AdaptNeigh`.
`neigh`	The number of neighbours over which the regression is performed at each step. If clo is false, then this in fact denotes the number of neighbours on each side of the removed point.
`int`	Indicates whether or not the regression curve includes an intercept.
`clo`	Refers to the configuration of the chosen neighbours. If clo is false, the neighbours will be chosen symmetrically around the removed point. Otherwise, the closest neighbours will be chosen.
`keep`	The number of scaling coefficients to be kept in the final representation of the initial signal. This must be at least two.
`varonly`	A boolean variable indicating whether only the coefficient variances should be returned, i.e. just the diagonal of the transform matrix `Wnew`.

The function uses Amatdual to form the refinement matrices A_j, from which the augmented matrices T_j are constructed. This process is iterated, to find the transform matrix (the top level augmented matrix). The rows and columns of this matrix are then reordered to be in the order of out$coeff, i.e. so that the columns correspond to f_1 … f_n.

`out`	the output from the forward transform.
`Wnew`	the matrix associated to the wavelet transform.
`x`	the original gridpoint vector.

This function has been left in the package for completeness. However, the transform matrix is (optionally) computed within the forward lifting transform function fwtnp.

Matt Nunes (nunesrpackages@gmail.com), Marina Knight

fwtnp, Amatdual

x1<-runif(10)
y1<-make.signal2("doppler",x=x1)
#
a<-transmatdual(x1,y1,AdaptNeigh,2,TRUE,TRUE,2)
#
a$Wnew
#
#the transform matrix for this adaptive lifting scheme