Works out the transform matrix for a particular prediction scheme and neighbourhood structure.
Usage
transmatdual(x, f, Pred = AdaptNeigh, neigh = 1, int = TRUE, clo = TRUE,
keep = 2,varonly=FALSE)
Value
out
the output from the forward transform.
Wnew
the matrix associated to the wavelet transform.
x
the original gridpoint vector.
Arguments
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 \(f_1 \dots f_n\).