basisfns: basisfns

Description

This function plots all mother and father wavelets associated with a given wavelet transform.

Usage

basisfns(x, f, pred, neigh, int, clo, keep, plot.f = FALSE, plot.bas = FALSE,
 separate = FALSE)

Arguments

a gridpoint vector.

the vector of associated function values.

pred

The type of regression to be performed. Possible options are LinearPred, QuadPred, CubicPred,

neigh

The number of neighbours over which the regression is performed at each step. If closest 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 closest 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.

plot.f

a boolean value indicating whether to plot the original function or not. If so, the signal is plotted with vertical coloured lines, showing which prediction method was used on the different parts of the signal. The plot also shows which gridpoints corresp

plot.bas

subset of 1:length(f), denoting which basis functions to plot. Each basis function is colour-coded according to which prediction scheme was used in the lifting of the corresponding gridpoint.

separate

a boolean argument indicating if the basis functions should be plotted on a single graphsheet.

Value

outthe output from the forward transform which is specified in the arguments to this function
$
pointsinthe vector of indices of points still to be removed.
schhista character string vector of the prediction scheme used for the prediction of each gridpoint (in the order of x).
inthistvector of boolean values indicating whether an intercept was used in the prediction steps during the transform (in the order of x).
basmata matrix of wavelet basis function values. The row i represents the function values corresponding to the grid for the basis function associated to the gridpoint $i$.

Details

The procedure constructs W, the matrix representation of the forward transform specified in the arguments to the function, and then uses the inverse matrix to calculate the vectors of basis function values: to work out the basis function values, one inverts the transform with a delta vector, with a one in the position corresponding to the basis function required. Since this is equivalent to pre-multiplying the delta vector by the matrix representation for the inverse transform $(W^{-1})$, the basis function values are precisely the columns of $W^{-1}$. The procedure then plots the basis functions (each on a separate graphsheet, if chosen), colour coded according to the prediction scheme used or whether it is a scaling function.

Examples

Run this code

#create test signal data
#
x<-runif(100)
y<-make.signal2("blocks",x=x)
#
#perform procedure...
#
a<-basisfns(x,y,AdaptNeigh,2,TRUE,TRUE,2,FALSE,c(1,14,15),FALSE)
#
#this produces plots of three basis functions all on one graph.