adlift (version 1.2-3)

matcond: matcond

Description

Works out two alternative condition numbers for the transform associated to the prediction scheme given in the arguments to the function.

Usage

matcond(x, f, Pred, neigh, int, clo, keep)

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,

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.

Value

• cno
  the condition numbers for the augmented transform matrices, calculated using the Frobenius norm (see condno).
• v
  the condition numbers for the augmented transform matrices, calculated using the ratio between the largest to the smallest singular values in the singular value decomposition of the augmented matrices.
• a
  the transform matrix information for the transform (output from transmatdual).

Details

The function uses the transform matrices to work out their norms and singular value decompositions. Condition numbers are calculated by $||T_j ||*||T_j^{-1} ||$ and svd$d[1]/svd$d[nrow(T_j)] respectively.

See Also

condno, transmatdual

Examples

x1<-runif(256)
y1<-make.signal2("doppler",x=x1)
#
m<-matcond(x1,y1,AdaptNeigh,2,TRUE,TRUE,2)
#
m$cno
#
m$v
# shows the two different condition number measures for the matrix associated
# to the transform performed.
#