best.unbal.haar: Best top-down Unbalanced Haar decomposition
Description
The function finds the ``best'' top-down Unbalanced Haar (UH) decomposition of the input vector
x, according to a selection rule (criterion) which specifies which
UH vector gets chosen at each scale and location.
Usage
best.unbal.haar(x, criterion = inner.prod.max)
Arguments
x
a vector
criterion
a function which takes a vector of length n and returns an integer between 1 and n-1
Value
tree
A list of J matrices, where J represents the number of ``scales''. Each matrix is of size 5 x (the number of UH
coefficients at a given scale). Each column (= vector of length 5) contains an Unbalanced Haar coefficient
in the following format: 1st component - an index of the coefficient; 2nd component - the value of the coefficient;
3rd component - time point where the corresponding UH vector starts; 4th component - last time point before the
breakpoint of the UH vector; 5th component - end point of the UH vector.
smooth
the ``smooth'' component of x, equal to sum(x) / sqrt(n), where n is the length of x