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function [c,info]=uwpfbt(f,wt,varargin)
%-*- texinfo -*-
%@deftypefn {Function} uwpfbt
%@verbatim
%UWPFBT Undecimated Wavelet Packet FilterBank Tree
% Usage: c=uwpfbt(f,wt);
% [c,info]=uwpfbt(...);
%
% Input parameters:
% f : Input data.
% wt : Wavelet Filterbank tree
%
% Output parameters:
% c : Coefficients in a L xM matrix.
%
% c=UWPFBT(f,wt) returns coefficients c obtained by applying the
% undecimated wavelet filterbank tree defined by wt to the input data
% f using the "a-trous" algorithm. Number of columns in c (*M*) is
% defined by the total number of outputs of each node. The outputs c(:,jj)
% are ordered in the breadth-first node order manner.
%
% [c,info]=UWPFBT(f,wt) additionally returns struct. info containing
% the transform parameters. It can be conviniently used for the inverse
% transform IUWPFBT e.g. fhat = iUWPFBT(c,info). It is also required
% by the PLOTWAVELETS function.
%
% If f is a matrix, the transformation is applied to each of W columns
% and the coefficients in c are stacked along the third dimension.
%
% Please see help for WFBT description of possible formats of wt.
%
% Scaling of intermediate outputs:
% --------------------------------
%
% The following flags control scaling of intermediate outputs and
% therefore the energy relations between coefficient subbands. An
% intermediate output is an output of a node which is further used as an
% input to a descendant node.
%
% 'intsqrt'
% Each intermediate output is scaled by 1/sqrt(2).
% If the filterbank in each node is orthonormal, the overall
% undecimated transform is a tight frame.
% This is the default.
%
% 'intnoscale'
% No scaling of intermediate results is used. This is
% necessaty for the WPBEST function to correctly work with
% the cost measures.
%
% 'intscale'
% Each intermediate output is scaled by 1/2.
%
% If 'intnoscale' is used, 'intscale' must be used in IUWPFBT (and vice
% versa) in order to obtain a perfect reconstruction.
%
% Scaling of filters:
% -------------------
%
% When compared to WPFBT, the subbands produced by UWPFBT are
% gradually more and more redundant with increasing depth in the tree.
% This results in energy grow of the coefficients. There are 3 flags
% defining filter scaling:
%
% 'sqrt'
% Each filter is scaled by 1/sqrt(a), there a is the hop
% factor associated with it. If the original filterbank is
% orthonormal, the overall undecimated transform is a tight
% frame.
% This is the default.
%
% 'noscale'
% Uses filters without scaling.
%
% 'scale'
% Each filter is scaled by 1/a.
%
% If 'noscale' is used, 'scale' must be used in IUWPFBT (and vice
% versa) in order to obtain a perfect reconstruction.
%
% Examples:
% ---------
%
% A simple example of calling the UWPFBT function using the "full
% decomposition" wavelet tree:
%
% [f,fs] = greasy;
% J = 6;
% [c,info] = uwpfbt(f,{'db10',J,'full'});
% plotwavelets(c,info,fs,'dynrange',90);
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/wavelets/uwpfbt.html}
%@seealso{iuwpfbt, wfbtinit}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
complainif_notenoughargs(nargin,2,'UWPFBT');
definput.import = {'wfbtcommon','uwfbtcommon'};
definput.flags.interscaling = {'intsqrt', 'intscale', 'intnoscale'};
[flags,kv]=ltfatarghelper({},definput,varargin);
% Initialize the wavelet tree structure
wt = wfbtinit(wt,flags.forder);
%% ----- step 1 : Verify f and determine its length -------
[f,Ls]=comp_sigreshape_pre(f,upper(mfilename),0);
if(Ls<2)
error('%s: Input signal seems not to be a vector of length > 1.',...
upper(mfilename));
end
%% ----- step 3 : Run computation
wtPath = nodeBForder(0,wt);
nodesUps = nodesFiltUps(wtPath,wt);
rangeLoc = nodesLocOutRange(wtPath,wt);
c = comp_uwpfbt(f,wt.nodes(wtPath),rangeLoc,nodesUps,flags.scaling,...
flags.interscaling);
%% ----- Optional : Fill the info struct. -----
if nargout>1
info.fname = 'uwpfbt';
info.wt = wt;
info.fOrder = flags.forder;
info.isPacked = 0;
info.interscaling = flags.interscaling;
info.scaling = flags.scaling;
end
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