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function [V,D]=gabmuleigs(K,c,p3,varargin)
%-*- texinfo -*-
%@deftypefn {Function} gabmuleigs
%@verbatim
%GABMULEIGS Eigenpairs of Gabor multiplier
% Usage: h=gabmuleigs(K,c,g,a);
% h=gabmuleigs(K,c,a);
% h=gabmuleigs(K,c,ga,gs,a);
%
% Input parameters:
% K : Number of eigenvectors to compute.
% c : symbol of Gabor multiplier
% g : analysis/synthesis window
% ga : analysis window
% gs : synthesis window
% a : Length of time shift.
% Output parameters:
% V : Matrix containing eigenvectors.
% D : Eigenvalues.
%
% GABMULEIGS has been deprecated. Please use construct a frame multiplier
% and use FRAMEMULEIGS instead.
%
% A call to GABMULEIGS(K,c,ga,gs,a) can be replaced by :
%
% [Fa,Fs]=framepair('dgt',ga,gs,a,M);
% [V,D]=framemuleigs(Fa,Fs,s,K);
%
% Original help:
% --------------
%
% GABMULEIGS(K,c,g,a) computes the K largest eigenvalues and eigen-
% vectors of the Gabor multiplier with symbol c and time shift a. The
% number of channels is deduced from the size of the symbol c. The
% window g will be used for both analysis and synthesis.
%
% GABMULEIGS(K,c,ga,gs,a) does the same using the window the window ga*
% for analysis and gs for synthesis.
%
% GABMULEIGS(K,c,a) does the same using the a tight Gaussian window of
% for analysis and synthesis.
%
% If K is empty, then all eigenvalues/pairs will be returned.
%
% GABMULEIGS takes the following parameters at the end of the line of input
% arguments:
%
% 'tol',t Stop if relative residual error is less than the
% specified tolerance. Default is 1e-9
%
% 'maxit',n Do at most n iterations.
%
% 'iter' Call eigs to use an iterative algorithm.
%
% 'full' Call eig to sole the full problem.
%
% 'auto' Use the full method for small problems and the
% iterative method for larger problems. This is the
% default.
%
% 'crossover',c
% Set the problem size for which the 'auto' method
% switches. Default is 200.
%
% 'print' Display the progress.
%
% 'quiet' Don't print anything, this is the default.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/deprecated/gabmuleigs.html}
%@seealso{gabmul, dgt, idgt, gabdual, gabtight}
%@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/>.
warning(['LTFAT: GABMULEIGS has been deprecated, please use FRAMEMULEIGS ' ...
'instead. See the help on FRAMEMULEIGS for more details.']);
% Change this to 1 or 2 to see the iterative method in action.
printopts=0;
if nargin<3
error('%s: Too few input parameters.',upper(mfilename));
end;
if nargout==2
doV=1;
else
doV=0;
end;
M=size(c,1);
N=size(c,2);
istight=1;
if numel(p3)==1
% Usage: h=gabmuleigs(c,K,a);
a=p3;
L=N*a;
ga=gabtight(a,M,L);
gs=ga;
arglist=varargin;
else
if numel(varargin{1})==1
% Usage: h=gabmuleigs(c,K,g,a);
ga=p3;
gs=p3;
a=varargin{1};
L=N*a;
arglist=varargin(2:end);
else
if numel(varargin{2})==1
% Usage: h=gabmuleigs(c,K,ga,gs,a);
ga=p3;
gs=varargin{1};
a =varargin{2};
L=N*a;
istight=0;
arglist=varargin(3:end);
end;
end;
end;
definput.keyvals.maxit=100;
definput.keyvals.tol=1e-9;
definput.keyvals.crossover=200;
definput.flags.print={'quiet','print'};
definput.flags.method={'auto','iter','full'};
[flags,kv]=ltfatarghelper({},definput,arglist);
% Do the computation. For small problems a direct calculation is just as
% fast.
if (flags.do_iter) || (flags.do_auto && L>kv.crossover)
if flags.do_print
opts.disp=1;
else
opts.disp=0;
end;
opts.isreal = false;
opts.maxit = kv.maxit;
opts.tol = kv.tol;
% Setup afun
afun(1,c,ga,gs,a,M,L);
if doV
[V,D] = eigs(@afun,L,K,'LM',opts);
else
D = eigs(@afun,L,K,'LM',opts);
end;
else
% Compute the transform matrix.
bigM=tfmat('gabmul',c,ga,gs,a);
if doV
[V,D]=eig(bigM);
else
D=eig(bigM);
end;
end;
% The output from eig and eigs is a diagonal matrix, so we must extract the
% diagonal.
D=diag(D);
% Sort them in descending order
[~,idx]=sort(abs(D),1,'descend');
D=D(idx(1:K));
if doV
V=V(:,idx(1:K));
end;
% Clean the eigenvalues, if we know that they are real-valued
%if isreal(ga) && isreal(gs) && isreal(c)
% D=real(D);
%end;
% The function has been written in this way, because Octave (at the time
% of writing) does not accept additional parameters at the end of the
% line of input arguments for eigs
function y=afun(x,c_in,ga_in,gs_in,a_in,M_in,L_in)
persistent c;
persistent ga;
persistent gs;
persistent a;
persistent M;
persistent L;
if nargin>1
c = c_in;
ga = ga_in;
gs = gs_in;
a = a_in;
M = M_in;
L = L_in;
else
y=comp_idgt(c.*comp_dgt(x,ga,a,M,[0 1],0,0,0),gs,a,[0 1],0,0);
end;
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