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function y = s0norm(f,varargin)
%S0NORM S0-norm of signal
% Usage: y = s0norm(f);
% y = s0norm(f,...);
%
% `s0norm(f)` computes the $S_0$-norm of a vector.
%
% If the input is a matrix or ND-array, the $S_0$-norm is computed along
% the first (non-singleton) dimension, and a vector of values is returned.
%
% **WARNING**: The $S_0$-norm is computed by computing a full Short-time
% Fourier transform of a signal, which can be quite time-consuming. Use
% this function with care for long signals.
%
% `s0norm` takes the following flags at the end of the line of input
% parameters:
%
% 'dim',d Work along specified dimension. The default value of []
% means to work along the first non-singleton one.
%
% 'rel' Return the result relative to the $l^2$ norm (the energy) of the
% signal.
% AUTHOR : Peter L. Soendergaard
%% ------ Checking of input parameters ---------
if ~isnumeric(f)
error('%s: Input must be numerical.',upper(mfilename));
end;
if nargin<1
error('%s: Too few input parameters.',upper(mfilename));
end;
definput.flags.rel={'norel','rel'};
definput.keyvals.dim=[];
[flags,kv]=ltfatarghelper({},definput,varargin);
%% ------ Computation --------------------------
[f,L,Ls,W,dim,permutedsize,order]=assert_sigreshape_pre(f,[],kv.dim, ...
upper(mfilename));
permutedsize(1)=1;
y=zeros(permutedsize);
g=pgauss(L);
for ii=1:W
% Compute the STFT by the simple algorithm and sum each column of the
% STFT as they are computed, to avoid L^2 memory usage.
for jj=0:L-1
y(1,ii)=y(1,ii)+sum(abs(fft(f(:,ii).*circshift(g,jj))));
end;
if flags.do_rel
y(1,ii)=y(1,ii)/norm(f(:,ii));
end;
end;
y=y/L;
y=assert_sigreshape_post(y,dim,permutedsize,order);