## Copyright (C) 2012 Benjamin Lewis <benjf5@gmail.com>
##
## 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/>.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{t} =} lscomplex (@var{time}, @var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctaves})
## 
## Return the complex least-squares transform of the (@var{time},@var{mag})
## series, considering frequencies up to @var{maxfreq}, over @var{numoctaves}
## octaves and @var{numcoeff} coefficients.
##
## @seealso{lsreal}
## @end deftypefn


function transform = fastlscomplex (t, x, omegamax, ncoeff, noctave)

  ## t will be unrolled to a column vector below
  ## no metter what its original shape is
  n = numel (t); 
   
  iter = 0 : (ncoeff * noctave - 1);
  omul = (2 .^ (- iter / ncoeff));

  ot = t(:) * (omul * omegamax);

  ## See the paper for the expression below
  transform = sum ((cos (ot) - (sin (ot) .* i)) .* x(:), 1) / n; 
  
endfunction 

%!test
%! maxfreq = 4 / ( 2 * pi );
%! t = [0:0.008:8];
%! x = ( 2 .* sin (maxfreq .* t) +
%!       3 .* sin ( (3 / 4) * maxfreq .* t)-
%!       0.5 .* sin ((1/4) * maxfreq .* t) -
%!       0.2 .* cos (maxfreq .* t) + 
%!       cos ((1/4) * maxfreq .* t));
%! assert (fastlscomplex (t, x, maxfreq, 2, 2), 
%!       [(-0.400924546169395 - 2.371555305867469i), ...
%!        (1.218065147708429 - 2.256125004156890i), ... 
%!        (1.935428592212907 - 1.539488163739336i), ...
%!        (2.136692292751917 - 0.980532175174563i)], 5e-10);