function [dipout] = ft_eloreta(dip, grad, headmodel, dat, Cf, varargin)
%
% Use as
%   [dipout] = ft_eloreta(dipin, grad, headmodel, dat, cov, varargin)
% where
%   dipin       is the input dipole model
%   grad        is the gradiometer definition
%   headmodel   is the volume conductor definition
%   dat         is the data matrix with the ERP or ERF
%   cov         is the data covariance or cross-spectral density matrix
% and
%   dipout      is the resulting dipole model with all details
%
% The input dipole model consists of
%   dipin.pos   positions for dipole, e.g. regular grid, Npositions x 3
%   dipin.mom   dipole orientation (optional), 3 x Npositions
%   dipin.filter precomputed filter cell-array of 1 x Npositions, each cell
%               containing nchannels x 3 matrix
%
% Additional options should be specified in key-value pairs and can be
%  'keepfilter'       = remember the beamformer filter,    can be 'yes' or 'no'
%  'keepleadfield'    = remember the forward computation,  can be 'yes' or 'no'
%  'keepmom'          = remember the dipole moment,        can be 'yes' or 'no'
%  'lambda'           = scalar, regularisation parameter (default = 0.05)

% These options influence the forward computation of the leadfield
%  'reducerank'       = reduce the leadfield rank, can be 'no' or a number (e.g. 2)
%  'normalize'        = normalize the leadfield
%  'normalizeparam'   = parameter for depth normalization (default = 0.5)
%
% If the dipole definition only specifies the dipole location, a rotating
% dipole (regional source) is assumed on each location. If a dipole moment
% is specified, its orientation will be used and only the strength will
% be fitted to the data.
%
% This implements: R.D. Pascual-Marqui; Discrete, 3D distributed, linear imaging
% methods of electric neuronal activity. Part 1: exact, zero error localization.
% arXiv:0710.3341 [math-ph], 2007-October-17, http://arxiv.org/pdf/0710.3341

% Copyright (C) 2013, Marlene Boenstrup, Jan-Mathijs Schoffelen and Guido
% Nolte
%
% This file is part of FieldTrip, see http://www.fieldtriptoolbox.org
% for the documentation and details.
%
%    FieldTrip 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.
%
%    FieldTrip 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 FieldTrip. If not, see <http://www.gnu.org/licenses/>.
%
% $Id$

if mod(nargin-5,2)
  % the first 5 arguments are fixed, the other arguments should come in pairs
  ft_error('invalid number of optional arguments');
end

% these optional settings do not have defaults
keepfilter      = ft_getopt(varargin, 'keepfilter',      'no');
keepmom         = ft_getopt(varargin, 'keepmom',         'no');
keepleadfield   = ft_getopt(varargin, 'keepleadfield',   'no');
lambda          = ft_getopt(varargin, 'lambda', 0.05);
reducerank      = ft_getopt(varargin, 'reducerank');
normalize       = ft_getopt(varargin, 'normalize');
normalizeparam  = ft_getopt(varargin, 'normalizeparam');

% convert the yes/no arguments to the corresponding logical values
keepfilter     = istrue(keepfilter);
keepmom        = istrue(keepmom);
keepleadfield  = istrue(keepleadfield);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% find the dipole positions that are inside/outside the brain
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if ~isfield(dip, 'inside')
  dip.inside = ft_inside_vol(dip.pos, headmodel);
end

% ensure logical representation
dip.inside = logical(dip.inside);

% keep the original details on inside and outside positions
originside = dip.inside;
origpos    = dip.pos;

% select only the dipole positions inside the brain for scanning
dip.pos    = dip.pos(originside,:);
dip.inside = true(size(dip.pos,1),1);
if isfield(dip, 'mom'),
  dip.mom = dip.mom(:,originside);
end
if isfield(dip, 'leadfield'), fprintf('using precomputed leadfields\n');
  dip.leadfield = dip.leadfield(originside);
end
if isfield(dip, 'filter')
  fprintf('using precomputed filters\n');
  dip.filter = dip.filter(originside);
end

% deal with the regularition in the low level function

% use existing leadfields, or compute them
if ~isfield(dip, 'leadfield')
  % compute the leadfield
  fprintf('computing leadfields\n');
  for i=1:size(dip.pos,1)
    dip.leadfield{i} = ft_compute_leadfield(dip.pos(i,:), grad, headmodel, 'reducerank', reducerank, 'normalize', normalize, 'normalizeparam', normalizeparam);
  end
end

% deal with dip.mom
if isfield(dip, 'mom') && size(dip.leadfield{1},2)==size(dip.mom,1)
  fprintf('projecting the forward solutions using specified dipole moment\n');
  for i=1:size(dip.pos,1)
    dip.leadfield{i} = dip.leadfield{i}*dip.mom(:,i);
  end
end

% deal with reduced rank
% check the rank of the leadfields, and project onto the lower dimensional
% subspace if the number of columns per leadfield > rank: this to avoid
% numerical issues in the filter computation
rank_lf = zeros(1,size(dip.pos,1));
for i=1:size(dip.pos,1)
  rank_lf(i) = rank(dip.leadfield{i});
end
if ~all(rank_lf==rank_lf(1))
  ft_error('the forward solutions have a different rank for each location, which is not supported');
end
if rank_lf(1)<size(dip.leadfield{1})
  fprintf('the forward solutions have a rank of %d, but %d orientations\n',rank_lf(1),size(dip.leadfield{1},2));
  fprintf('projecting the forward solutions on the lower dimensional subspace\n');
  for i=1:size(dip.pos,1)
    [u,s,v{i}] = svd(dip.leadfield{i}, 'econ');
    dip.leadfield{i} = dip.leadfield{i}*v{i}(:,1:rank_lf(i));
  end
end

% convert the leadfield into NchanxNdipxNori
[Nchan, Nori] = size(dip.leadfield{1});
Ndip          = numel(dip.leadfield);
leadfield     = permute(reshape(cat(2,dip.leadfield{:}),Nchan,Nori,Ndip),[1 3 2]);

% use existing filters, or compute them
if ~isfield(dip, 'filter')
  filt = mkfilt_eloreta(leadfield, lambda);
  for i=1:size(dip.pos,1)
    dip.filter{i,1} = squeeze(filt(:,i,:))';
  end
end

% get the power
dip.pow = zeros(size(dip.pos,1),1);
dip.ori = cell(size(dip.pos,1),1);
for i=1:size(dip.pos,1)
  csd        = dip.filter{i}*Cf*dip.filter{i}';
  [u,s,vv]    = svd(real(csd));
  dip.pow(i) = s(1);
  dip.ori{i} = u(:,1);
end

% get the dipole moment
if keepmom && ~isempty(dat)
  % remove the dipole moment from the input
  if isfield(dip, 'mom')
    dip = rmfield(dip, 'mom');
  end
  for i=1:size(dip.pos,1)
    dip.mom{i} = dip.filter{i}*dat;
  end
end

% wrap it all up, prepare the complete output
dipout.inside  = originside;
dipout.pos     = origpos;

% reassign the scan values over the inside and outside grid positions
if isfield(dip, 'pow') % here pow is cell
  dipout.pow( originside) = dip.pow;
  dipout.pow(~originside) = nan;
end
if isfield(dip, 'ori') % here ori is cell
  dipout.ori( originside) = dip.ori;
  dipout.ori(~originside) = {[]};
end
if isfield(dip, 'leadfield') && keepleadfield
  dipout.leadfield( originside) = dip.leadfield;
  dipout.leadfield(~originside) = {[]};
end
if isfield(dip, 'filter') && keepfilter
  dipout.filter( originside) = dip.filter;
  dipout.filter(~originside) = {[]};
end
if isfield(dip, 'mom') && keepmom
  dipout.mom( originside) = dip.mom;
  dipout.mom(~originside) = {[]};
end
