% Small edits to the EEGLAB file
% Cleaned up and removed irrelevant sections.
%
% eeg_interp() - interpolate data channels
%
% Usage: EEGOUT = eeg_interp(EEG, badchans, method);
%
% Inputs:
%     EEG      - EEGLAB dataset
%     badchans - [integer array] indices of channels to interpolate.
%                For instance, these channels might be bad.
%                [chanlocs structure] channel location structure containing
%                either locations of channels to interpolate or a full
%                channel structure (missing channels in the current
%                dataset are interpolated).
%     method   - [string] method used for interpolation (default is 'spherical').
%                'invdist' uses inverse distance on the scalp
%                'spherical' uses superfast spherical interpolation.
%                'spacetime' uses griddata3 to interpolate both in space
%                and time (very slow and cannot be interupted).
% Output:
%     EEGOUT   - data set with bad electrode data replaced by
%                interpolated data
%
% Author: Arnaud Delorme, CERCO, CNRS, Mai 2006-

% Copyright (C) Arnaud Delorme, CERCO, 2006, arno@salk.edu
%
% 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 2 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, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

% $Log: eeg_interp.m,v $
% Revision 1.7  2009/08/05 03:20:42  arno
% new interpolation function
%
% Revision 1.6  2009/07/30 03:32:47  arno
% fixed interpolating bad channels
%
% Revision 1.5  2009/07/02 19:30:33  arno
% fix problem with empty channel
%
% Revision 1.4  2009/07/02 18:23:33  arno
% fixing interpolation
%
% Revision 1.3  2009/04/21 21:48:53  arno
% make default spherical in eeg_interp
%
% Revision 1.2  2008/04/16 17:34:45  arno
% added spherical and 3-D interpolation
%
% Revision 1.1  2006/09/12 18:46:30  arno
% Initial revision
%

function EEG = h_eeg_interp_spl(EEG, badchans, ignore_chans)

if nargin < 2
    help eeg_interp;
    return;
end;

if ~exist('ignore_chans','var')
    ignore_chans=[];
end

badchans = setdiff(badchans,ignore_chans);

if isempty(badchans)
    return;
end

goodchans = setdiff(1:EEG.nbchan, badchans);
goodchans = setdiff(goodchans, ignore_chans);

% find non-empty good channels
% ----------------------------
nonemptychans = find(~cellfun('isempty', { EEG.chanlocs.theta }));
goodchans = intersect(goodchans, nonemptychans);
badchans  = intersect(badchans, nonemptychans);
fprintf('Interpolating %d channels:', length(badchans));fprintf(' %d',badchans);fprintf('\n');

% scan data points
% ----------------
% get theta, rad of electrodes
% ----------------------------
xelec = [ EEG.chanlocs(goodchans).X ];
yelec = [ EEG.chanlocs(goodchans).Y ];
zelec = [ EEG.chanlocs(goodchans).Z ];
rad = sqrt(xelec.^2+yelec.^2+zelec.^2);
xelec = xelec./rad;
yelec = yelec./rad;
zelec = zelec./rad;
xbad = [ EEG.chanlocs(badchans).X ];
ybad = [ EEG.chanlocs(badchans).Y ];
zbad = [ EEG.chanlocs(badchans).Z ];
rad = sqrt(xbad.^2+ybad.^2+zbad.^2);
xbad = xbad./rad;
ybad = ybad./rad;
zbad = zbad./rad;

EEG.data(badchans,:) = spheric_spline( xelec, yelec, zelec, xbad, ybad, zbad, EEG.data(goodchans,:));
EEG = eeg_checkset(EEG);

function allres = spheric_spline( xelec, yelec, zelec, xbad, ybad, zbad, values)

newchans = length(xbad);
numpoints = size(values,2);

Gelec = computeg(xelec,yelec,zelec,xelec,yelec,zelec);
Gsph  = computeg(xbad,ybad,zbad,xelec,yelec,zelec);

% compute solution for parameters C
% ---------------------------------
meanvalues = mean(values);
values = values - repmat(meanvalues, [size(values,1) 1]); % make mean zero

values = [values;zeros(1,numpoints)];
C = pinv([Gelec;ones(1,length(Gelec))]) * values;
clear values;
allres = zeros(newchans, numpoints);

% apply results
% -------------
for j = 1:size(Gsph,1)
    allres(j,:) = sum(C .* repmat(Gsph(j,:)', [1 size(C,2)]));
end
allres = allres + repmat(meanvalues, [size(allres,1) 1]);

% compute G function
% ------------------
function g = computeg(x,y,z,xelec,yelec,zelec)

unitmat = ones(length(x(:)),length(xelec));
EI = unitmat - sqrt((repmat(x(:),1,length(xelec)) - repmat(xelec,length(x(:)),1)).^2 +...
    (repmat(y(:),1,length(xelec)) - repmat(yelec,length(x(:)),1)).^2 +...
    (repmat(z(:),1,length(xelec)) - repmat(zelec,length(x(:)),1)).^2);

g = zeros(length(x(:)),length(xelec));
%dsafds
m = 4; % 3 is linear, 4 is best according to Perrin's curve
for n = 1:7
    L = legendre(n,EI);
    g = g + ((2*n+1)/(n^m*(n+1)^m))*squeeze(L(1,:,:));
end
g = g/(4*pi);