% RUNPCA -  perform principal component analysis (PCA) using singular value 
%             decomposition (SVD) using Matlab SVD or SVDS
%                        >> inv(eigvec)*data = pc;
% Usage:
%    >> [pc,eigvec,sv] = runpca(data);
%    >> [pc,eigvec,sv] = runpca(data,num,norm)
%
% Inputs:
%   data   - input data matrix (rows are variables, columns observations)
%   num    - number of principal comps to return  {def|0|[] -> rows in data}
%   norm   - 1/0 = do/don't normalize the eigvec's to be equivariant 
%                                                {def|0 -> no normalization}
% Outputs:
%   pc     - the principal components, i.e.        >> inv(eigvec)*data = pc;
%   eigvec - the inverse weight matrix (=eigenvectors). >> data = eigvec*pc; 
%   sv     - the singular values (=eigenvalues)
%
% Author: Colin Humphries, CNL / Salk Institute, 1997
%
% See also: RUNICA

% Copyright (C) Colin Humphries, CNL / Salk Institute, Aug, 1997
%
% This file is part of EEGLAB, see http://www.eeglab.org
% for the documentation and details.
%
% Redistribution and use in source and binary forms, with or without
% modification, are permitted provided that the following conditions are met:
%
% 1. Redistributions of source code must retain the above copyright notice,
% this list of conditions and the following disclaimer.
%
% 2. Redistributions in binary form must reproduce the above copyright notice,
% this list of conditions and the following disclaimer in the documentation
% and/or other materials provided with the distribution.
%
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
% THE POSSIBILITY OF SUCH DAMAGE.

% 01/31/00 renamed RUNPCA and improved usage message -sm
% 01-25-02 reformated help & license, added links -ad 

function [pc,M,S] = runpca(data,N,norm)

BIG_N = 50; % for efficiency, switch to sdvs() when BIG_N<=N or N==rows

if nargin < 1
  help runpca
  return
end

rows = size(data,1);

% remove the mean
for i = 1:rows
  data(i,:) = data(i,:) - mean(data(i,:));
end

if nargin < 3
  norm = 0;
elseif isempty(norm)
  norm = 0;
end

if nargin < 2
  N = 0;
end
if isempty(N)
  N = 0;
end


if N == 0  || N == rows
  N = rows;
  [U,S,V] = svd(data',0);   % performa SVD
  if norm == 0
    pc = U';
    M = (S*V')';
  else % norm
    pc = (U*S)';
    M = V;
  end
else
  if N > size(data,1)
    error('N must be <= the number of rows in data.')
  end
  %if N <= BIG_N | N == rows
  %[U,S,V] = svd(data',0);
  %else
  [U,S,V] = svds(data',N);
  %end
  if norm == 0
    pc = U';
    M = (S*V')';
  else % norm
    pc = (U*S)';
    M = V;
  end  
  %if N > BIG_N & N < rows
  %pc = pc(1:N,:);
  %M = M(:,1:N);
  %end
end
%S = diag(S(1:N,1:N));