function [ d ] = cumVariance( eigvals, t_d )
% 
% The cummulative variance method for selecting the number of components to 
% take in principle component analysis (PCA).  This method selects the number
% of PCA eigenvectors to include such that the percentage of total variances 
% included exceedes the threshold t_d.  This is taken from page 38 of 
%
% Exploratory Data Analysis with MATLAB 
% by Martinez and Martinez.
%
% Written by:
% -- 
% John L. Weatherwax                2005-08-14
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% Pick a threshold between 70-95% from Jackson [1991]
if( nargin < 2 ) 
  t_d = 0.85; 
end

% make sure we have a row vector (with postive values): 
eigvals = abs(eigvals(:).'); 

% Ensure that the eigenvalues are sorted in decreasing order:
eigvals = sort( eigvals ); eigvals = fliplr( eigvals ); 

% Compute the total variance: 
tv = sum( eigvals );

% Find the sums of variances that are greater than t_d threshold:
inds = ( cumsum( eigvals ) / tv ) > t_d ;

% Extract the indices:
cumVarL = find( inds );

% Send out the first one:
d = cumVarL(1);