%TESTN Error estimate of discriminant for normal distribution.% % 	E = TESTN(W,U,G,N)% % INPUT%   W  Trained classifier mapping%   U  C x K dataset with C class means, labels and priors (default: [0 .. 0])%   G  K x K x C matrix with C class covariance matrices (default: identity)%   N  Number of test examples (default 10000)%% OUTPUT%   E  Estimated error%      % DESCRIPTION% This routine estimates as good as possible the classification error% of Gaussian distributed problems with known means and covariances. N% normally distributed data vectors with means, labels and prior% probabilities defined by the dataset U (size [C,K]) and covariance% matrices G (size [K,K,C]) are generated with the specified labels and are% tested against the discriminant W. The fraction of incorrectly classified% data vectors is returned. If W is a linear 2-class discriminant and N % is not specified, the error is computed analytically.% % SEE ALSO% MAPPINGS, DATASETS, QDC, NBAYESC, TESTC% Copyright: R.P.W. Duin, duin@ph.tn.tudelft.nl% Faculty of Applied Physics, Delft University of Technology% P.O. Box 5046, 2600 GA Delft, The Netherlands% $Id: testn.m,v 1.5 2003/10/19 14:41:12 bob Exp $function e = testn(w,U,G,m)	prtrace(mfilename);		% Assert that W is a trained mapping.	istrained(w);	[k,c] = size(w);	if (nargin < 4) & ~( isaffine(w) & (c == 2) )		prwarning(4,'number of samples N to test with not specified, assuming 10000');		m = 10000; 	end	if (nargin < 3)		prwarning(3,'covariance matrices not specified, assuming identity for each class');		G = eye(k); 	end	if (nargin < 2)		error('Class means are not specified');	else		[cc,k] = size(U); p = getprior(U); u = +U;		if (cc ~= c)			error('Specified number of class means does not fit classifier')		end	end	% If a single covariance is specified, use it for each class.	if (length(size(G)) == 2)		g = G;		for j = 2:c			G = cat(3,G,g);		end	else		if (size(G,3) ~= c)			error('Specified number of covariances does not fit classifier')		end	end		% Check for analytical case: linear classifier and no data samples requested.	if (nargin < 4) & (isaffine(w)) & (c == 2)		prwarning(1,'computing Bayes error analytically');		e = 0;		v = w.data.rot(:,1); f = w.data.offset(1);		for j = 1:c			% Find the index J of mean j stored in U.			J = findnlab(U,j);			if (length(J) ~= 1)				error('The mean U does not contain correct labels.')			end			q = real(sqrt(v'*G(:,:,j)*v)); % std dev in direction of classifier			d = (2*j-3)*(v'*u(J,:)'+f);    % normalized distance to classifier			if (q == 0)				if (d >= 0), e = e + p(j); end			else				e = e + p(j) * (erf(d/(q*sqrt(2)))/2 + 0.5);			end		end	else 		% Cannot solve analytically: generate data and test.		a = gauss(m,U,G); 		% Generate normally distributed data.		a = setlablist(a,getlab(w));		e = testc(a,w);   		% Find the error of discriminant on the data.	endreturn