function A = auroc(tp, fp)
%
% AUROC - area under ROC curve
%
% An ROC (receiver operator characteristic) curve is a plot of the true
% positive rate as a function of the false positive rate of a classifier
% system. The area under the ROC curve is a reasonable performance
% statistic for classifier systems assuming no knowledge of the true ratio
% of misclassification costs.
%
% A = AUROC(TP, FP) computes the area under the ROC curve, where TP and FP
% are column vectors defining the ROC or ROCCH curve of a classifier
% system.
%
% [1] Fawcett, T., "ROC graphs : Notes and practical
% considerations for researchers", Technical report, HP
% Laboratories, MS 1143, 1501 Page Mill Road, Palo Alto
% CA 94304, USA, April 2004.
%
% See also : ROC, ROCCH
%
% File : auroc.m
%
% Date : Wednesdaay 11th November 2004
%
% Author : Dr Gavin C. Cawley
%
% Description : Calculate the area under the ROC curve for a two-class
% probabilistic classifier.
%
% References : [1] Fawcett, T., "ROC graphs : Notes and practical
% considerations for researchers", Technical report, HP
% Laboratories, MS 1143, 1501 Page Mill Road, Palo Alto
% CA 94304, USA, April 2004.
%
% History : 22/03/2001 - v1.00
% 10/11/2004 - v1.01 minor improvements to comments etc.
%
% Copyright : (c) G. C. Cawley, November 2004.
%
% 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
%
n = size(tp, 1);
A = sum((fp(2:n) - fp(1:n-1)).*(tp(2:n)+tp(1:n-1)))/2;
% bye bye...