function auc=areaundercurve(FPR,TPR);
% given true positive rate and false positive rate calculates the area under the curve
% true positive are on the y-axis and false positives on the x-axis
% sum rectangular area between all points
% example: auc=areaundercurve(FPR,TPR);
[x2,inds]=sort(FPR);
x2=[x2,1];  % the trick is in inventing a last point 1,1
y2=TPR(inds); 
y2=[y2,1];
xdiff=diff(x2);
xdiff=[x2(1),xdiff];
auc1=sum(y2.*xdiff); % upper point area
auc2=sum([0,y2([1:end-1])].*xdiff); % lower point area
auc=mean([auc1,auc2]);

http://www.myoutsourcedbrain.com/2008/11/receiver-operating-characteristic-roc.html

My implementation corresponding to Tom Fawcett's algorithm 3 in "roc graphs: notes and practical considerations for researchers, " 2004. Please see blog post for explanations and leave comments there.

area under the curve (AUC)

MatLab