# area under precision recall curve = 0 while AUCROC=1

I have the following data:

predictions = [8;8;8;5;4;3;2;1];
true_target = [1;1;1;0;0;0;0;0];


When I compute the area under the precision recall curve using Matlab ([X,Y,T,AUPR] = perfcurve(true_target,prediction,1,'XCrit','tpr','YCrit','ppv')), I get a value of 0.

The precision at different thresholds are [NaN;1;0.75;0.6;0.5;0.4286;0.375]

The recall at different thresholds are [0;1;1;1;1;1;1];

Mathematically it make sense to me that the area under the precision recall curve is 0, since the precision recall curve looks like a vertical line, due to the tie in the prediction for the positive cases. However, I feel like in this case the 0 value for the area under the precision recall curve is not an indication of a bad classifier, since (1) AUCROC is 1 (2) there is a ideal threshold for precision/recall, e.g. threshold of > 5 gives precision=1 and recall=1;

Am I missing something? how should I interpret/report this?