What are correct values for precision and recall when the denominators equal 0?

Question

Precision is defined as:

p = true positives / (true positives + false positives)

What is the value of precision if (true positives + false positives) = 0? Is it just undefined?

Same question for recall:

r = true positives / (true positives + false negatives)

In this case, what is the value of recall if (true positives + false negatives) = 0?

P.S. This question is very similar to the question What are correct values for precision and recall in edge cases?.

Answer 1

The answers to the linked earlier question apply here too.

If (true positives + false negatives) = 0 then no positive cases in the input data, so any analysis of this case has no information, and so no conclusion about how positive cases are handled. You want N/A or something similar as the ratio result, avoiding a division by zero error

If (true positives + false positives) = 0 then all cases have been predicted to be negative: this is one end of the ROC curve. Again, you want to recognise and report this possibility while avoiding a division by zero error.