# FPR in Confusion Matrix

I was trying to manually calculate $$\text{TPR}$$ and $$\text{FPR}$$ for the given data. But unfortunately I dont have any false positive cases in my dataset and even no true positive cases. So I am getting divided by zero error in pandas. So I have an intuition that $$\text{FPR=1-TPR}$$. Please let me know my intuition is correct if not let know how to fix this issue.

If there are no true/false positives, your classifier has no positive labelings. FPR is simply $$\frac{FP}{N}$$, where $$N$$ is number of negatives in the dataset. Assuming there are negative cases in the data, FPR is $$0$$. TPR is actually $$1-\text{FNR}$$ (false negative rate), and that is $$TP \over P$$. Since you have $$\text{TP}=0$$, and assuming there are positive samples in the dataset, $$\text{TPR}$$ is also $$0$$.
The TPR is defined as $$\frac{TP}{P}$$ (see, e.g. Wikipedia) or Encyclopedia of Systems Biology which says it is