Macro and Micro F1, From the Confusion Matrix Alone

Multiclass F1 comes in two flavours that quietly disagree with each other the moment classes are imbalanced, and the most common bug is averaging the wrong things before combining them.

Write multiclass_f1(confusion). Given a (C, C) confusion matrix — rows are true classes, columns are predicted classes, exactly the convention a confusion matrix always uses — return (macro_f1, micro_f1).

• Macro-F1: compute precision, recall and F1 for each class separately, then average the F1 scores across classes, unweighted. Every class counts equally regardless of how common it is.
• Micro-F1: pool true positives, false positives and false negatives across all classes first, then compute one precision, one recall and one F1 from the totals. Common classes dominate in proportion to their size.

As always, a zero denominator anywhere gives 0.0, never nan.