Micro and macro F1

The problem, from first principles

With more than two classes, "the F1 score" is ambiguous. You can pool every decision together and compute one F1 (micro), which weights each row equally and so favors large classes. Or you can compute F1 for each class and average those (macro), which weights each class equally and so exposes a model that ignores a rare class.

Implement two functions for single-label multiclass predictions.

• f1_micro(y_true, y_pred): pool TP, FP, and FN across all classes, then return 2·TP / (2·TP + FP + FN).
• f1_macro(y_true, y_pred): for each label in the union of y_true and y_pred, compute its own F1 as 2·TP / (2·TP + FP + FN), using 0.0 when the denominator is zero, then return the mean.

Constraints

• Inputs must have the same length and be non-empty, otherwise raise ValueError.
• Each class's counts come from one-vs-rest: a row is a false positive for class c when it is predicted c and its true label is not c.

Hints

Open one at a time. Each gives away a little more than the last.