Cohort Retention Matrix in Pandas

You're given a small event log of user activity: each row is one (user, month) pair in which that user was active, along with the month they originally signed up. Build a cohort retention matrix: rows are signup cohort (month), columns are months-since-signup (0, 1, 2, ...), and values are the retention rate — the share of that cohort active in that month.

Steps:

1. For each row, compute months_since_signup = (active_month − signup_month) in whole months.
2. Compute each cohort's size (distinct users whose signup_month equals that cohort).
3. For each (signup_month, months_since_signup), count distinct active users and divide by the cohort size to get the retention rate.
4. Pivot into a matrix: index=signup_month, columns=months_since_signup, values=retention rate. Months with no data for a cohort should be left as NaN (not zero) — a cohort simply hasn't reached that age yet.

Reset the index so signup_month is a normal column, round all rate values to 4 decimals, and assign the DataFrame to result.