A Monthly Retention Cohort Grid

Every growth deck has a retention curve in it, and building the grid behind it touches almost everything else in this arena: period arithmetic that has to mean calendar months rather than a day count, a denominator that must not shift once it is set, and a grid that has to include the cells where nothing happened.

Write retention_matrix(df). Given a DataFrame of activity events with user_id and event_date (datetime64):

1. Each user's cohort is the calendar month of their first-ever event, as "YYYY-MM".
2. For every event, its period is the number of whole calendar months between that event's month and the user's cohort month (0 for the cohort month itself, 1 for the next calendar month, and so on — this is calendar-month arithmetic, not a count of 30-day spans).
3. A cohort's size is the number of distinct users whose first event fell in that month. It is fixed once, and does not change depending on which period you are looking at.
4. Active users for a (cohort, period) cell is the number of distinct users from that cohort who had at least one event in that period.
5. Retention for that cell is active_users / cohort_size * 100, rounded to 1 decimal place.

Return one row per (cohort, period) with columns cohort, period, cohort_size, active_users, retention_pct. Every cohort must have a row for every period from 0 up to the largest period reached by any cohort in the data, even periods that cohort itself has no events in yet — those get active_users = 0 and retention_pct = 0.0.

Sorted by cohort ascending, then period ascending. An empty input returns an empty frame with these columns.