To write a method that returns a dictionary that contains the mapped names of countries to a recordset of all active partners from that country, you need to perform the following steps:

1. Write a class extending res.partner:

class ResPartner(models.Model): 
    _inherit = 'res.partner' 

2. Add a method called partners_by_country():

    @api.model 
    def partners_by_country(self):

3. In the method, write the following SQL query:

   sql = ('SELECT country_id, array_agg(id) ' 
          'FROM res_partner ' 
          'WHERE active=true AND country_id IS NOT NULL ' 
          'GROUP BY country_id') 

4. Execute the query:

   self.env.cr.execute(sql) 

5. Iterate over the results of the query to populate the result dictionary:

    country_model = self.env['res.country'] 
    result = {} 
    for country_id, partner_ids in self.env.cr.fetchall(): 
        country = country_model.browse(country_id) 
        partners = self.search( 
            [('id', 'in', tuple(partner_ids))] 
        ) 
        result[country] = partners 
    return result