create table if not exists test
(
  id bigserial primary key,
  fld varchar(255),
  mark varchar(255),
  nil varchar(255)
);
insert into test
select data.id, case when data.id % 2 = 0 then now()::text else null end, case when data.id % 2 = 0 then 'test_string'::text else null end, null
from generate_series(1, 100000) as data(id);
create index if not exists i_test_fld_with_nulls on test (fld);
create index if not exists i_test_fld_without_nulls on test (fld) where fld is not null;
create index if not exists i_test_mark_with_nulls on test (mark);
create index if not exists i_test_mark_without_nulls on test (mark) where mark is not null;
create index if not exists i_test_nil_with_nulls on test (nil);
create index if not exists i_test_nil_without_nulls on test (nil) where nil is not null;

docker run --name postgres-13 -e POSTGRES_USER=testuser -e POSTGRES_PASSWORD=testpwd -e POSTGRES_DB=testdb -d -p 5432:5432 -v /absolute/path/to/initdb.sql:/docker-entrypoint-initdb.d/initdb.sql postgres:13.2
docker run --name postgres-12 -e POSTGRES_USER=testuser -e POSTGRES_PASSWORD=testpwd -e POSTGRES_DB=testdb -d -p 6432:5432 -v /absolute/path/to/initdb.sql:/docker-entrypoint-initdb.d/initdb.sql postgres:12.6

psql -U testuser -d testdb

select
  x.indrelid::regclass as table_name,
  x.indexrelid::regclass as index_name,
  pg_size_pretty(pg_relation_size(x.indexrelid)) as index_size
from pg_index x
join pg_stat_all_indexes psai on x.indexrelid = psai.indexrelid and psai.schemaname = 'public'
order by 1,2;