According to the official documentation of a postgresql, the difference between the function ts_rank and ts_rank_cd is not clear.
According to the documentation:
ts_rank ranks vectors based on the frequency of their matching lexemes.
And ts_rank_cd :
This function computes the cover density ranking for the given document vector and query. Cover density is similar to ts_rankranking except that the proximity of matching lexemes to each other is taken into consideration.
But when trying some examples:
SELECT ts_rank( to_tsvector('name lastname name lastname'), to_tsquery('name & lastname'));
ts_rank:0,3400053
SELECT ts_rank( to_tsvector('name lastname zzzzzzzz tttttt name lastname'), to_tsquery('name & lastname'));
ts_rank:0,3344279
SELECT ts_rank( to_tsvector('name lastname xxxxx yyyyyyy zzzzzzzz tttttt name lastname'), to_tsquery('name & lastname'));
ts_rank:0,3187879
Based to these results I found that even the ts_rank maybe uses the proximity of matching lexemes which is a feature of ts_rank_cd.
Could you provide us some more examples fo the different ranking functions and what is the difference between them?