postgresql subtract between row while column shift

I have a simple table like this

date            day0   day1   day2   day3
2020-01-01         3      2      1     -1
2020-01-02         2      3      1      0
2020-01-03         4      1     -1      2
2020-01-04         5      2      0      1

I would like to subtract row of yesterday on day(i+1) to row of today on day(i). For example, if today is 2020-01-02 the expected results should be

date         day0    day1    day2    day3
2020-01-02      0      -2      -2     NaN

the 0 (day0) was obtained by 2 (from 2020-01-01 day1) – 2 (from 2020-01-02 day0)
the -2 (day1) was obtained by 1 (from 2020-01-01 day2) – 3 (from 2020-01-02 day1)
the -2 (day2) was obtained by -1 (from 2020-01-01 day3) – 1 (from 2020-01-02 day2)

I’m thinking of select a particular date and its yesterday then transpose and shift row of the yesterday then subtract between 2 transpose column. But i think there might be another elegant way to do. May I have your suggestions?

Answer

You can join the table with itself if you only need to subtract the values for two dates:

select t.date, 
       y.day0 - t.day0 as day0,
       y.day2 - t.day1 as day1,
       y.day3 - t.day2 as day2,
       'NaN'::numeric as day3
from data t
  join data y on y.date = t.date - 1 -- join to the previous date
where t.date = date '2020-01-02'; -- or replace with t.date = current_date

This assumes there is actually a previous date for the given date. If there are gaps in the dates, then this would be a bit more complicated.

Online example