inverse_matrix

inverse_matrix.sql

# @author https://github.com/agemcipe
# Calculate inverse of X * X

create table XtX_inverse (row_num int, col_num int, value float);

insert into XtX_inverse
select mat_pos.col_num as row_num # transponse
     , mat_pos.row_num as col_num 
     , (1 / @determinant) * power(-1, mat_pos.row_num + mat_pos.col_num) * 
     (mat_1.value * mat_4.value - mat_2.value
     * mat_3.value)
     value
  from XtX mat_1
       left join XtX mat_2
            on mat_1.row_num = mat_2.row_num 
            and mat_1.col_num < mat_2.col_num
       left join XtX mat_3
            on mat_3.col_num = mat_1.col_num 
            and mat_3.row_num > mat_1.row_num
       left join XtX mat_4
            on mat_4.col_num = mat_2.col_num 
            and mat_4.row_num > mat_2.row_num
       left join XtX mat_pos
            on mat_pos.row_num not in (mat_1.row_num, mat_4.row_num) 
            and mat_pos.col_num not in (mat_1.col_num, mat_4.col_num) 
where 
    (mat_1.col_num + mat_4.col_num + mat_1.row_num + mat_4.row_num)
    = (mat_2.col_num + mat_3.col_num + mat_2.row_num + mat_3.row_num)
order by mat_pos.row_num, mat_pos.col_num;