Why does calc subscr work with index vectors in org tables?

Question

In my org table I use the next formula to sum rows 1,5,7 of column 6.

|   | Start date       | End date         | Task     | State     | Duration (hours) |
|---+------------------+------------------+----------+-----------+------------------|
| # | 15.08.2019 10:30 | 15.08.2019 12:00 | T-320    | Taken     |             1.50 |
| # | 15.08.2019 13:00 | 15.08.2019 14:00 | T-320    | Taken     |             1.00 |
| # | 15.08.2019 14:30 | 15.08.2019 18:00 | T-321    | Taken     |             3.50 |
| # | 16.08.2019 10:30 | 16.08.2019 12:00 | T-321    | Taken     |             1.50 |
| # | 16.08.2019 13:30 | 16.08.2019 15:30 | T-321    | Taken     |             2.00 |
| # | 16.08.2019 15:30 | 16.08.2019 18:00 | T-322    | Taken     |             2.50 |
| # | 28.08.2019 14:00 | 28.08.2019 17:00 | T-330    | Taken     |             3.00 |
| # | 28.08.2019 17:00 | 28.08.2019 18:00 | T-331    | Taken     |             1.00 |
| # | 29.08.2019 10:30 | 29.08.2019 15:00 | INIT-117 | Done      |             4.50 |
| # | 29.08.2019 15:30 | 29.08.2019 16:00 | FM-222   | Done      |             0.50 |
| # | 29.08.2019 16:00 | 29.08.2019 18:00 | T-331    | Postponed |             2.00 |
| # | 30.08.2019 10:30 | 30.08.2019 12:00 | INIT-121 | Taken     |             1.50 |
| # | 30.08.2019 13:30 | 30.08.2019 21:00 | INIT-121 | Taken     |             7.50 |
|---+------------------+------------------+----------+-----------+------------------|
|   |                  |                  |          |           |              6.5 |

#+TBLFM: $6=$3-$2;t::@>$6=vsum(subscr(@I$6..@II$6,{1,5,7}));%.2f

Nice. It's work fine.

But I have a question: What is the return value of subscr?

Answer 1

I've given you a link to the calc manual in my other answer.

The manual describes that subscr is a synonym of mrow and the extension to vectors of indexes is described in the paragraph on mrow:

If the index is itself a vector of integers, the result is a vector of the corresponding elements of the input vector, or a matrix of the corresponding rows of the input matrix. This command can be used to obtain any permutation of a vector.

Furthermore, the org-manual says that with org tables you have all the power of calc at your fingertips.

Note further that @I$6..@II$6 in the org table formula expands to the calc vector [1.50,1.00,3.50,1.50,2.00,2.50,3.00,1.00,4.50,0.50,2.00,1.50,7.50] and that your expanded formula looks like:

vsum(subscr([1.50,1.00,3.50,1.50,2.00,2.50,3.00,1.00,4.50,0.50,2.00,1.50,7.50],{1,5,7}))

You can discover that for yourself by debugging your org table formula. Switch on Tbl -> Debug Formulas before evaluating the formula.