How to compute Inner product between block weights and feature table?

Question

I have two tables: Table 1 (tb1): Shows which symbols belong to which blocks (1 = belongs, NULL = doesn't belong)

SYMBOL | block1 | block2 | block3 | block4
-------|--------|--------|--------|-------
sym1   |        |        | 1      |      
sym2   |        | 1      |        | 1
sym3   | 1      |        |        |      
sym4   |        |        | 1      |      
sym5   |        |        |        | 1

Table 2 (tb2): Contains three numerical features for some symbols (note: not all symbols are included)

SYMBOL | col1 | col2 | col3
-------|------|------|------
sym1   | 1.1  | 2.1  | 3.1
sym3   | 1.2  | 2.2  | 3.2
sym4   | 1.3  | 2.3  | 3.3

For each block in tb1:

Find all symbols marked with 1.
For those symbols, look up their feature values (col1, col2, col3) in tb2 (if they exist).
Calculate the inner product between:
- The weight vector (from tb1's block column)
- Each feature column (col1/col2/col3) from tb2

For example:

block1: Only sym3 is marked → Use its values (1.2, 2.2, 3.2).
block3: sym1 + sym4 → Sum their values: (1.1+1.3, 2.1+2.3, 3.1+3.3) = (2.4, 4.4, 6.4).
block2/block4: Their symbols (sym2, sym5) aren’t in tb2 → Return empty.

Here is my expected output:

        col1 col2 col3             
        ---- ---- -----
block1| 1.2  2.2  3.2              
block2|                                        
block3| 2.4  4.4  6.4
block4|

How to implement this inner product calculation in DolphinDB?

saki · Accepted Answer · 2025-06-11 09:30:12Z

You can achieve this calculation using matrix operations. Here's how to implement it step by step:
First, convert the data into labeled matrices.

tb1 = table(`sym1`sym2`sym3`sym4`sym5 as SYMBOL, NULL NULL 1 NULL NULL as block1, NULL 1 NULL NULL NULL as block2, 1 NULL NULL 1 NULL as block3, NULL 1 NULL NULL 1 as block4)
tb2 = table(`sym1`sym3`sym4 as SYMBOL, 1+double(seq(1,3))/10 as col1, 2+double(seq(1,3))/10 as col2, 3+double(seq(1,3))/10 as col3)

m1 = matrix(tb1[:,1:]).rename!(tb1.SYMBOL, tb1.colNames()[1:])
m2 = matrix(tb2[:,1:]).rename!(tb2.SYMBOL, tb2.colNames()[1:])

Then use the cross function to compute the inner products between all pairs of columns from the two matrices.

mm1, mm2 = align(m1, m2, 'fj', true)
re = cross(wsum, mm1, mm2)

If the row labels of the two matrices don't completely match, you can first align them using the align function.

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