Intersection of two matrices

[Jesse Wursten]

This feels like a super basic question, but how do I find the intersection of two matrices in mata? Say I have two matrices A and B

A = (1, 2, 3)
B = (2, 3, 4)

What is then the best way to find the elements that occur in A and B?

(2, 3)

Is the only way to do this to loop over all values of one matrix and see if selectindex() produces anything?

PS: Some additional context. I want to do a heckman selection model with twoway clustered standard errors. I currently do this by running the Heckman three times and recalculating the variance matrix (V_twoway = V1 + V2 - V1&2). Unfortunately, I have a couple dozen million observations and not the best external instrument, so running the Heckman once can take days (187 iterations). Running it three times then isn't very appealing. Instead, I want to calculate the twoway clustered variance matrix directly from the Xs and residuals. At some point in this process I need to determine if an observation is part of both cluster 1 and cluster 2. I can determine the separate elements using selectindex(), but I'm struggling how to then determine that they are present in both.

PS2: I suppose the question could be rephrased as, "how to do a select with two if-conditions".

[William Lisowski]

I have very little faith that I understand what you are trying to do, nor that what I propose below will scale to the size of your problem. But here's something that seems to address your small example.

: A = (1, 2, 3)

: B = (2, 3, 4)

: a = J(1,max((A,B)),0)

: b = a

: a[A] = J(1,cols(A),1)

: a
       1   2   3   4
    +-----------------+
  1 |  1   1   1   0  |
    +-----------------+

: b[B] = J(1,cols(B),1)

: b
       1   2   3   4
    +-----------------+
  1 |  0   1   1   1  |
    +-----------------+

: dupl = select(range(1,max((A,B)),1)',(a :& b))

: dupl
       1   2
    +---------+
  1 |  2   3  |
    +---------+

[Niels Henrik Bruun]

You say intersection of 2 matrices, but your examples are 2 vectors.
Assuming intersection of 2 vectors, possibly with duplicates I suggest the following oneliner (love sunday afternoon puzzzles):

: A = 1..10

: B = 4..6, 5..12

: select((b = uniqrows(B')), rowsum(J(rows(b),1,uniqrows(A')') :== b))'
        1    2    3    4    5    6    7
    +------------------------------------+
  1 |   4    5    6    7    8    9   10  |
    +------------------------------------+

Is this what you wanted?