Saving nonzero matrix elements

[Bill Smith]

I have a covariance matrix that is lower triangular where the ones represent values:

 
 			0










 			0
 			1









 			0
 			1
 			1








 			0
 			1
 			1
 			1







 			0
 			1
 			1
 			1
 			1






 			0
 			0
 			0
 			0
 			0
 			0





 			0
 			1
 			1
 			1
 			1
 			0
 			1




 			0
 			1
 			1
 			1
 			1
 			0
 			1
 			1



 			0
 			1
 			1
 			1
 			1
 			0
 			1
 			1
 			1


 			0
 			1
 			1
 			1
 			1
 			0
 			1
 			1
 			1
 			1

I'd like to delete the rows and columns that are all zero:

 
 			1








 			1
 			1







 			1
 			1
 			1






 			1
 			1
 			1
 			1





 			1
 			1
 			1
 			1
 			1




 			1
 			1
 			1
 			1
 			1
 			1



 			1
 			1
 			1
 			1
 			1
 			1
 			1


 			1
 			1
 			1
 			1
 			1
 			1
 			1
 			1

I know that there is probably some way of doing this with st_select and st_matrix in mata, but everything I've tried has been met with a error. Can someone help me out?

[Frank Erickson]

Could you create a reproducible example with code? I'm thinking like

1, 1 \ 0, 1

both for input and desired output.

I am not really clear on what a covariance matrix object *is* in Mata, since I've never come across one.

[Christophe Kolodziejczyk]

Here is one solution. You can make a function out of this.
In this example J should be triangular where the second row and the third column have zeros and should be removed.

J =(1,0,0,0,0\0,0,0,0,0\1,1,0,0,0\1,1,0,1,0\1,1,0,1,1)


I=select(J,rowsum(J):!=0)
I=select(I,colsum(I):!=0)

[Niels Henrik Bruun]

As I read

where the ones represent values

all sorts of numbers can be placed instead of ones.
If so Christophe's solution can not be used directly, take for instance

J =(1,0,0,0,0\0,0,0,0,0\1,-1,0,0,0\1,1,0,1,0\1,1,0,1,1)

[Christophe Kolodziejczyk]

Niels, you're right. Thanks for pointing that. We can then modify the code as follows

I = J:!=0
I = select(I,rowsum(I):!=0)
I = select(I,colsum(I):!=0)

[Niels Henrik Bruun]

Ah, excellent. I tried to figure out that solution myself, but I got stuck at the one thing missing in your solution as well.
We have to select the rows and columns of J, not I, so I think the answer is:

J = select(J,rowsum(J:!=0):!=0)
J = select(J,colsum(J:!=0):!=0)

Or something like it

[Christophe Kolodziejczyk]

Seems right to me .
What about this one (if you would like to keep J)?

rIndex = select((1..rows(J))',rowsum(J:!=0):!=0)
cIndex = select((1..cols(J)),colsum(J:!=0):!=0)

I = J[rIndex,cIndex]

[Frank Erickson]

That double :!= condition looks a little complicated. I would define

test    = !!J
rIndex  = select(1::rows(J),rowsum(test))
cIndex  = select(1..cols(J),colsum(test))

select already treats nonzero/zero as true/false.

[William Lisowski]

!!J is very elegant. Since the original question proposed a covariance (and thus symmetric), matrix, taking this into account reduces the number of selects, since each row of zeros corresponds to a column of zeros.

mata:
J =(1,0,0,1,1\0,0,0,0,0\0,0,2,-2,0\1,0,-2,1,0\1,0,0,0,1)
index  = select(1::rows(J),rowsum(!!J))
I = J[index,index]
J
I
end