Precision in Matrix Multiplication

[Chang Lee]

Hello Statalist,

I am trying to multiply symmetric square matrices, A and B, in the following form:
C = A*B*A

where C should be a symmetric matrix of the same size as A and B. However, when I multiply using Mata, I end up with a non-symmetric matrix for C. I suspect that this has to do with the precision in multiplication as the elements in matrices A*B and C are both very close to zero (to the order of 10^-14 and smaller).

So far, I have tried using quadcross(A,B) to improve precision to no avail. Unfortunately, I cannot rule out a singular B, so it is not possible to decompose B into say B=LU and calculate C=(AL)*(UA). Is there any way in Mata to improve the precision in obtaining C?

Thanks,
Chang

[Joseph Coveney]

help mf_edittozero
help mf_makesymmetric
help mf__equilrc

are some functions that you might want to look into.

It's a bit surprising that quadcross() wasn't adequate . . .

[Hua Peng (StataCorp)]

Please try the following and report back the results:

mata:
issymmetriconly(A) 
issymmetriconly(B) 
end

[Chang Lee]

Please try the following and report back the results:

mata:
issymmetriconly(A)
issymmetriconly(B)
end

I get 1 for both matrices A and B. To make it more clear, matrix B is equal to X'YX where Y is a k-by-k matrix of ones.

Interesting thing about this is that I found out that when I make off-diagonal elements of Y slightly different than one (say 0.9999), then I get a symmetric matrix C but B doesn't pass the

 issymmetriconly(B)

test.