[eigen] Re: efficient trace of product of symmetric matrices

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Hi everyone, 

I'm wondering whether it is currently possible to compute

tr(A*B),   where   A \in Sym(n,n), B \in Sym(n,n)

efficiently using the development branch of Eigen3. 
Since A and B are symmetric and 

tr(A*B) = sum_ij a_ij * b_ij,

the best way I can think of doing this is 

double tr=0;
for(size_t i=0; i<A.rows(); ++i)
    tr += A(i,i) * B(i,i);
    for(size_t j=0; j<i; ++j)
        tr += 2 * A(i,j)*B(i,j);

I noticed that the triangularView methods do not expose the array 
interface, so am I correct in assuming I cannot vectorise this using 
triangular views?

Furthermore, when trying to make a matrix symmetric by calling 

A.triangularView<StrictlyUpper>() = A.triangularView<StrictlyLower>(),

I noticed that no assignment was taking place, i.e. the matrix A remained as is.
Is this the expected behaviour?


Kind regards,


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