|Re: [eigen] Re: efficient trace of product of symmetric matrices|
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- To: eigen@xxxxxxxxxxxxxxxxxxx
- Subject: Re: [eigen] Re: efficient trace of product of symmetric matrices
- From: Gael Guennebaud <gael.guennebaud@xxxxxxxxx>
- Date: Tue, 21 Feb 2012 23:20:16 +0100
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On Mon, Feb 20, 2012 at 11:28 PM, Patrick <pat05.mlst@xxxxxxxxx> wrote:
> 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?
what you need here is a lazy triangular * triangular product, and
indeed there is no such thing yet. Nevertheless you can still write
your inner loop using an Eigen expression and get vectorization if A
is row major and B column major.
> 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 this the expected behaviour?
Yes that's the intended behavior. You have to transpose the right hand side:
Actually, you can even do:
A.triangularView<StrictlyUpper>() = A.transpose();
The triangularView on the lhs behave like a writing mask.
> Kind regards,