I want to compute a symmetric matrix A from a vector b by: A = b * b'.

Does the Eigen library automatically take into account that it does not need to do all calculations to get A (because of the symmetry which repeats most of the matrix entries)?

No, not automatically. You need to specify this yourself. The .rankUpdate() member function performs the computation A = A + b * b' on the upper or lower triangular part of A (here, b' is the transpose of b, which is I assume the notation you use). So you can do:

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A.triangularView<Lower>().setZero(); // set lower triangular part of A to zero
A.selfadjointView<Lower>().rankUpdate(b); // compute b * b' and put in lower triangular part
A.triangularView<StrictlyUpper>() = A.triangularView<StrictlyLower>().transpose(); // reflect lower triangular part in upper triangular part


Depending on your application, the last line might not be necessary

jitseniesen wrote:No, not automatically. You need to specify this yourself. The .rankUpdate() member function performs the computation A = A + b * b' on the upper or lower triangular part of A (here, b' is the transpose of b, which is I assume the notation you use). So you can do:

Code: Select all

A.triangularView<Lower>().setZero(); // set lower triangular part of A to zero
A.selfadjointView<Lower>().rankUpdate(b); // compute b * b' and put in lower triangular part
A.triangularView<StrictlyUpper>() = A.triangularView<StrictlyLower>().transpose(); // reflect lower triangular part in upper triangular part


Depending on your application, the last line might not be necessary

Thanks, that's exactly what I was looking for.

Do you have any indication of the speed differences between this method and the ordinary A = b * b' ?

You can expect a x2 for large matrices (>1000^2) and no speed up for small ones (around 30^2). Also, the rankUpdate version is not multi-threaded, so even for large matrices it can be slower if you enabled OpenMP.