Hi,

we implemented a UDU^T decomposition AddOn for MatrixBase with U as upper unit triangular matrix and D as diagonal matrix. The result is saved in the upper triangular part and the diagonal of the same matrix.

When I want to do the recomposition:

Code: Select all

Matrix<double,6,6> M_ud;
M_ud = M_ud.triangularView<UnitUpper>() * M_ud.diagonal().asDiagonal() * M_ud.triangularView<UnitUpper>().transpose();


I get a compiler error:
error: no match for ‘operator*’ ...

What I can do is:

Code: Select all

Matrix<double, 3, 3> M_ud;
Matrix<double, 3, 3> M2;
M2 = M_ud.diagonal().asDiagonal();

M_ud = M_ud.triangularView<UnitUpper>() * M2 * M_ud.triangularView<UnitUpper>().transpose();


But in this way I would loose the optimization I could get with the knowledge of M2 beeing diagonal (and I would have to create a temporal...).

Is there another way?

Cheers Korbi

it seems your decomposition is just a variant of the LDLT we have in the Cholesky mode but without pivoting.

To reconstruct the original matrix you can do:

M_ud = M_ud.triangularView<UnitUpper>();
M_ud = (M_ud * M_ud.diagonal().asDiagonal()) * M_ud.triangularView<UnitUpper>().transpose();

Yes that's not optimal but still better than converting the diagonal into a full matrix.

Thank you ggael for the idea. It's apparently the best solution without modifying eigen.

You are right, the UDU^T is just a modified Cholesky decomposition that is used for square root filters (without square roots

Would it make sense to add a mult operator to the triangular wrapper to multiply with diagonal matrices and one to diagonal matrices the other way around. Is this an already requested feature?

Cheers
Korbi