How to assign the complex conjugate of the upper triangular matrix to the lower triangular matrix with Eigen

Question

I have a square Eigen::MatrixXcd x that has complex values assigned to the upper triangular part including the diagonal axis and some random values assigned to the lower triangular part like that (4x4 example):

X00  X01  X02  X03
X10  X11  X12  X13
X20  X21  X22  X23
X30  X31  X32  X33

I want to assign the complex conjugate values of the upper triangular part to the lower one so that it looks like that:

X00       X01        X02        X03
conj(X01) X11        X12        X13
conj(X02) conj(X12)  X22        X23
conj(X03) conj(X13)  conj(X23)  X33

How do I express this assignment for arbitrary sized matrices nicely?

Answer 1

In many cases you don't need to do that and instead just use (instead of X):

X.selfadjointView<Eigen::Upper>()

Especially, for bigger matrices this can reduce the needed memory-throughput (and cache space). For smaller matrices it introduces quite some overhead, though. So to copy the adjoint of the upper right to the strictly lower left write:

X.triangularView<Eigen::StrictlyLower>() = X.adjoint();

For both variants X has to be square, of course.