# triqs::gfs::is_gf_hermitian¶

#include <triqs/gfs.hpp>

Synopsis

template<typename G>
bool is_gf_hermitian (G const & g, double tolerance = 1.e-12)

Test if a Green function object fullfills the fundamental property mentioned below up to a fixed tolerance $$\epsilon$$ Depending on the mesh and target rank one of the following properties is checked $$G[i\omega] == \frac{1}{2} ( G[i\omega] + conj(G[-i\omega]) )$$ $$G[\tau] == \frac{1}{2} ( G[\tau] + conj(G[\tau]) )$$ $$G[i\omega](i,j) == \frac{1}{2} ( G[i\omega](i,j) + conj(G[-i\omega](j,i)) )$$ $$G[\tau](i,j) == \frac{1}{2} ( G[\tau](i,j) + conj(G[\tau](j,i)) )$$ $$G[i\omega](i,j,k,l) == \frac{1}{2} ( G[i\omega](i,j,k,l) + conj(G[-i\omega](k,l,i,j)) )$$ $$G[\tau](i,j,k,l) == \frac{1}{2} ( G[\tau](i,j,k,l) + conj(G[\tau](k,l,i,j)) )$$

## Template parameters¶

• The Green function type

## Parameters¶

• g The Green function object to check the symmetry for
• tolerance The tolerance $$\epsilon$$ for the check [default=1e-12]

## Returns¶

true iif the fundamental property holds for all points of the mesh