Partial evaluation

Multivariable Green functions can be both partially evalued.

Partial evaluation

Purpose :

Having a function (x,y) -> f(x,y), fix x = x0 in order to obtain a function of y only.

Synopsis

If g is a multivar function, and
   auto _ = var_t{};

   g[w][_] // is the gf partially evaluated for the first mesh.

When a Green function is evaluated with [][], and there is at least once var_t as an argument, the result is a view of the partially evaluated gf with :

• a mesh corresponding of the mesh components of the _ variables.

• the tag type is computed accordingly

• the target is unchanged.

• the data is a sliced view of the original function

• singularity : in the case where the singularity is non trivial, is it also partially evaluated (in practice, G(k,omega). EXPLAIN).

Example :

#include <triqs/gfs.hpp>
#include <triqs/mesh.hpp>
using namespace triqs::gfs;
using namespace triqs;
using nda::clef::placeholder;
int main() {
  double beta = 1, tmin = 0, tmax = 1.0;
  int n_re_time = 5, n_im_time = 10;

  using g_t_tau_s = gf<prod<retime, imtime>, scalar_valued>;

  // a scalar valued function
  auto g = g_t_tau_s{{{tmin, tmax, n_re_time}, {beta, Fermion, n_im_time}}};

  auto _ = all_t{}; // a dedicated placeholder for partial evaluation

  auto g_sliced = g[3, _]; // 3 is the index of the point

  // or if we loop over the first component of the mesh of g
  for (auto w : std::get<0>(g.mesh())) {
    std::cout << g[w, _] << std::endl; // or do anything with it ...
  }
}

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