void Demo() {
const int nspins=2;
const int nfreq=10;
const double beta=5;
// Construct the meshes:
g::matsubara_positive_mesh m_mesh(beta, nfreq);
g::momentum_index_mesh k_mesh(generate_momentum_mesh());
g::index_mesh s_mesh(nspins);
// construct a GF using a pre-defined convenience type
g::omega_k_sigma_gf gf(m_mesh, k_mesh, s_mesh);
// initialize a GF to all-zeros
gf.initialize();
// Make indices:
g::matsubara_index omega;
omega=4;
g::momentum_index ii(2);
g::index sigma(0);
// Assign a GF element:
gf(omega,ii,sigma)=std::complex<double>(3,4);
// Density matrix as a double-valued GF
// on momentum and integer-index space:
typedef
g::two_index_gf<double, g::momentum_index_mesh, g::index_mesh>
density_matrix_type;
// Construct the object:
density_matrix_type denmat=density_matrix_type(k_mesh,s_mesh);
// prepare diagonal matrix
const double U=3.0;
denmat.initialize();
// loop over first mesh index:
for (g::momentum_index i=g::momentum_index(0);
i<denmat.mesh1().extent(); ++i) {
denmat(i,g::index(0))=0.5*U;
denmat(i,g::index(1))=0.5*U;
}
// construct a tailed GF using predefined convenience type:
g::omega_k_sigma_gf_with_tail gft(gf);
gft.set_tail(0, denmat); // set the tail
density_matrix_type gftail=gft.tail(0); // retrieve the tail
// access the tailed GF element
std::complex<double> x=gft(omega,ii,sigma);
}
TEST_F(ThreeIndexTestGF, TailSaveLoad)
{
namespace g=alps::gf;
typedef g::two_index_gf<double, g::momentum_index_mesh, g::index_mesh> density_matrix_type;
density_matrix_type denmat=density_matrix_type(g::momentum_index_mesh(get_data_for_momentum_mesh()),
g::index_mesh(nspins));
// prepare diagonal matrix
double U=3.0;
denmat.initialize();
for (g::momentum_index i=g::momentum_index(0); i<denmat.mesh1().extent(); ++i) {
denmat(i,g::index(0))=0.5*U;
denmat(i,g::index(1))=0.5*U;
}
// Attach a tail to the GF
int order=0;
// FIXME: TODO: gf.set_tail(min_order, max_order, denmat, ...);
g::omega_k_sigma_gf_with_tail gft(gf);
g::omega_k_sigma_gf_with_tail gft2(gft);
EXPECT_EQ(g::TAIL_NOT_SET,gft.min_tail_order());
EXPECT_EQ(g::TAIL_NOT_SET,gft.max_tail_order());
gft.set_tail(order, denmat);
EXPECT_EQ(0,gft.min_tail_order());
EXPECT_EQ(0,gft.max_tail_order());
EXPECT_EQ(0,(denmat-gft.tail(0)).norm());
{
alps::hdf5::archive oar("gft.h5","w");
gft(g::matsubara_index(4),g::momentum_index(3), g::index(1))=std::complex<double>(7., 3.);
gft.save(oar,"/gft");
}
{
alps::hdf5::archive iar("gft.h5");
gft2.load(iar,"/gft");
}
EXPECT_EQ(gft2.tail().size(), gft.tail().size()) << "Tail size mismatch";
EXPECT_NEAR(0, (gft.tail(0)-gft2.tail(0)).norm(), 1E-8)<<"Tail loaded differs from tail stored";
EXPECT_EQ(7, gft2(g::matsubara_index(4),g::momentum_index(3), g::index(1)).real()) << "GF real part mismatch";
EXPECT_EQ(3, gft2(g::matsubara_index(4),g::momentum_index(3), g::index(1)).imag()) << "GF imag part mismatch";
}
TEST_F(GreensFunctionTailTest, TailSaveLoad)
{
typedef gfns::greenf<std::complex<double>, gfns::matsubara_mesh<gfns::mesh::POSITIVE_ONLY>, gfns::index_mesh> omega_sigma_gf;
typedef gfns::gf_tail<omega_sigma_gf, gfns::greenf<double, gfns::index_mesh> > omega_sigma_gf_with_tail;
typedef gfns::greenf<double, gfns::index_mesh> density_matrix_type;
density_matrix_type denmat = density_matrix_type(gfns::index_mesh(nspins));
omega_sigma_gf gf(gfns::matsubara_positive_mesh(beta,nfreq), alps::gf::index_mesh(nspins));
// prepare diagonal matrix
double U=3.0;
denmat.initialize();
denmat(gfns::index(0))=0.5*U;
denmat(gfns::index(1))=0.5*U;
// Attach a tail to the GF
int order=0;
omega_sigma_gf_with_tail gft(gf);
omega_sigma_gf_with_tail gft2(gft);
EXPECT_EQ(gfns::TAIL_NOT_SET,gft.min_tail_order());
EXPECT_EQ(gfns::TAIL_NOT_SET,gft.max_tail_order());
gft.set_tail(order, denmat);
EXPECT_EQ(0,gft.min_tail_order());
EXPECT_EQ(0,gft.max_tail_order());
EXPECT_EQ(0,(denmat - gft.tail(0)).norm());
{
alps::hdf5::archive oar("gf_2i_tailsaveload.h5","w");
gft(gfns::matsubara_index(4),gfns::index(1))=std::complex<double>(7., 3.);
oar["/gft"] << gft;
}
{
alps::hdf5::archive iar("gf_2i_tailsaveload.h5");
iar["/gft"] >> gft2;
}
EXPECT_EQ(gft2.tail().size(), gft.tail().size()) << "Tail size mismatch";
EXPECT_NEAR(0, (gft.tail(0)-gft2.tail(0)).norm(), 1E-8)<<"Tail loaded differs from tail stored";
EXPECT_EQ(7, gft2(gfns::matsubara_index(4), gfns::index(1)).real()) << "GF real part mismatch";
EXPECT_EQ(3, gft2(gfns::matsubara_index(4), gfns::index(1)).imag()) << "GF imag part mismatch";
}
// Check incompatible broadcast of tails
TEST_F(FourIndexGFTest,MpiWrongTailBroadcast)
{
namespace g=alps::gf;
typedef g::three_index_gf<double,
g::momentum_index_mesh,
g::momentum_index_mesh,
g::index_mesh> density_matrix_type;
density_matrix_type denmat=density_matrix_type(g::momentum_index_mesh(get_data_for_momentum_mesh()),
g::momentum_index_mesh(get_data_for_momentum_mesh()),
g::index_mesh(this->nspins));
// Get the rank
int rank;
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
// prepare diagonal matrix
double U=3.0;
denmat.initialize();
for (g::momentum_index i=g::momentum_index(0); i<denmat.mesh1().extent(); ++i) {
denmat(i,i,g::index(0))=0.5*U;
denmat(i,i,g::index(1))=0.5*U;
}
g::omega_k1_k2_sigma_gf_with_tail gft(gf);
int order=0;
if (rank==MASTER) { // on master only
// attach a tail to the GF:
gft.set_tail(order, denmat);
// change the GF
gft(g::matsubara_index(4),g::momentum_index(3), g::momentum_index(2), g::index(1))=std::complex<double>(7., 3.);
}
// slaves do not have the tail attached to their GF.
gft.broadcast(MASTER,MPI_COMM_WORLD);
EXPECT_EQ(7, gft(g::matsubara_index(4),g::momentum_index(3), g::momentum_index(2), g::index(1)).real()) << "GF real part mismatch on rank " << rank;
EXPECT_EQ(3, gft(g::matsubara_index(4),g::momentum_index(3), g::momentum_index(2), g::index(1)).imag()) << "GF imag part mismatch on rank " << rank;
ASSERT_EQ(1, gft.tail().size()) << "Tail size mismatch on rank " << rank;
EXPECT_NEAR(0, (gft.tail(0)-denmat).norm(), 1E-8) << "Tail broadcast differs from the received on rank " << rank;
}
TEST_F(TwoIndexGFTest, TailSaveLoad)
{
namespace g=alps::gf;
typedef g::one_index_gf<double, g::index_mesh> density_matrix_type;
density_matrix_type denmat=density_matrix_type(g::index_mesh(nspins));
// prepare diagonal matrix
double U=3.0;
denmat.initialize();
denmat(g::index(0))=0.5*U;
denmat(g::index(1))=0.5*U;
// Attach a tail to the GF
int order=0;
g::omega_sigma_gf_with_tail gft(gf);
g::omega_sigma_gf_with_tail gft2(gft);
EXPECT_EQ(g::TAIL_NOT_SET,gft.min_tail_order());
EXPECT_EQ(g::TAIL_NOT_SET,gft.max_tail_order());
gft.set_tail(order, denmat);
EXPECT_EQ(0,gft.min_tail_order());
EXPECT_EQ(0,gft.max_tail_order());
EXPECT_EQ(0,(denmat-gft.tail(0)).norm());
{
alps::hdf5::archive oar("gft.h5","w");
gft(g::matsubara_index(4),g::index(1))=std::complex<double>(7., 3.);
gft.save(oar,"/gft");
}
{
alps::hdf5::archive iar("gft.h5");
gft2.load(iar,"/gft");
}
EXPECT_EQ(gft2.tail().size(), gft.tail().size()) << "Tail size mismatch";
EXPECT_NEAR(0, (gft.tail(0)-gft2.tail(0)).norm(), 1E-8)<<"Tail loaded differs from tail stored";
EXPECT_EQ(7, gft2(g::matsubara_index(4), g::index(1)).real()) << "GF real part mismatch";
EXPECT_EQ(3, gft2(g::matsubara_index(4), g::index(1)).imag()) << "GF imag part mismatch";
}
TEST_F(ThreeIndexTestGF, tail)
{
namespace g=alps::gf;
typedef g::two_index_gf<double, g::momentum_index_mesh, g::index_mesh> density_matrix_type;
density_matrix_type denmat=density_matrix_type(g::momentum_index_mesh(get_data_for_momentum_mesh()),
g::index_mesh(nspins));
// prepare diagonal matrix
double U=3.0;
denmat.initialize();
for (g::momentum_index i=g::momentum_index(0); i<denmat.mesh1().extent(); ++i) {
denmat(i,g::index(0))=0.5*U;
denmat(i,g::index(1))=0.5*U;
}
// Attach a tail to the GF
int order=0;
// FIXME: TODO: gf.set_tail(min_order, max_order, denmat, ...);
g::omega_k_sigma_gf_with_tail gft(gf);
gft.set_tail(order, denmat)
// .set_tail(order+1, other_gf) ....
;
EXPECT_NEAR((denmat-gft.tail(order)).norm(), 0, 1.e-8);
/* The following does not compile, as expected:
typedef g::three_index_gf<double, g::momentum_index_mesh, g::momentum_index_mesh, g::index_mesh> some_matrix_type;
typedef g::three_index_gf_with_tail<some_matrix_type, g::two_index_gf<double, g::momentum_index_mesh, g::index_mesh> > some_matrix_type_with_tail;
some_matrix_type* ptr=0;
some_matrix_type_with_tail wrong(*ptr);
*/
/* The following does not compile, as expected:
typedef g::three_index_gf<double, g::itime_mesh, g::itime_mesh, g::index_mesh> some_gf_type;
typedef g::three_index_gf_with_tail<some_gf_type, g::two_index_gf<double, g::momentum_index_mesh, g::index_mesh> > some_gf_type_with_tail;
some_gf_type_with_tail wrong(*(some_gf_type*)0);
*/
}
TEST_F(TwoIndexGFTest, tail)
{
namespace g=alps::gf;
typedef g::one_index_gf<double, g::index_mesh> density_matrix_type;
density_matrix_type denmat=density_matrix_type(g::index_mesh(nspins));
// prepare diagonal matrix
double U=3.0;
denmat.initialize();
denmat(g::index(0))=0.5*U;
denmat(g::index(1))=0.5*U;
// Attach a tail to the GF
int order=0;
g::omega_sigma_gf_with_tail gft(gf);
gft.set_tail(order, denmat);
EXPECT_NEAR((denmat-gft.tail(order)).norm(), 0, 1.e-8);
}
static void gftCallFunc(const iocshArgBuf *args) { gft(args[0].sval);}
