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https://github.com/triqs/dft_tools
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bdac3e159c
- little details : code cleaning, clang formatting, along with documentation writing for c++ gf. - separated the mesh in small class for better doc. - work on documentation : reorganize specialisation, ...
128 lines
3.5 KiB
ReStructuredText
128 lines
3.5 KiB
ReStructuredText
.. highlight:: c
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.. _gf_imtime:
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Matsubara imaginary time
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==========================================================
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This is a specialisation of :ref:`gf<gf_and_view>` for imaginary Matsubara time.
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Synopsis
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------------
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.. code::
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gf<imtime, Target, Opt>
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The *Target* template parameter can take the following values :
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+-------------------------+-----------------------------------------------------+
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| Target | Meaning |
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+=========================+=====================================================+
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| scalar_valued | The function is scalar valued (double, complex...). |
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+-------------------------+-----------------------------------------------------+
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| matrix_valued [default] | The function is matrix valued. |
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+-------------------------+-----------------------------------------------------+
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Domain & mesh
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----------------
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The domain is the set of real numbers between 0 and :math:`\beta`
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since the function is periodic (resp. antiperiodic) for bosons (resp. fermions), i.e.
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* :math:`G(\tau+\beta)=-G(\tau)` for fermions
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* :math:`G(\tau+\beta)=G(\tau)` for bosons.
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The domain is implemented in the class :doxy:`matsubara_time_domain<triqs::gfs::matsubara_domain>`.
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The mesh is :doxy:`matsubara_time_mesh<triqs::gfs::matsubara_time_mesh>`.
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Singularity
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-------------
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The singularity is a high frequency expansion, :ref:`gf_tail`.
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Evaluation method
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---------------------
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* Use a linear interpolation between the two closest point of the mesh.
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* Return type :
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* If Target==scalar_valued : a complex
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* If Target==matrix_valued : an object modeling ImmutableMatrix concept.
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* When the point is outside of the mesh, the evaluation of the gf returns :
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* the evaluation of the high frequency tail if no_tail is not set.
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* 0 otherwise
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Data storage
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---------------
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* If Target==scalar_valued :
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* `data_t` : 1d array of complex<double>.
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* g.data()(i) is the value of g for the i-th point of the mesh.
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* If Target==matrix_valued :
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* `data_t` : 3d array (C ordered) of complex<double>.
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* g.data()(i, range(), range()) is the value of g for the i-th point of the mesh.
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TO DO : complex OR DOUBLE : FIX and document !!
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HDF5 storage convention
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---------------------------
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h5 tag : `ImTime`
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Examples
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---------
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.. compileblock::
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#include <triqs/gfs.hpp>
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using namespace triqs::gfs;
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int main(){
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double beta=10, a = 1;
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int n_times=1000;
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// --- first a matrix_valued function ------------
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// First give information to build the mesh, second to build the target
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auto g1 = gf<imtime, matrix_valued, no_tail> { {beta,Fermion,n_times}, {1,1} };
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// or a more verbose/explicit form ...
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auto g2 = gf<imtime> { gf_mesh<imtime>{beta,Fermion,n_times}, make_shape(1,1) };
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// Filling the gf with something... COMMENT HERE : ok only because of no_tail
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triqs::clef::placeholder<0> tau_;
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g1(tau_) << exp ( - a * tau_) / (1 + exp(- beta * a));
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// evaluation at tau=3.2
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std::cout << triqs::arrays::make_matrix(g1(3.2)) << " == "<< exp ( - a * 3.2) / (1 + exp(- beta * a)) << std::endl;
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// --- a scalar_valued function ------------
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// same a before, but without the same of the target space ...
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auto g3 = gf<imtime, scalar_valued, no_tail> { {beta,Fermion,n_times} };
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g3(tau_) << exp ( - a * tau_) / (1 + exp(- beta * a));
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// evaluation at tau=3.2
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std::cout << g3(3.2) << " == "<< exp ( - a * 3.2) / (1 + exp(- beta * a)) << std::endl;
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}
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