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8c1f7945e4
- documentation of matsubara_freq_mesh - fixing doc of fit_tail - fixing right conventions for matsubara_freq_mesh
122 lines
3.4 KiB
ReStructuredText
122 lines
3.4 KiB
ReStructuredText
.. highlight:: c
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.. _gf_imfreq:
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Green function on Matsubara frequencies
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==========================================================
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This is a specialisation of :ref:`gf<gf_and_view>` for imaginary Matsubara frequencies.
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Synopsis
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------------
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.. code::
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gf<imfreq, 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 :doxy:`matsubara_freq_domain<triqs::gfs::matsubara_domain>`.
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The Matsubara frequencies are :math:`\omega_n=\frac{(2n+1)\pi}{\beta}` for fermions and :math:`\omega_n=\frac{2n\pi}{\beta}` for bosons.
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The mesh is :doc:`matsubara_freq_mesh<matsubara_freq_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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* No interpolation.
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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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HDF5 storage convention
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---------------------------
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h5 tag : `ImFreq`
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TODO : DECIDE if we have 2 tag, one for scalar, one for matrix....
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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;
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int Nfreq =100;
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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<imfreq> { {beta,Fermion,Nfreq}, {1,1} };
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// or a more verbose/explicit form ...
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auto g2 = gf<imfreq> { gf_mesh<imfreq>{beta,Fermion,Nfreq}, make_shape(1,1) };
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// Filling the gf with something...
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triqs::clef::placeholder<0> wn_;
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g1(wn_) << 1/ (wn_ + 2);
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// evaluation at n=3
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std::cout << g1(3) << " == "<< 1/ ( 1_j * M_PI / beta * (2*3+1) + 2) << std::endl;
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// the high frequency expansion was automatically computed.
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//std::cout << g1.singularity() << std::endl; // a bit verbose..
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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<imfreq,scalar_valued> { {beta,Fermion,Nfreq} };
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auto g4 = gf<imfreq,scalar_valued> { gf_mesh<imfreq>{beta,Fermion,Nfreq} };
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g3(wn_) << 1/ (wn_ + 2);
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// evaluation at n=3.
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std::cout << g3(3) << " == "<< 1/ ( 1_j * std::acos(-1) / beta * (2*3+1) + 2) << std::endl;
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}
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