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A first general restructuration of the doc according to the pattern [tour|tutorial|reference]. In the reference part, objects are documented per topic. In each topic, [definition|c++|python|hdf5] (not yet implemented)
86 lines
2.2 KiB
ReStructuredText
86 lines
2.2 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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.. triqs_example:: ./gf_imfreq_0.cpp
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