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https://github.com/triqs/dft_tools
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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)
161 lines
4.2 KiB
ReStructuredText
161 lines
4.2 KiB
ReStructuredText
.. highlight:: c
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Domains & Meshes
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##################
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The :doxy:`full C++ documentation<triqs::gfs::matsubara_freq_mesh>` is available here.
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The linear meshes
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==================
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The mesh kind
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--------------
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This option is particularly important for the Matsubara Green functions in imaginary time.
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Briefly, if we want to describe a function on an interval:
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* ``full_bins`` includes both endpoints,
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* ``half_bins`` includes none of the endpoints
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* ``without_last`` includes only the first endpoint.
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We then have to be careful for example when we fourier transform the function (to not take twice the same point).
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How to access to a mesh point with its index
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---------------------------------------------
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.. compileblock::
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#include <triqs/gfs/refreq.hpp>
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using namespace triqs::gfs;
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int main() {
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//we construct a GF
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double wmin = 0.0;
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double wmax = 1.0;
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int nw = 101;
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auto Gw = make_gf<refreq, scalar_valued>(wmin, wmax, nw);
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//we print the mesh parameters and print te value of the 10th point
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std::cout << "The kind of the mesh is " << Gw.mesh().kind() << std::endl;
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std::cout << "The smallest mesh point value is w_min=" << Gw.mesh().x_min() << std::endl;
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std::cout << "The largest mesh point value is w_max=" << Gw.mesh().x_max() << std::endl;
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std::cout << "The number of mesh points is n=" << Gw.mesh().size() << std::endl;
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std::cout << "Between two consecutive mesh points: delta=" << Gw.mesh().delta() << std::endl;
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std::cout << "The 10th mesh point is w=" << Gw.mesh()[10] << std::endl;
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}
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How to access to a mesh point with a value
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-------------------------------------------
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In this case, we look for the closest mesh point, but can need the distance of the value to the mesh point.
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``windowing`` gives all these informations:
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.. compileblock::
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#include <triqs/gfs/refreq.hpp>
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using namespace triqs::gfs;
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int main() {
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double wmin = 0.0;
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double wmax = 1.0;
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int nw=101;
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auto Gw= make_gf<refreq, scalar_valued>(wmin, wmax, nw);
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double w=0.25156;
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size_t index; double wd; bool in;
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std::tie(in, index, wd) = windowing ( Gw.mesh(), w);
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std::cout << "Is the point w="<< w <<" in the mesh range ? " << in << std::endl;
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if(in){
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std::cout << "The point before is the " << index << "th" << std::endl;
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std::cout << "The position in the intervall is " << wd << std::endl;
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}
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}
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The four basic linear meshes
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============================
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Real time
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----------
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The domain is the set of real numbers.
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By default, the mesh kind is ``full_bins``.
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Be careful to the value of a function at a point in case of discontinuities: is its value equal to the limit from below ? To the limit from above ? By none of these limits ?
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Real frequency
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---------------
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The domain is the set of real numbers.
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By default, the mesh kind is ``full_bins``.
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Products of meshes
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===================
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We detail the case of a two mesh product, but what follows is true for any number of meshes.
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A mesh point can be labelled by a linear index, or by a tuple of indices. Each mesh point correspond to a point of the domain, which is a tuple of points of the subdomains.
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We can navigate between these representations, through ``closest_mesh_pt``, ``get_closest_pt``, ``index_to_linear``,...
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How to access to the closest mesh point
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---------------------------------------
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.. compileblock::
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#include <triqs/gfs/two_real_times.hpp>
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using namespace triqs::gfs;
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int main() {
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double tmax = 1.0;
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int nt = 101;
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auto Gtt = make_gf<two_real_times>(tmax, nt, triqs::arrays::make_shape(1,1));
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//does not work for instance
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//double t1 = 0.256, t2 = 0.758;
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//Gtt(closest_mesh_pt(i1,i2)) = 1.5;
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}
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How to access to a mesh point with its index
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---------------------------------------------
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.. compileblock::
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#include <triqs/gfs/two_real_times.hpp>
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using namespace triqs::gfs;
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int main() {
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double tmax = 1.0;
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int nt = 101;
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auto Gtt = make_gf<two_real_times>(tmax, nt, triqs::arrays::make_shape(1,1));
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int i1 = 14, i2 = 86;
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Gtt.on_mesh(i1, i2) = 1.8;
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std::cout << Gtt.on_mesh(i1, i2)(0,0) << std::endl;
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}
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