mirror of
https://github.com/triqs/dft_tools
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e1c113b745
- evaluator - G(k,tau) is real - partial_eval for matrix_valued functions - details : simplifying traits (using decay_t)
176 lines
7.9 KiB
C++
176 lines
7.9 KiB
C++
/*******************************************************************************
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*
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* TRIQS: a Toolbox for Research in Interacting Quantum Systems
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*
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* Copyright (C) 2013 by O. Parcollet
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*
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* TRIQS is free software: you can redistribute it and/or modify it under the
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* terms of the GNU General Public License as published by the Free Software
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* Foundation, either version 3 of the License, or (at your option) any later
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* version.
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*
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* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
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* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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* details.
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*
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* You should have received a copy of the GNU General Public License along with
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* TRIQS. If not, see <http://www.gnu.org/licenses/>.
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*
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******************************************************************************/
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#pragma once
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#include "./tools.hpp"
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#include "./gf.hpp"
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#include "./meshes/product.hpp"
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#include "./evaluators.hpp"
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namespace triqs {
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namespace gfs {
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template <typename... Ms> struct cartesian_product {
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using type = std::tuple<Ms...>;
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static constexpr size_t size = sizeof...(Ms);
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};
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// use alias
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template <typename... Ms> struct cartesian_product<std::tuple<Ms...>> : cartesian_product<Ms...> {};
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// the mesh is simply a cartesian product
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template <typename Opt, typename... Ms> struct gf_mesh<cartesian_product<Ms...>, Opt> : mesh_product<gf_mesh<Ms, Opt>...> {
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// using mesh_product< gf_mesh<Ms,Opt> ... >::mesh_product< gf_mesh<Ms,Opt> ... > ;
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using B = mesh_product<gf_mesh<Ms, Opt>...>;
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gf_mesh() = default;
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gf_mesh(gf_mesh<Ms, Opt>... ms) : B{std::move(ms)...} {}
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};
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namespace gfs_implementation {
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/// --------------------------- hdf5 ---------------------------------
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// h5 name : name1_x_name2_.....
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template <typename Opt, typename... Ms> struct h5_name<cartesian_product<Ms...>, matrix_valued, Opt> {
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static std::string invoke() {
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return triqs::tuple::fold([](std::string a, std::string b) { return a + std::string(b.empty() ? "" : "_x_") + b; },
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std::make_tuple(h5_name<Ms, matrix_valued, Opt>::invoke()...), std::string());
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}
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};
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template <typename Opt, int R, typename... Ms>
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struct h5_name<cartesian_product<Ms...>, tensor_valued<R>, Opt> : h5_name<cartesian_product<Ms...>, matrix_valued, Opt> {};
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// a slight difference with the generic case : reinterpret the data array to avoid flattening the variables
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template <typename Opt, int R, typename... Ms> struct h5_rw<cartesian_product<Ms...>, tensor_valued<R>, Opt> {
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using g_t = gf<cartesian_product<Ms...>, tensor_valued<R>, Opt>;
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static void write(h5::group gr, typename g_t::const_view_type g) {
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h5_write(gr, "data", reinterpret_linear_array(g.mesh(), g().data()));
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h5_write(gr, "singularity", g._singularity);
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h5_write(gr, "mesh", g._mesh);
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h5_write(gr, "symmetry", g._symmetry);
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}
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template <bool IsView>
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static void read(h5::group gr, gf_impl<cartesian_product<Ms...>, tensor_valued<R>, Opt, IsView, false> &g) {
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using G_t = gf_impl<cartesian_product<Ms...>, tensor_valued<R>, Opt, IsView, false>;
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h5_read(gr, "mesh", g._mesh);
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auto arr = arrays::array<typename G_t::data_t::value_type, sizeof...(Ms) + R>{};
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h5_read(gr, "data", arr);
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auto sh = arr.shape();
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arrays::mini_vector<size_t, R + 1> sh2;
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sh2[0] = g._mesh.size();
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for (int u = 1; u < R + 1; ++u) sh2[u] = sh[sizeof...(Ms) - 1 + u];
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g._data = arrays::array<typename G_t::data_t::value_type, R + 1>{sh2, std::move(arr.storage())};
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h5_read(gr, "singularity", g._singularity);
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h5_read(gr, "symmetry", g._symmetry);
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}
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};
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/// --------------------------- data access ---------------------------------
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template <typename Opt, typename... Ms>
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struct data_proxy<cartesian_product<Ms...>, scalar_valued, Opt> : data_proxy_array<std::complex<double>, 1> {};
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template <typename Opt, typename... Ms>
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struct data_proxy<cartesian_product<Ms...>, matrix_valued, Opt> : data_proxy_array<std::complex<double>, 3> {};
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template <int R, typename Opt, typename... Ms>
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struct data_proxy<cartesian_product<Ms...>, tensor_valued<R>, Opt> : data_proxy_array<std::complex<double>, R + 1> {};
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template <typename Opt, typename M0>
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struct data_proxy<cartesian_product<M0,imtime>, matrix_valued, Opt> : data_proxy_array<double, 3> {};
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/// --------------------------- evaluator ---------------------------------
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/**
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* This the multi-dimensional evaluator.
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* It combine the evaluator of each components, as long as they are a linear form
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* eval(g, x) = \sum_i w_i g( n_i(x)) , with w some weight and n_i some points on the grid.
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* Mathematically, it is written as (example of evaluating g(x1,x2,x3,x4)).
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* Notation : eval(X) : g -> g(X)
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* eval(x1,x2,x3,x4) (g) = eval (x1) ( binder ( g, (), (x2,x3,x4)) )
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* binder( g, (), (x2,x3,x4)) (p1) = eval(x2)(binder (g,(p1),(x3,x4)))
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* binder( g, (p1), (x3,x4)) (p2) = eval(x3)(binder (g,(p1,p2),(x4)))
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* binder( g, (p1,p2), (x4)) (p3) = eval(x4)(binder (g,(p1,p2,p3),()))
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* binder( g, (p1,p2,p3),()) (p4) = g[p1,p2,p3,p4]
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*
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* p_i are points on the grids, x_i points in the domain.
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*
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* Unrolling the formula gives (for 2 variables, with 2 points interpolation)
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* eval(xa,xb) (g) = eval (xa) ( binder ( g, (), (xb)) ) =
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* w_1(xa) binder ( g, (), (xb))( n_1(xa)) + w_2(xa) binder ( g, (), (xb))( n_2(xa))
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* = w_1(xa) ( eval(xb)( binder ( g, (n_1(xa) ), ()))) + 1 <-> 2
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* = w_1(xa) ( W_1(xb) * binder ( g, (n_1(xa) ), ())(N_1(xb)) + 1<->2 ) + 1 <-> 2
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* = w_1(xa) ( W_1(xb) * g[n_1(xa), N_1(xb)] + 1<->2 ) + 1 <-> 2
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* = w_1(xa) ( W_1(xb) * g[n_1(xa), N_1(xb)] + W_2(xb) * g[n_1(xa), N_2(xb)] ) + 1 <-> 2
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* which is the expected formula
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*/
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// implementation : G = gf, Tn : tuple of n points, Ev : tuple of evaluators (the evals functions),
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// pos = counter from #args-1 =>0
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// NB : the tuple is build in reverse with respect to the previous comment.
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template <typename G, typename Tn, typename Ev, int pos> struct binder;
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template <int pos, typename G, typename Tn, typename Ev> binder<G, Tn, Ev, pos> make_binder(G const *g, Tn tn, Ev const &ev) {
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return binder<G, Tn, Ev, pos>{g, std::move(tn), ev};
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}
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template <typename G, typename Tn, typename Ev, int pos> struct binder {
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G const *g;
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Tn tn;
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Ev const &evals;
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auto operator()(size_t p) const
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DECL_AND_RETURN(std::get<pos>(evals)(make_binder<pos - 1>(g, triqs::tuple::push_front(tn, p), evals)));
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};
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template <typename G, typename Tn, typename Ev> struct binder<G, Tn, Ev, -1> {
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G const *g;
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Tn tn;
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Ev const &evals;
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auto operator()(size_t p) const DECL_AND_RETURN(triqs::tuple::apply(on_mesh(*g), triqs::tuple::push_front(tn, p)));
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};
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// now the multi d evaluator itself.
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template <typename Target, typename Opt, typename... Ms> struct evaluator<cartesian_product<Ms...>, Target, Opt> {
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static constexpr int arity = sizeof...(Ms);
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mutable std::tuple<evaluator_fnt_on_mesh<Ms>...> evals;
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struct _poly_lambda { // replace by a polymorphic lambda in C++14
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template <typename A, typename B, typename C> void operator()(A &a, B const &b, C const &c) const {
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a = A{b, c};
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}
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};
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template <typename G, typename... Args>
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// std::complex<double> operator() (G const * g, Args && ... args) const {
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auto operator()(G const *g, Args &&... args)
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const -> decltype(std::get<sizeof...(Args) - 1>(evals)(make_binder<sizeof...(Args) - 2>(g, std::make_tuple(), evals)))
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// when do we get C++14 decltype(auto) ...!?
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{
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static constexpr int R = sizeof...(Args);
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// build the evaluators, as a tuple of ( evaluator<Ms> ( mesh_component, args))
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triqs::tuple::call_on_zip(_poly_lambda(), evals, g->mesh().components(), std::make_tuple(args...));
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return std::get<R - 1>(evals)(make_binder<R - 2>(g, std::make_tuple(), evals));
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}
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};
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} // gf_implementation
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}
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}
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