dft_tools/triqs/gfs/meshes/linear.hpp

/*******************************************************************************
 *
 * TRIQS: a Toolbox for Research in Interacting Quantum Systems
 *
 * Copyright (C) 2012 by M. Ferrero, O. Parcollet
 *
 * TRIQS is free software: you can redistribute it and/or modify it under the
 * terms of the GNU General Public License as published by the Free Software
 * Foundation, either version 3 of the License, or (at your option) any later
 * version.
 *
 * TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
 * details.
 *
 * You should have received a copy of the GNU General Public License along with
 * TRIQS. If not, see <http://www.gnu.org/licenses/>.
 *
 ******************************************************************************/
#ifndef TRIQS_GF_MESH_LINEAR_H
#define TRIQS_GF_MESH_LINEAR_H
#include "./mesh_tools.hpp"

// ADDED for Krylov : to be clean and removed if necessary
#include <algorithm>
#include <boost/math/special_functions/round.hpp>
namespace triqs {
namespace gfs {

 // Three possible meshes
 enum mesh_kind {
  half_bins,
  full_bins,
  without_last
 };

 template <typename Domain> struct linear_mesh {

  typedef Domain domain_t;
  typedef size_t index_t;
  typedef typename domain_t::point_t domain_pt_t;

  linear_mesh() : _dom(), L(0), a_pt(0), b_pt(0), xmin(0), xmax(0), del(0), meshk(half_bins) {}

  explicit linear_mesh(domain_t dom, double a, double b, size_t n_pts, mesh_kind mk)
     : _dom(std::move(dom)), L(n_pts), a_pt(a), b_pt(b), meshk(mk) {
   switch (mk) {
    case half_bins:
     del = (b - a) / L;
     xmin = a + 0.5 * del;
     break;
    case full_bins:
     del = (b - a) / (L - 1);
     xmin = a;
     break;
    case without_last:
     del = (b - a) / L;
     xmin = a;
     break;
   }
   xmax = xmin + del * (L - 1);
  }

  domain_t const &domain() const { return _dom; }
  size_t size() const { return L; }
  double delta() const { return del; }
  double x_max() const { return xmax; }
  double x_min() const { return xmin; }
  mesh_kind kind() const { return meshk; }

  /// Conversions point <-> index <-> linear_index
  domain_pt_t index_to_point(index_t ind) const {
   return embed(xmin + ind * del, std::integral_constant<bool, std::is_base_of<std::complex<double>, domain_pt_t>::value>());
  }

  private: // multiply by I is the type is a complex ....
  domain_pt_t embed(double x, std::false_type) const { return x; }
  domain_pt_t embed(double x, std::true_type) const { return std::complex<double>(0, x); }

  public:
  size_t index_to_linear(index_t ind) const { return ind; }

  /// The wrapper for the mesh point
  class mesh_point_t : tag::mesh_point, public arith_ops_by_cast<mesh_point_t, domain_pt_t> {
   linear_mesh const *m;
   index_t _index;

   public:
   mesh_point_t(linear_mesh const &mesh, index_t const &index_) : m(&mesh), _index(index_) {}
   void advance() { ++_index; }
   typedef domain_pt_t cast_t;
   operator cast_t() const { return m->index_to_point(_index); }
   size_t linear_index() const { return _index; }
   size_t index() const { return _index; }
   bool at_end() const { return (_index == m->size()); }
   void reset() { _index = 0; }
  };

  /// Accessing a point of the mesh
  mesh_point_t operator[](index_t i) const { return mesh_point_t(*this, i); }

  // ADDED for krylov : to be CLEANED AND CHANGED
  // Find the index of the mesh point which is nearest to x
  index_t nearest_index(domain_pt_t x) const {
   double x_real = real_or_imag(x, std::is_base_of<std::complex<double>, domain_pt_t>());
   using boost::math::round;
   using std::min;
   using std::max;
   switch (meshk) {
    case half_bins:
    case full_bins:
     return min(max(round((x_real - xmin) / del), .0), static_cast<double>(L - 1));
    case without_last:
     return min(max(round((x_real - xmin) / del), .0), static_cast<double>(L - 2));
   }
  }

  private:
  static double real_or_imag(domain_pt_t x, std::false_type) { return x; }
  static double real_or_imag(domain_pt_t x, std::true_type) { return imag(x); }

  public:
  /// Iterating on all the points...
  typedef mesh_pt_generator<linear_mesh> const_iterator;
  const_iterator begin() const { return const_iterator(this); }
  const_iterator end() const { return const_iterator(this, true); }
  const_iterator cbegin() const { return const_iterator(this); }
  const_iterator cend() const { return const_iterator(this, true); }

  /// Mesh comparison
  bool operator==(linear_mesh const &M) const {
   return ((_dom == M._dom) && (size() == M.size()) && (std::abs(xmin - M.xmin) < 1.e-15) && (std::abs(xmax - M.xmax) < 1.e-15));
  }
  bool operator!=(linear_mesh const &M) const { return !(operator==(M)); }

  /// Write into HDF5
  friend void h5_write(h5::group fg, std::string subgroup_name, linear_mesh const &m) {
   h5::group gr = fg.create_group(subgroup_name);
   int k;
   switch (m.meshk) {
    case half_bins:
     k = 0;
     break;
    case full_bins:
     k = 1;
     break;
    case without_last:
     k = 2;
     break;
   }
   h5_write(gr, "domain", m.domain());
   h5_write(gr, "min", m.a_pt);
   h5_write(gr, "max", m.b_pt);
   h5_write(gr, "size", m.size());
   h5_write(gr, "kind", k);
  }

  /// Read from HDF5
  friend void h5_read(h5::group fg, std::string subgroup_name, linear_mesh &m) {
   h5::group gr = fg.open_group(subgroup_name);
   typename linear_mesh::domain_t dom;
   double a, b;
   size_t L;
   int k;
   mesh_kind mk;
   h5_read(gr, "domain", dom);
   h5_read(gr, "min", a);
   h5_read(gr, "max", b);
   h5_read(gr, "size", L);
   h5_read(gr, "kind", k);
   switch (k) {
    case 0:
     mk = half_bins;
     break;
    case 1:
     mk = full_bins;
     break;
    case 2:
     mk = without_last;
     break;
   }
   m = linear_mesh(std::move(dom), a, b, L, mk);
  }

  //  BOOST Serialization
  friend class boost::serialization::access;
  template <class Archive> void serialize(Archive &ar, const unsigned int version) {
   ar &boost::serialization::make_nvp("domain", _dom);
   ar &boost::serialization::make_nvp("a_pt", a_pt);
   ar &boost::serialization::make_nvp("b_pt", b_pt);
   ar &boost::serialization::make_nvp("xmin", xmin);
   ar &boost::serialization::make_nvp("xmax", xmax);
   ar &boost::serialization::make_nvp("del", del);
   ar &boost::serialization::make_nvp("size", L);
   ar &boost::serialization::make_nvp("kind", meshk);
  }

  friend std::ostream &operator<<(std::ostream &sout, linear_mesh const &m) { return sout << "Linear Mesh of size " << m.L; }

  private:
  domain_t _dom;
  size_t L;
  double a_pt, b_pt;
  double xmin, xmax;
  double del;
  mesh_kind meshk;
 };


 // UNUSED
 /// Simple approximation of a point of the domain by a mesh point. No check
 template <typename D> size_t get_closest_mesh_pt_index(linear_mesh<D> const &mesh, typename D::point_t const &x) {
  double a = (x - mesh.x_min()) / mesh.delta();
  return std::floor(a);
 }

 /// Approximation of a point of the domain by a mesh point
 template <typename D> std::tuple<bool, long, double> windowing(linear_mesh<D> const &mesh, typename D::point_t const &x) {
  double a = (x - mesh.x_min()) / mesh.delta();
  long i = std::floor(a), imax = long(mesh.size()) - 1;
  bool in = (i >= 0) && (i < imax);
  double w = a - i;
  if (i == imax) {
   --i;
   in = (std::abs(w) < 1.e-14);
   w = 1.0;
  }
  return std::make_tuple(in, i, w);
  // return std::make_tuple(in, (in ? i : 0),w);
 }
}
}
#endif