ellipsoid_fit.h

/* -----------------------------------------------------------------------------
 *
 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
 * Copyright (C) 2015 by Anton Ermakov
 *
 * This file is part of the deal.II code gallery.
 *
 * -----------------------------------------------------------------------------
 *
 * Author: antonermakov
 */

#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/function.h>
#include <deal.II/base/logstream.h>
#include <deal.II/lac/vector.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/precondition.h>
#include <deal.II/grid/tria.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/dofs/dof_tools.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/matrix_tools.h>
#include <deal.II/numerics/data_out.h>
#include <deal.II/grid/grid_in.h>
#include <deal.II/grid/grid_out.h>
#include <deal.II/base/point.h>
#include <deal.II/grid/grid_generator.h>

#include <fstream>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdlib>


#include "local_math.h"

using namespace dealii;

template <int dim>
class ellipsoid_fit
{
public:
  inline ellipsoid_fit (Triangulation<dim,dim> *pi)
  {
    p_triangulation = pi;
  };
  void compute_fit(std::vector<double> &ell, unsigned char bndry);


private:
  Triangulation<dim,dim>   *p_triangulation;

};


// This function computes ellipsoid fit to a set of vertices that lie on the
// boundary_that_we_need
template <int dim>
void ellipsoid_fit<dim>::compute_fit(std::vector<double> &ell, unsigned char boundary_that_we_need)
{
  typename Triangulation<dim>::active_cell_iterator cell = p_triangulation->begin_active();
  typename Triangulation<dim>::active_cell_iterator endc = p_triangulation->end();

  FullMatrix<double> A(p_triangulation->n_vertices(),dim);
  Vector<double>     x(dim);
  Vector<double>     b(p_triangulation->n_vertices());

  std::vector<bool> vertex_touched (p_triangulation->n_vertices(),
                                    false);

  unsigned int j = 0;
  unsigned char boundary_ids;
  std::vector<unsigned int> ind_bnry_row;
  std::vector<unsigned int> ind_bnry_col;

  // assemble the sensitivity matrix and r.h.s.
  for (; cell != endc; ++cell)
    {
      if (boundary_that_we_need != 0)
        cell->set_manifold_id(cell->material_id());
      for (unsigned int f = 0; f < GeometryInfo<dim>::faces_per_cell; ++f)
        {
          if (boundary_that_we_need == 0) //if this is the outer surface, then look for boundary ID 0; otherwise look for material ID change.
            {
              boundary_ids = cell->face(f)->boundary_id();
              if (boundary_ids == boundary_that_we_need)
                {
                  for (unsigned int v = 0;
                       v < GeometryInfo<dim>::vertices_per_face; ++v)
                    if (vertex_touched[cell->face(f)->vertex_index(v)]
                        == false)
                      {
                        vertex_touched[cell->face(f)->vertex_index(v)] =
                          true;
                        for (unsigned int i = 0; i < dim; ++i)
                          {
                            // stiffness matrix entry
                            A(j, i) = pow(cell->face(f)->vertex(v)[i], 2);
                            // r.h.s. entry
                            b[j] = 1.0;
                            // if mesh if not full: set the indicator
                          }
                        ind_bnry_row.push_back(j);
                        j++;
                      }
                }
            }
          else     //find the faces that are at the boundary between materials, get the vertices, and write them into the stiffness matrix
            {
              if (cell->neighbor(f) != endc)
                {
                  if (cell->material_id() != cell->neighbor(f)->material_id()) //finds face is at internal boundary
                    {
                      int high_mat_id = std::max(cell->material_id(),
                                                 cell->neighbor(f)->material_id());
                      if (high_mat_id == boundary_that_we_need) //finds faces at the correct internal boundary
                        {
                          for (unsigned int v = 0;
                               v < GeometryInfo<dim>::vertices_per_face;
                               ++v)
                            if (vertex_touched[cell->face(f)->vertex_index(
                                                 v)] == false)
                              {
                                vertex_touched[cell->face(f)->vertex_index(
                                                 v)] = true;
                                for (unsigned int i = 0; i < dim; ++i)
                                  {
                                    // stiffness matrix entry
                                    A(j, i) = pow(
                                                cell->face(f)->vertex(v)[i], 2);
                                    // r.h.s. entry
                                    b[j] = 1.0;
                                    // if mesh if not full: set the indicator
                                  }
                                ind_bnry_row.push_back(j);
                                j++;
                              }
                        }
                    }
                }
            }
        }
    }
  if (ind_bnry_row.size()>0)
    {

      // maxtrix A'*A and vector A'*b;  A'*A*x = A'*b -- normal system of equations
      FullMatrix<double> AtA(dim,dim);
      Vector<double>     Atb(dim);

      FullMatrix<double> A_out(ind_bnry_row.size(),dim);
      Vector<double>     b_out(ind_bnry_row.size());

      for (unsigned int i=0; i<dim; ++i)
        ind_bnry_col.push_back(i);

      for (unsigned int i=0; i<ind_bnry_row.size(); ++i)
        b_out(i) = 1;

      A_out.extract_submatrix_from(A, ind_bnry_row, ind_bnry_col);
      A_out.Tmmult(AtA,A_out,true);
      A_out.Tvmult(Atb,b_out,true);

      // solve normal system of equations
      SolverControl           solver_control (1000, 1e-12);
      SolverCG<>              solver (solver_control);
      solver.solve (AtA, x, Atb, PreconditionIdentity());

      // find ellipsoidal axes
      for (unsigned int i=0; i<dim; ++i)
        ell.push_back(sqrt(1.0/x[i]));
    }
  else
    std::cerr << "fit_ellipsoid: no points to fit" << std::endl;

}