/*===========================================================================

 Copyright (C) 2002-2020 Yves Renard.

 This file is a part of GetFEM

 GetFEM  is  free software;  you  can  redistribute  it  and/or modify it
 under  the  terms  of the  GNU  Lesser General Public License as published
 by  the  Free Software Foundation;  either version 3 of the License,  or
 (at your option) any later version along with the GCC Runtime Library
 Exception either version 3.1 or (at your option) any later version.
 This program  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 Lesser General Public
 License and GCC Runtime Library Exception for more details.
 You  should  have received a copy of the GNU Lesser General Public License
 along  with  this program;  if not, write to the Free Software Foundation,
 Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.

===========================================================================*/
/***************************************************************************/
/*                                                                         */
/*  Test the interpolated fem method.                                      */
/*                                                                         */
/***************************************************************************/

#include "getfem/getfem_assembling.h"
#include "getfem/getfem_export.h"
#include "getfem/getfem_regular_meshes.h"
#include "gmm/gmm.h"
#include "getfem/getfem_interpolated_fem.h"
#include "getfem/getfem_mesh_fem_sum.h"
using std::endl; using std::cout; using std::cerr;
using std::ends; using std::cin;

using bgeot::base_vector;
using bgeot::base_small_vector;
using bgeot::base_node;
using bgeot::scalar_type;
using bgeot::size_type;
using bgeot::dim_type;

typedef gmm::wsvector<scalar_type> sparse_vector_type;
typedef gmm::col_matrix<sparse_vector_type> sparse_matrix_type;
typedef std::vector<scalar_type> linalg_vector;

/**************************************************************************/
/*  structure representing the problem.                                   */
/**************************************************************************/

struct lap_pb {
  getfem::mesh mesh1, mesh2;
  getfem::mesh_im      mim1, mim2;
  getfem::mesh_fem     mef1,  mef2, mefinterpolated;

  scalar_type LX, LY, LZ;
  int NX1, NX2, N, K, KI, integration;

  bgeot::md_param PARAM;

  void assemble(void);
  void init(void);
  lap_pb(void) : mim1(mesh1), mim2(mesh2), mef1(mesh1), mef2(mesh2),
		 mefinterpolated(mesh1) {}
};

void lap_pb::init(void) {
  dal::bit_vector nn;

  /***********************************************************************/
  /* READING PARAMETER FILE                                              */
  /***********************************************************************/
  
  N = int(PARAM.int_value("N", "Domaine dimension"));
  LX = PARAM.real_value("LX", "Size in X");
  LY = PARAM.real_value("LY", "Size in Y");
  LZ = PARAM.real_value("LZ", "Size in Y");
  NX1 = int(PARAM.int_value("NX1", "Nomber of sace steps "));
  NX2 = int(PARAM.int_value("NX2", "Nomber of sace steps "));
  integration = int(PARAM.int_value("INTEGRATION", "integration method"));
  K = int(PARAM.int_value("K", "Finite element degree"));
  KI = int(PARAM.int_value("KI", "Integration degree"));
  
  /***********************************************************************/
  /*  BUILD MESH.                                                        */
  /***********************************************************************/

  cout << "Mesh generation\n";

  base_node org(N); gmm::clear(org);
  std::vector<base_small_vector> vtab(N);
  std::vector<size_type> ref(N);
  std::fill(ref.begin(), ref.end(), NX1);
  for (dim_type i = 0; i < N; i++)
  { 
    vtab[i] = base_small_vector(N); gmm::clear(vtab[i]);
    (vtab[i])[i] = ((i == 0) ? LX : ((i == 1) ? LY : LZ)) / scalar_type(NX1);
  }
  getfem::parallelepiped_regular_simplex_mesh(mesh1, dim_type(N), org,
					      vtab.begin(), ref.begin());
  mesh1.optimize_structure();

  std::fill(ref.begin(), ref.end(), NX2);
  for (dim_type i = 0; i < N; i++)
  { 
    vtab[i] = base_small_vector(N); gmm::clear(vtab[i]);
    (vtab[i])[i] = ((i == 0) ? LX : ((i == 1) ? LY : LZ)) / scalar_type(NX2);
  }
  getfem::parallelepiped_regular_simplex_mesh(mesh2, dim_type(N), org,
					      vtab.begin(), ref.begin());
  mesh2.optimize_structure();
  cout << "Selecting finite element method.\n";
  char meth[500];
  getfem::pintegration_method ppi;
  switch (integration) {
  case 0  : snprintf(meth, 499, "IM_EXACT_SIMPLEX(%d)", int(N)); break;
  case 1  : snprintf(meth, 499, "IM_NC(%d, %d)", int(N), int(KI)); break;
  case 2  : snprintf(meth, 499, "IM_GAUSS1D(%d)", int(KI)); break;
  case 3  : snprintf(meth, 499, "IM_STRUCTURED_COMPOSITE(IM_NC(%d, %d), %d)",
		    int(N), int(2*K), int(KI)); break;
  case 11 : snprintf(meth, 499, "IM_TRIANGLE(1)"); break;
  case 12 : snprintf(meth, 499, "IM_TRIANGLE(2)"); break;
  case 13 : snprintf(meth, 499, "IM_TRIANGLE(3)"); break;
  case 14 : snprintf(meth, 499, "IM_TRIANGLE(4)"); break;
  case 15 : snprintf(meth, 499, "IM_TRIANGLE(5)"); break;
  case 16 : snprintf(meth, 499, "IM_TRIANGLE(6)"); break;
  case 17 : snprintf(meth, 499, "IM_TRIANGLE(7)"); break;
  case 21 : snprintf(meth, 499, "IM_TETRAHEDRON(1)"); break;
  case 22 : snprintf(meth, 499, "IM_TETRAHEDRON(2)"); break;
  case 23 : snprintf(meth, 499, "IM_TETRAHEDRON(3)"); break;
  case 25 : snprintf(meth, 499, "IM_TETRAHEDRON(5)"); break;
  default : GMM_ASSERT1(false, "Undefined integration method");
  }
  ppi = getfem::int_method_descriptor(meth);
  
  snprintf(meth, 499, "FEM_PK(%d,%d)", int(N), int(K));
  nn = mesh1.convex_index(dim_type(N));
  mim1.set_integration_method(nn, ppi);
  mef1.set_finite_element(nn, getfem::fem_descriptor(meth));
  nn = mesh2.convex_index(dim_type(N));
  mim2.set_integration_method(nn, ppi);
  mef2.set_finite_element(nn, getfem::fem_descriptor(meth));
  nn = mesh1.convex_index(dim_type(N));
  mefinterpolated.set_finite_element
    (nn, getfem::new_interpolated_fem(mef2, mim1));
}

void lap_pb::assemble(void) {
  int nb_dof1 = int(mef1.nb_dof()), nb_dof2 = int(mef2.nb_dof());
  sparse_matrix_type RM1(nb_dof2, nb_dof2);
  double sum, diff;
  
  cout << "Number of dof : " << nb_dof1 << " : " << nb_dof2 << endl;

  cout << "Number of dof of interpolated method: "
       << mefinterpolated.nb_dof() << endl;
 
  cout << "Assembling interpolated mass matrix" << endl;
  getfem::asm_mass_matrix(RM1, mim1, mefinterpolated, mefinterpolated);

  cout << "Mass Matrix\n";
  sum = 0.0;
  for (size_type i = 0; i < RM1.nrows(); i++) { 
    cout << "line " << i << " [ ";
    scalar_type slig = 0;
    for (size_type l = 0; l < RM1.nrows(); l++)
      if (RM1(i, l) != 0.0) {
	cout << "(" << l << "," << RM1(i, l) << ")  ";
	slig += RM1(i, l);
      }
    sum += slig;
    cout << "] -> sum(line)=" << slig << endl;
  }
  cout << endl << " sum: " << sum << endl << endl;

  sparse_matrix_type RM2 = sparse_matrix_type(nb_dof2, nb_dof2);
  cout << "Assembling normal mass matrix" << endl;
  getfem::asm_mass_matrix(RM2, mim2, mef2);
  
  cout << "Mass Matrix\n";
  sum = 0.0; diff = 0.0;
  for (size_type i = 0; i < RM2.nrows(); i++) { 
    cout << "line " << i << " [ ";
    scalar_type slig = 0;
    for (size_type l = 0; l < RM2.nrows(); l++) {
      diff += gmm::abs(RM2(i, l) - RM1(i, l));
      if (RM2(i, l) != 0.0) {
	cout << "(" << l << "," << RM2(i, l) << ")  ";
	slig = slig + RM2(i, l);
      }
    }
    sum += slig;
    cout << "] -> sum(line)=" << slig << endl;
  }
  cout << endl << " sum: " << sum << endl << endl;
  cout << endl << " diff: " << diff << "max_norm="
       << gmm::mat_maxnorm(RM1) << endl << endl;  
}


/* integration of a quarter of circle (approximated with a degree 5 segment) against a planar regular mesh */
void test2() {
  getfem::mesh m1, m2;
  std::vector<size_type> nsubdiv(2); nsubdiv[0] = nsubdiv[1] = 5;

  getfem::regular_unit_mesh
    (m1, nsubdiv, bgeot::geometric_trans_descriptor("GT_QK(2,2)"), false);

  std::vector<base_node> v;
  for (size_type k=0; k < 6; ++k) {
    scalar_type c = scalar_type(k)/5. * M_PI/2;
    v.push_back(base_node(cos(c), sin(c)));
  }
  m2.add_convex_by_points(bgeot::geometric_trans_descriptor("GT_PK(1,5)"),
			  v.begin());
  //m2.add_segment_by_points(bgeot::base_node(.45,.35),
  //                         bgeot::base_node(.75,.65));
  //m2.add_segment_by_points(bgeot::base_node(.8,.7),bgeot::base_node(.23,.3));
  getfem::mesh_fem mf1(m1), mf2(m2);
  getfem::mesh_im mim(m2);
  // getfem::pintegration_method pim1
  //   = getfem::int_method_descriptor("IM_QUAD(17)");
  getfem::pintegration_method pim2
    = getfem::int_method_descriptor("IM_GAUSS1D(10)");
  mim.set_integration_method(m2.convex_index(), pim2);
  mf1.set_finite_element(m1.convex_index(),
			 getfem::fem_descriptor("FEM_QK(2,1)"));
  mf2.set_finite_element(m2.convex_index(),
			 getfem::fem_descriptor("FEM_PK(1,3)"));
  
  getfem::mesh_fem mflnk(m2);
  getfem::pfem ifem = getfem::new_interpolated_fem(mf1, mim);
  mflnk.set_finite_element(m2.convex_index(), ifem);
  sparse_matrix_type MM = sparse_matrix_type(mf2.nb_dof(),
					     mflnk.nb_dof());
  getfem::asm_mass_matrix(MM, mim, mf2, mflnk);
  cout << "MM=" << MM << "\n";
  cout << "mflnk.nb_dof()=" << mflnk.nb_dof() << ", mf2.nb_dof()="
       << mf2.nb_dof() << ", mf1.nb_dof=" << mf1.nb_dof() << "\n";
  cout << "Mass Matrix\n";
  scalar_type sum = 0.0; 
  for (size_type i = 0; i < MM.nrows(); i++) { 
    scalar_type slig = 0;
    for (size_type l = 0; l < MM.ncols(); l++) {
      slig = slig + MM(i, l);
      // cout << "M(" << i << "," << l << ")=" << MM(i,l) << ", slig = "
      //      << slig << "\n";
    }
    sum += slig;
    cout << "sum(line)=" << slig << endl;
  }
  cout << endl << " sum: " << sum << endl << endl;
  GMM_ASSERT1(gmm::abs(sum - M_PI/2.0) < 1e-5,
	      "Test for scalar fem failed : " << gmm::abs(sum - M_PI/2.0));
  sparse_matrix_type MM2 = sparse_matrix_type(mf2.nb_dof(), mf2.nb_dof());
  getfem::asm_mass_matrix(MM2, mim, mf2, mf2);
  cout << "MM2=" << MM2 << "\n";
  sparse_matrix_type MM3 = sparse_matrix_type(mflnk.nb_dof(), mflnk.nb_dof());

  asm_stiffness_matrix_for_homogeneous_laplacian(MM3, mim, mflnk);
}


/* integration of a quarter of circle (approximated with a degree 5 segment) against a planar regular mesh : vector version */
void test3() {
  getfem::mesh m1, m2;
  std::vector<size_type> nsubdiv(2); nsubdiv[0] = nsubdiv[1] = 5;

  getfem::regular_unit_mesh
    (m1, nsubdiv, bgeot::geometric_trans_descriptor("GT_QK(2,2)"), false);

  std::vector<base_node> v;
  for (size_type k=0; k < 6; ++k) {
    scalar_type c = scalar_type(k)/5. * M_PI/2;
    v.push_back(base_node(cos(c), sin(c)));
  }
  m2.add_convex_by_points(bgeot::geometric_trans_descriptor("GT_PK(1,5)"),
			  v.begin());
  //m2.add_segment_by_points(bgeot::base_node(.45,.35),
  //                         bgeot::base_node(.75,.65));
  //m2.add_segment_by_points(bgeot::base_node(.8,.7),bgeot::base_node(.23,.3));
  getfem::mesh_fem mf1(m1), mf2(m2);
  getfem::mesh_im mim(m2);
  // getfem::pintegration_method pim1
  //   = getfem::int_method_descriptor("IM_QUAD(17)");
  getfem::pintegration_method pim2
    = getfem::int_method_descriptor("IM_GAUSS1D(10)");
  mim.set_integration_method(m2.convex_index(), pim2);
  mf1.set_finite_element(m1.convex_index(),
			 getfem::fem_descriptor("FEM_QK(2,1)"));
  mf1.set_qdim(2);
  mf2.set_finite_element(m2.convex_index(),
			 getfem::fem_descriptor("FEM_PK(1,3)"));
  mf2.set_qdim(2);
  
  getfem::mesh_fem mflnk(m2);
  mflnk.set_qdim(2);
  getfem::pfem ifem = getfem::new_interpolated_fem(mf1, mim);
  mflnk.set_finite_element(m2.convex_index(), ifem);
  sparse_matrix_type MM = sparse_matrix_type(mf2.nb_dof(), mflnk.nb_dof());
  getfem::asm_mass_matrix(MM, mim, mf2, mflnk);
  cout << "MM=" << MM << "\n";
  cout << "mflnk.nb_dof()=" << mflnk.nb_dof() << ", mf2.nb_dof()="
       << mf2.nb_dof() << ", mf1.nb_dof=" << mf1.nb_dof() << "\n";
  cout << "Mass matrix\n";
  scalar_type sum = 0.0; 
  for (size_type i = 0; i < MM.nrows(); i++) { 
    scalar_type slig = 0;
    for (size_type l = 0; l < MM.ncols(); l++) {
      slig = slig + MM(i, l);
      // cout << "M(" << i << "," << l << ")=" << MM(i,l) << ", slig = "
      //      << slig << "\n";
    }
    sum += slig;
    cout << "sum(line)=" << slig << endl;
  }
  cout << endl << " sum: " << sum << endl << endl;
  GMM_ASSERT1(gmm::abs(sum - M_PI) < 5e-5,
	      "Test for vectorial fem failed : " << gmm::abs(sum - M_PI));

  // Il faudrait tester les gradients aussi ...
}







/**************************************************************************/
/*  main program.                                                         */
/**************************************************************************/

int main(int argc, char *argv[]) {
  
  GETFEM_MPI_INIT(argc, argv);

  test3(); // test for vectorial fems
  test2(); // test for scalar fems
  lap_pb p;
    
  cout << "initialisation ...\n";
  p.PARAM.read_command_line(argc, argv);
  p.init();
  
  cout << "Assembling \n";
  p.assemble();
  
  GETFEM_MPI_FINALIZE;
  
  return 0; 
}