/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================

 Copyright (C) 2004-2020 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.

 As a special exception, you  may use  this file  as it is a part of a free
 software  library  without  restriction.  Specifically,  if   other  files
 instantiate  templates  or  use macros or inline functions from this file,
 or  you compile this  file  and  link  it  with other files  to produce an
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===========================================================================*/

/**@file getfem_spider_fem.h
   @author Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 29, 2004.
   @brief work in progress...
*/

#ifndef GETFEM_SPIDER_FEM_H__
#define GETFEM_SPIDER_FEM_H__

#include "getfem/getfem_interpolated_fem.h"
#include "getfem_Xfem.h"
#include "getfem/getfem_regular_meshes.h"

namespace getfem {
  
  
  struct Xfem_sqrtr : public virtual_Xfem_func {
    
    
    virtual scalar_type val(const Xfem_func_context &c)
    { return ::sqrt(c.xreal[0]); }
    //   { return ::sqrt(c.xreal[0])*cos(log(c.xreal[0])); }
    virtual base_small_vector grad(const Xfem_func_context &c)
    { base_small_vector V(2); 
      V[0] = 1. / (2.* ::sqrt(c.xreal[0])); return V; }
    // V[0] =  (1./::sqrt(c.xreal[0]))( (cos(log(::sqrt(c.xreal[0])^2)))/2. - sin(log(::sqrt(c.xreal[0])^2)) ); return V; }
    virtual base_matrix hess(const Xfem_func_context &c) {
      base_matrix m(2,2); 
      m(0,0) = 1. / (4.* ::sqrt(c.xreal[0])*c.xreal[0]);
      //m(0,0) = ((1./::sqrt(c.xreal[0]))^(3))( (3. * cos(log(::sqrt(c.xreal[0])^2)))/4. - sin(log(::sqrt(c.xreal[0])^2)));
      return m;
    }
  };
  
  
  struct Xfem_sqrtrcos : public virtual_Xfem_func {
    
    scalar_type eps;
    virtual scalar_type val(const Xfem_func_context &c) {
      return ::sqrt(c.xreal[0]) * cos( eps*log(c.xreal[0]) ); 
    }
    
    virtual base_small_vector grad(const Xfem_func_context &c) {
      base_small_vector V(2); 
      V[0] =  ( 1./::sqrt( c.xreal[0]) ) * ( cos( eps*log(c.xreal[0]) )/2. - eps*sin( eps*log(c.xreal[0]) ) ); 
      return V; 
    }
    
    virtual base_matrix hess(const Xfem_func_context &c) {
      base_matrix m(2,2); 
      m(0,0) = (1./::pow(sqrt(c.xreal[0]),3.)) * (  ((-1./4.) - ::pow(eps,2.)) *  cos( eps*log(c.xreal[0]) ) );
      return m;
    }
  };
  

  struct Xfem_sqrtrsin : public virtual_Xfem_func {
    
    scalar_type eps; 
    virtual scalar_type val(const Xfem_func_context &c) {
      return ::sqrt(c.xreal[0]) * sin( eps*log(c.xreal[0]) );  
    }
      
    virtual base_small_vector grad(const Xfem_func_context &c) {
      base_small_vector V(2); 
      V[0] =  ( 1./::sqrt(c.xreal[0]) ) * ( sin( eps*log(c.xreal[0]) )/2. + eps*cos( eps*log(c.xreal[0]) ) );
      return V;
    }
      
    virtual base_matrix hess(const Xfem_func_context &c) {
      base_matrix m(2,2); 
      m(0,0) = (1./::pow(sqrt(c.xreal[0]),3.)) * (  ((-1./4.) - ::pow(eps,2.)) *  sin( eps*log(c.xreal[0]) ) );
      return m;
    }
  };


  
  /*
    struct Xfem_sqrtr : public virtual_Xfem_func {
    virtual scalar_type val(const Xfem_func_context &c)
    { return 1; }
    virtual base_small_vector grad(const Xfem_func_context &c)
    { base_small_vector V(2); return V; }
    virtual base_matrix hess(const Xfem_func_context &c) {
    base_matrix m(2,2); return m;
    }
    };
  */
  
  struct interpolated_transformation : public virtual_interpolated_func{
    /* Polar transformation and its gradient. */
    base_small_vector trans;
    scalar_type theta0;
    
    virtual void val(const base_node &xreal, base_node &v) const {
      base_node w =  xreal - trans;
      v[0] = gmm::vect_norm2(w);
      v[1] = atan2(w[1], w[0]) - theta0;
    }
    virtual void grad(const base_small_vector &xreal, base_matrix &m) const {
      base_node w =  xreal - trans;
      scalar_type r = gmm::vect_norm2(w); assert(gmm::abs(r)>1e-30);
      m(0,0) = w[0] / r; m(0,1) = w[1] / r;
      m(1,0) = -w[1] / gmm::sqr(r); m(1,1) = w[0] / gmm::sqr(r);
    }
    virtual void hess(const base_node &, base_matrix &) const
    { GMM_ASSERT1(false, "this interpolated_func has no hessian"); }
    
    
    virtual ~interpolated_transformation() {}
  };

  DAL_SIMPLE_KEY(special_cartesianfem_key, pfem);

  class spider_fem {
    
  protected :
    
    mesh cartesian;
    mesh_fem cartesian_fem;
    pfem Qk;
    std::shared_ptr<Xfem> penriched_Qk;
    scalar_type R;
    unsigned Nr, Ntheta, K;
    Xfem_sqrtr Sqrtr;
    Xfem_sqrtrcos Sqrtrcos;
    Xfem_sqrtrsin Sqrtrsin;
    int bimat_enrichment;
    scalar_type epsilon;
    pfem final_fem;
    interpolated_transformation itt;

  public :
    
    pfem get_pfem(void) { return final_fem; }
    
    ~spider_fem () {
      pfem pf(penriched_Qk);
      dal::del_stored_object(pf);
      if (final_fem) del_interpolated_fem(final_fem);
    }
    spider_fem(scalar_type R_, mesh_im &mim, unsigned Nr_, unsigned Ntheta_,
	       unsigned K_, base_small_vector translation, scalar_type theta0,
	       int bimat_enrichment_ = 0, scalar_type epsilon_ = scalar_type(0))
        : cartesian_fem(cartesian), R(R_), Nr(Nr_),
	  Ntheta(Ntheta_), K(K_), bimat_enrichment(bimat_enrichment_), epsilon(epsilon_), final_fem(0) {
        
	itt.trans = translation;
	itt.theta0 = theta0;

        /* make the cartesian mesh */
        bgeot::pgeometric_trans pgt = 
	  bgeot::geometric_trans_descriptor("GT_LINEAR_QK(2)");
        std::vector<size_type> nsubdiv(2);
	nsubdiv[0] = Nr; nsubdiv[1] = Ntheta;
        getfem::regular_unit_mesh(cartesian, nsubdiv, pgt, false);
	bgeot::base_matrix M(2,2);
	M(0,0) = R;   
	M(1,1) = 2. *  M_PI;
	cartesian.transformation(M);
	bgeot::base_small_vector V(2);
	V[1] = -M_PI;
	cartesian.translation(V); 

	getfem::mesh_region border_faces;
	getfem::outer_faces_of_mesh(cartesian, border_faces);
	for (getfem::mr_visitor it(border_faces); !it.finished(); ++it) {
	  base_node un = cartesian.normal_of_face_of_convex(it.cv(), it.f());
	  un /= gmm::vect_norm2(un);
	  if (un[0] >= 0.8) cartesian.region(0).add(it.cv(), it.f());
	}

	std::stringstream Qkname;
	Qkname << "FEM_QK(2," << K << ")";
	Qk = fem_descriptor(Qkname.str());
	penriched_Qk = std::make_shared<Xfem>(pfem());
	if(bimat_enrichment == 0){
	  cout << "Using SpiderFem homogenuous isotropic enrichment [sqrt(r)]..." << endl;
	  penriched_Qk->add_func(Qk, &Sqrtr);
	}
	else {
	  cout << "Using SpiderFem bimaterial enrichement..." << endl;
	  Sqrtrcos.eps = epsilon;
	  Sqrtrsin.eps = epsilon;
	  //cout << "epsilon = " << epsilon << endl;
	  penriched_Qk->add_func(Qk, &Sqrtrcos);
	  penriched_Qk->add_func(Qk, &Sqrtrsin);
	}
	penriched_Qk->valid();
	pfem pf(penriched_Qk);
	dal::pstatic_stored_object_key
	  pk = std::make_shared<special_cartesianfem_key>(pf);
	dal::add_stored_object(pk, pf, pf->ref_convex(0), pf->node_tab(0));

	cartesian_fem.set_finite_element(cartesian.convex_index(), pf);  
	GMM_ASSERT1(!cartesian_fem.is_reduced(), "To be adapted");
	dal::bit_vector blocked_dof = cartesian_fem.basic_dof_on_region(0);
	//	cout << "blocked dofs = " <<  blocked_dof << endl;

	final_fem = new_interpolated_fem(cartesian_fem, mim,&itt,blocked_dof, false);
      }
    void check() {
      const interpolated_fem &ife = dynamic_cast<const interpolated_fem&>(*final_fem);
      dal::bit_vector bv = ife.interpolated_convexes();
      cerr << "interpolated_convexes: nb=" << bv.card() << "; " << bv << "\n";
      unsigned ming, maxg;
      scalar_type meang;
      ife.gauss_pts_stats(ming,maxg,meang);
      cerr << " gauss pts in interpolated mesh_fem convexes: min=" << ming << ", max=" << maxg << ", meang=" << meang << "\n";
      if (bv.card() != cartesian.convex_index().card()) {
	cerr << cartesian.convex_index().card() - bv.card() << 
	  "convexes missed by interpolated_fem, increase the "
	  "number of integration points";
	GMM_ASSERT3(false, "");
      }
    }
  };



}  /* end of namespace getfem.                                            */

#endif
