/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2009-2012 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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 to be covered  by the GNU Lesser General Public License.  This   exception
 does not  however  invalidate  any  other  reasons why the executable file
 might be covered by the GNU Lesser General Public License.
 
===========================================================================*/

/**
   @file getfem_models.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date March 21, 2009.
   @brief Model representation in Getfem.
*/

#ifndef GETFEM_MODELS_H__
#define GETFEM_MODELS_H__

#include "getfem_partial_mesh_fem.h"

namespace getfem {

  class virtual_brick;
  /** type of pointer on a brick */
  typedef boost::intrusive_ptr<const getfem::virtual_brick> pbrick;

  class virtual_dispatcher;
  typedef boost::intrusive_ptr<const getfem::virtual_dispatcher> pdispatcher;

  // Event management : The model has to react when something has changed in
  //    the context and ask for corresponding (linear) bricks to recompute
  //    some terms.
  //    For the moment two events are taken into account
  //      - Change in a mesh_fem
  //      - Change in the data of a variable
  //    For this, a brick has to declare on which variable it depends and
  //    on which data. When a linear brick depend on a variable, the
  //    recomputation is done when the eventual corresponding mesh_fem
  //    is changed (or the size of the variable for a fixed size variable).
  //    When a linear brick depend on a data, the recomputation is done
  //    when the corresponding vector value is changed. If a variable is used
  //    as a data, it has to be declared as a data by the brick.
  //    A nonlinear brick is recomputed at each assembly of the tangent system.
  //    Remember this behavior when some changed are done on the variable
  //    and/or data.
  //    The change on a mesh_im is not taken into account for the moment.
  //    The different versions of the variables is not taken into account
  //    separately.

  //=========================================================================
  //
  //  Model object.
  //
  //=========================================================================


  typedef gmm::wsvector<scalar_type> model_real_sparse_vector;
  typedef gmm::wsvector<complex_type> model_complex_sparse_vector;
  typedef std::vector<scalar_type> model_real_plain_vector;
  typedef std::vector<complex_type> model_complex_plain_vector;

  // utiliser le même type que l'interface matlab/python pour représenter
  // les vecteurs/matrices ?
  // Cela faciliterait les échanges et réduirait les composantes de la
  // classe model.

  typedef gmm::col_matrix<model_real_sparse_vector> model_real_sparse_matrix;
  typedef gmm::col_matrix<model_complex_sparse_vector>
  model_complex_sparse_matrix;

  /** ``Model'' variables store the variables, the data and the
      description of a model. This includes the global tangent matrix, the
      right hand side and the constraints. There are two kinds of models, the
      ``real'' and the ``complex'' models.
  */
  class model : public context_dependencies {

    // State variables of the model
    bool complex_version;
    bool is_linear_;
    bool is_symmetric_;
    bool is_coercive_;
    mutable model_real_sparse_matrix rTM;    // tangent matrix, real version
    mutable model_complex_sparse_matrix cTM; // tangent matrix, complex version
    mutable model_real_plain_vector rrhs;
    mutable model_complex_plain_vector crhs;
    mutable scalar_type pseudo_potential_;
    mutable bool act_size_to_be_done;
    dim_type leading_dim;

    // Variables and parameters of the model

    enum  var_description_filter {
      VDESCRFILTER_NO,     // Variable being directly the dofs of a given fem
      VDESCRFILTER_REGION, /* Variable being the dofs of a fem on a mesh region
                            * (uses mf.dof_on_region). */
      VDESCRFILTER_INFSUP, /* Variable being the dofs of a fem on a mesh region
                            * with an additional filter on a mass matrix with
                            * respect to another fem. */
      VDESCRFILTER_CTERM   /* Variable being the dofs of a fem on a mesh region
                            * with an additional filter with the coupling
			    * termson with respect to another variable. */
    };

    struct var_description {

      bool is_variable;  // This is a variable or a parameter.
      bool is_disabled;  // For a variable, to be solved or not
      bool is_complex;   // The variable is complex numbers
      bool is_fem_dofs;  // The variable is the dofs of a fem
      var_description_filter filter; // A filter on the dofs is applied or not.
      size_type n_iter; //  Number of version of the variable stored for time
                        // integration schemes.
      size_type n_temp_iter; // Number of additional temporary versions
      size_type default_iter; // default iteration number.

      // fem description of the variable
      const mesh_fem *mf;        // Principal fem of the variable.
      size_type m_region;        // Optional region for the filter
      const mesh_im *mim;        // Optional integration method for the filter
      ppartial_mesh_fem partial_mf; // Filter with respect to mf.
      std::string filter_var;       // Optional variable name for the filter

      dim_type qdim;  // A data could have a qdim != of the fem.
                      // dim per dof for dof data.
      gmm::uint64_type v_num, v_num_data;

      gmm::sub_interval I; // For a variable : indices on the whole system

      std::vector<model_real_plain_vector> real_value;
      std::vector<model_complex_plain_vector> complex_value;
      std::vector<gmm::uint64_type> v_num_var_iter;
      std::vector<gmm::uint64_type> v_num_iter;

      var_description(bool is_var = false, bool is_com = false,
                      bool is_fem = false, size_type n_it = 1,
                      var_description_filter fil = VDESCRFILTER_NO,
                      const mesh_fem *mmf = 0,
                      size_type m_reg = size_type(-1), dim_type Q = 1,
                      const std::string &filter_v = std::string(""),
		      const mesh_im *mim_ = 0)
        : is_variable(is_var), is_disabled(false), is_complex(is_com),
	  is_fem_dofs(is_fem), filter(fil),
	  n_iter(std::max(size_type(1),n_it)), n_temp_iter(0),
          default_iter(0), mf(mmf), m_region(m_reg), mim(mim_),
	  filter_var(filter_v), qdim(Q), v_num(0), v_num_data(act_counter()) {
        if (filter != VDESCRFILTER_NO && mf != 0)
          partial_mf = new partial_mesh_fem(*mf);
        // v_num_data = v_num;
      }

      // add a temporary version for time integration schemes. Automatically
      // set the default iter to it. id_num is an identifier. Do not add
      // the version if a temporary already exist with this identifier.
      size_type add_temporary(gmm::uint64_type id_num);

      void clear_temporaries(void);

      const mesh_fem &associated_mf(void) const {
        GMM_ASSERT1(is_fem_dofs, "This variable is not linked to a fem");
        if (filter == VDESCRFILTER_NO) return *mf; else return *partial_mf;
      }

      const mesh_fem *passociated_mf(void) const {
        if (!is_fem_dofs) return 0;
        if (filter == VDESCRFILTER_NO) return mf;
        else return partial_mf.get();
      }

      size_type size(void) const // Should control that the variable is
      // indeed intitialized by actualize_sizes ...
      { return is_complex ? complex_value[0].size() : real_value[0].size(); }

      void set_size(size_type s);
    };

  public :

    typedef var_description *pvariable;
    typedef std::vector<std::string> varnamelist;
    typedef std::vector<const mesh_im *> mimlist;
    typedef std::vector<model_real_sparse_matrix> real_matlist;
    typedef std::vector<model_complex_sparse_matrix> complex_matlist;
    typedef std::vector<model_real_plain_vector> real_veclist;
    typedef std::vector<model_complex_plain_vector> complex_veclist;

    struct term_description {
      bool is_matrix_term; // tangent matrix term or rhs term.
      bool is_symmetric;   // Term have to be symmetrized.
      std::string var1, var2;
      term_description(const std::string &v)
        : is_matrix_term(false), is_symmetric(false), var1(v) {}
      term_description(const std::string &v1, const std::string &v2,
                       bool issym)
        : is_matrix_term(true), is_symmetric(issym), var1(v1), var2(v2) {}
    };

    typedef std::vector<term_description> termlist;

    enum build_version { BUILD_RHS = 1,
                         BUILD_MATRIX = 2,
                         BUILD_ALL = 3,
                         BUILD_ON_DATA_CHANGE = 4,
                         BUILD_WITH_COMPLETE_RHS = 8,
                         BUILD_COMPLETE_RHS = 9,
                         BUILD_PSEUDO_POTENTIAL = 16
                       };

  private :

    // rmatlist and cmatlist could be csc_matrix vectors to reduced the
    // amount of memory (but this should add a supplementary copy).
    struct brick_description {
      mutable bool terms_to_be_computed;
      mutable gmm::uint64_type v_num;
      pbrick pbr;               // brick pointer
      pdispatcher pdispatch;    // Optional dispatcher
      size_type nbrhs;          // Additional rhs for dispatcher.
      varnamelist vlist;        // List of variables used by the brick.
      varnamelist dlist;        // List of data used by the brick.
      termlist tlist;           // List of terms build by the brick
      mimlist mims;             // List of integration methods.
      size_type region;         // Optional region size_type(-1) for all.
      mutable model_real_plain_vector coeffs;
      mutable scalar_type matrix_coeff;
      mutable real_matlist rmatlist;    // Matrices the brick have to fill in
                                        // (real version).
      mutable std::vector<real_veclist> rveclist; // Rhs the brick have to
                                        // fill in (real version).
      mutable std::vector<real_veclist> rveclist_sym; // additional rhs for
                                        //  symmetric terms (real version).
      mutable complex_matlist cmatlist; // Matrices the brick have to fill in
                                        // (complex version).
      mutable std::vector<complex_veclist> cveclist; // Rhs the brick have to
                                        // fill in (complex version).
      mutable std::vector<complex_veclist> cveclist_sym;  // additional rhs
                                        // for symmetric terms (real version).

      brick_description(pbrick p, const varnamelist &vl,
                        const varnamelist &dl, const termlist &tl,
                        const mimlist &mms, size_type reg)
        : terms_to_be_computed(true), v_num(0), pbr(p), pdispatch(0), nbrhs(1),
          vlist(vl), dlist(dl), tlist(tl), mims(mms), region(reg),
          rveclist(1), rveclist_sym(1), cveclist(1),
          cveclist_sym(1)  { }
    };

    typedef std::map<std::string, var_description> VAR_SET;
    mutable VAR_SET variables;
    std::vector<brick_description> bricks;
    dal::bit_vector active_bricks;

    void actualize_sizes(void) const;
    bool check_name_valitity(const std::string &name,
                             bool assert = true) const;
    void brick_init(size_type ib, build_version version,
                      size_type rhs_ind = 0) const;

    void init(void) { complex_version = false; act_size_to_be_done = false; }

  public :

    // call the brick if necessary
    void update_brick(size_type ib, build_version version) const;
    void linear_brick_add_to_rhs(size_type ib, size_type ind_data,
                                 size_type n_iter) const;
    bool build_reduced_index(std::vector<size_type> &ind);
    void brick_call(size_type ib, build_version version,
                    size_type rhs_ind = 0) const;
    model_real_plain_vector &rhs_coeffs_of_brick(size_type ib) const
    { return bricks[ib].coeffs; }
    scalar_type &matrix_coeff_of_brick(size_type ib) const
    { return bricks[ib].matrix_coeff; }
    bool is_var_newer_than_brick(const std::string &varname,
                                 size_type ib) const;
    bool is_var_mf_newer_than_brick(const std::string &varname,
                                    size_type ib) const;
    pbrick get_brick(size_type ib) const IS_DEPRECATED {
      GMM_ASSERT1(ib < bricks.size(), "Inexistent brick");
      return bricks[ib].pbr;
    }
    pbrick brick_pointer(size_type ind_brick) const { 
      GMM_ASSERT1(ind_brick < bricks.size(), "Inexistent brick");
      return bricks[ind_brick].pbr;
    }


    void add_temporaries(const varnamelist &vl, gmm::uint64_type id_num) const;

    const mimlist &mimlist_of_brick(size_type ib) const
    { return bricks[ib].mims; }

    const varnamelist &varnamelist_of_brick(size_type ib) const
    { return bricks[ib].vlist; }

    const varnamelist &datanamelist_of_brick(size_type ib) const
    { return bricks[ib].dlist; }

    size_type region_of_brick(size_type ib) const
    { return bricks[ib].region; }

    bool temporary_uptodate(const std::string &varname,
                            gmm::uint64_type  id_num, size_type &ind) const;
    void set_default_iter_of_variable(const std::string &varname,
                                      size_type ind) const;
    void reset_default_iter_of_variables(const varnamelist &vl) const;

    void update_from_context(void) const {  act_size_to_be_done = true; }

    const model_real_sparse_matrix &linear_real_matrix_term
    (size_type ib, size_type iterm);

    const model_complex_sparse_matrix &linear_complex_matrix_term
    (size_type ib, size_type iterm);

    /** Disable a brick.  */
    void disable_brick(size_type ib) {
      GMM_ASSERT1(ib < bricks.size(), "Inexistent brick");
      active_bricks.sup(ib);
    }

    /** Enable a brick.  */
    void enable_brick(size_type ib) {
      GMM_ASSERT1(ib < bricks.size(), "Inexistent brick");
      active_bricks.add(ib);
    }

    /** Disable a variable.  */
    void disable_variable(const std::string &name) {
      variables[name].is_disabled = true;
    }

    /** Enable a variable.  */
    void enable_variable(const std::string &name) {
      variables[name].is_disabled = false;
    }

    /** Boolean which says if the model deals with real or complex unknowns
        and data. */
    bool is_complex(void) const { return complex_version; }

    /** Return true if all the model terms do not affect the coercivity of
        the whole tangent system. */
    bool is_coercive(void) const { return is_coercive_; }

    /** Return true if all the model terms are linear. */
    bool is_linear(void) const { return is_linear_; }

    /** Total number of degrees of freedom in the model. */
    size_type nb_dof(void) const {
      context_check(); if (act_size_to_be_done) actualize_sizes();
      if (complex_version)
        return gmm::vect_size(crhs);
      else
        return gmm::vect_size(rrhs);
    }

    /** Leading dimension of the meshes used in the model. */
    dim_type leading_dimension(void) const { return leading_dim; }

    /** Gives a non already existing variable name begining by `name`. */
    std::string new_name(const std::string &name);

    const gmm::sub_interval
    &interval_of_variable(const std::string &name) const
    { return variables[name].I; }

    /** Gives the access to the vector value of a variable. For the real
        version. */
    const model_real_plain_vector &
    real_variable(const std::string &name,
                  size_type niter = size_type(-1)) const;

    /** Gives the access to the vector value of a variable. For the complex
        version. */
    const model_complex_plain_vector &
    complex_variable(const std::string &name,
                     size_type niter = size_type(-1)) const;

    /** Gives the write access to the vector value of a variable. Make a
        change flag of the variable set. For the real version. */
    model_real_plain_vector &
    set_real_variable(const std::string &name,
                      size_type niter = size_type(-1)) const;

    /** Gives the write access to the vector value of a variable. Make a
        change flag of the variable set. For the complex version. */
    model_complex_plain_vector &
    set_complex_variable(const std::string &name,
                         size_type niter = size_type(-1)) const;

    template<typename VECTOR, typename T>
    void from_variables(VECTOR &V, T) const {
      for (VAR_SET::iterator it = variables.begin();
           it != variables.end(); ++it)
        if (it->second.is_variable)
          gmm::copy(it->second.real_value[0],
                    gmm::sub_vector(V, it->second.I));
    }

    template<typename VECTOR, typename T>
    void from_variables(VECTOR &V, std::complex<T>) const {
      for (VAR_SET::iterator it = variables.begin();
           it != variables.end(); ++it)
        if (it->second.is_variable)
          gmm::copy(it->second.complex_value[0],
                    gmm::sub_vector(V, it->second.I));
    }

    template<typename VECTOR> void from_variables(VECTOR &V) const {
      typedef typename gmm::linalg_traits<VECTOR>::value_type T;
      context_check(); if (act_size_to_be_done) actualize_sizes();
      from_variables(V, T());
    }


    template<typename VECTOR, typename T>
    void to_variables(VECTOR &V, T) {
      for (VAR_SET::iterator it = variables.begin();
           it != variables.end(); ++it)
        if (it->second.is_variable) {
          gmm::copy(gmm::sub_vector(V, it->second.I),
                    it->second.real_value[0]);
          it->second.v_num_data = act_counter();
        }
    }

    template<typename VECTOR, typename T>
    void to_variables(VECTOR &V, std::complex<T>) {
      for (VAR_SET::iterator it = variables.begin();
           it != variables.end(); ++it)
        if (it->second.is_variable) {
          gmm::copy(gmm::sub_vector(V, it->second.I),
                    it->second.complex_value[0]);
          it->second.v_num_data = act_counter();
        }
    }

    template<typename VECTOR> void to_variables(VECTOR &V) {
      typedef typename gmm::linalg_traits<VECTOR>::value_type T;
      context_check(); if (act_size_to_be_done) actualize_sizes();
      to_variables(V, T());
    }

    /** Add a fixed size variable to the model. niter is the number of version
        of the variable stored, for time integration schemes. */
    void add_fixed_size_variable(const std::string &name, size_type size,
                                 size_type niter = 1);

    /** Add a fixed size data to the model. niter is the number of version
        of the data stored, for time integration schemes. */
    void add_fixed_size_data(const std::string &name, size_type size,
                             size_type niter = 1);

    /** Resize a fixed size variable (or data) of the model. */
    void resize_fixed_size_variable(const std::string &name, size_type size);


    /** Add a fixed size data to the model initialized with V. */
    template <typename VECT>
    void add_initialized_fixed_size_data(const std::string &name,
                                         const VECT &v) {
      this->add_fixed_size_data(name, gmm::vect_size(v), 1);
      if (this->is_complex()) // to be templated .. see later
        gmm::copy(v, this->set_complex_variable(name));
      else
        gmm::copy(gmm::real_part(v), this->set_real_variable(name));
    }

    /** Add a scalar data (i.e. of size 1) to the model initialized with e. */
    template <typename T>
    void add_initialized_scalar_data(const std::string &name, T e) {
      this->add_fixed_size_data(name, 1, 1);
      if (this->is_complex()) // to be templated .. see later
        this->set_complex_variable(name)[0] = e;
      else
        this->set_real_variable(name)[0] = gmm::real(e);
    }


    /** Add a variable being the dofs of a finite element method to the model.
        niter is the number of version of the variable stored, for time
        integration schemes. */
    void add_fem_variable(const std::string &name, const mesh_fem &mf,
                          size_type niter = 1);

    /** Add a variable linked to a fem with the dof filtered with respect 
	to a mesh region. Only the dof returned by the dof_on_region
	method of `mf` will be kept. niter is the number of version
	of the data stored, for time integration schemes. */
    void add_filtered_fem_variable(const std::string &name, const mesh_fem &mf,
				   size_type region, size_type niter = 1);

    /** Add a data being the dofs of a finite element method to the model.
        The data is initialized with V. */
    void add_fem_data(const std::string &name, const mesh_fem &mf,
                      dim_type qdim = 1, size_type niter = 1);

    /** Add a fixed size data to the model. niter is the number of version
        of the data stored, for time integration schemes. */
    template <typename VECT>
    void add_initialized_fem_data(const std::string &name, const mesh_fem &mf,
                                  const VECT &v) {
      this->add_fem_data(name, mf,
                         dim_type(gmm::vect_size(v) / mf.nb_dof()), 1);
      if (this->is_complex()) // to be templated .. see later
        gmm::copy(v, this->set_complex_variable(name));
      else
        gmm::copy(gmm::real_part(v), this->set_real_variable(name));
    }

    /** Add a particular variable linked to a fem being a multiplier with
        respect to a primal variable. The dof will be filtered with the
        gmm::range_basis function applied on the terms of the model which
        link the multiplier and the primal variable. Optimized for boundary
        multipliers. niter is the number of version of the data stored,
        for time integration schemes. */
    void add_multiplier(const std::string &name, const mesh_fem &mf,
                        const std::string &primal_name,
                        size_type niter = 1);

    /** Add a particular variable linked to a fem being a multiplier with
        respect to a primal variable. The dof will be filtered with the
        gmm::range_basis function applied on the mass matrix between the fem
	of the multiplier and the one of the primal variable.
	Optimized for boundary multipliers. niter is the number of version
	of the data stored, for time integration schemes. */
    void add_multiplier(const std::string &name, const mesh_fem &mf,
                        const std::string &primal_name, const mesh_im &mim,
			size_type region, size_type niter = 1);

    /** Gives the access to the mesh_fem of a variable if any. Throw an
        exception otherwise. */
    const mesh_fem &mesh_fem_of_variable(const std::string &name) const;

    /** Gives a pointer to the mesh_fem of a variable if any. 0 otherwise.*/
    const mesh_fem *pmesh_fem_of_variable(const std::string &name) const;


    /** Gives the access to the tangent matrix. For the real version. */
    const model_real_sparse_matrix &real_tangent_matrix(void) const {
      GMM_ASSERT1(!complex_version, "This model is a complex one");
      context_check(); if (act_size_to_be_done) actualize_sizes();
      return rTM;
    }

    /** Gives the access to the tangent matrix. For the complex version. */
    const model_complex_sparse_matrix &complex_tangent_matrix(void) const {
      GMM_ASSERT1(complex_version, "This model is a real one");
      context_check(); if (act_size_to_be_done) actualize_sizes();
      return cTM;
    }

    /** Gives the access to the right hand side of the tangent linear system.
        For the real version. An assembly of the rhs has to be done first. */
    const model_real_plain_vector &real_rhs(void) const {
      GMM_ASSERT1(!complex_version, "This model is a complex one");
      context_check(); if (act_size_to_be_done) actualize_sizes();
      return rrhs;
    }

    /** Gives the access to the part of the right hand side of a term of a particular nonlinear brick. Does not account of the eventual time dispatcher. An assembly of the rhs has to be done first. For the real version. */
    const model_real_plain_vector &real_brick_term_rhs(size_type ib, size_type ind_term = 0, bool sym = false, size_type ind_iter = 0) const {
      GMM_ASSERT1(!complex_version, "This model is a complex one");
      context_check(); if (act_size_to_be_done) actualize_sizes();
      GMM_ASSERT1(ib < bricks.size(), "Inexistent brick");
      GMM_ASSERT1(ind_term < bricks[ib].tlist.size(), "Inexistent term");
      GMM_ASSERT1(ind_iter < bricks[ib].nbrhs, "Inexistent iter");
      GMM_ASSERT1(!sym || bricks[ib].tlist[ind_term].is_symmetric,
                  "Term is not symmetric");

      if (sym)
        return bricks[ib].rveclist_sym[ind_iter][ind_term];
      else
        return bricks[ib].rveclist[ind_iter][ind_term];
    }

    /** Gives the access to the pseudo potential. It has to be computed first
        by the call of assembly(model::BUILD_PSEUDO_POTENTIAL); */
    scalar_type pseudo_potential(void) const {
      return pseudo_potential_;
    }

    /** Gives the access to the right hand side of the tangent linear system.
        For the complex version. */
    const model_complex_plain_vector &complex_rhs(void) const {
      GMM_ASSERT1(complex_version, "This model is a real one");
      context_check(); if (act_size_to_be_done) actualize_sizes();
      return crhs;
    }

    /** Gives the access to the part of the right hand side of a term of a particular nonlinear brick. Does not account of the eventual time dispatcher. An assembly of the rhs has to be done first. For the real version. */
    const model_complex_plain_vector &complex_brick_term_rhs(size_type ib, size_type ind_term = 0, bool sym = false, size_type ind_iter = 0) const {
      GMM_ASSERT1(!complex_version, "This model is a complex one");
      context_check(); if (act_size_to_be_done) actualize_sizes();
      GMM_ASSERT1(ib < bricks.size(), "Inexistent brick");
      GMM_ASSERT1(ind_term < bricks[ib].tlist.size(), "Inexistent term");
      GMM_ASSERT1(ind_iter < bricks[ib].nbrhs, "Inexistent iter");
      GMM_ASSERT1(!sym || bricks[ib].tlist[ind_term].is_symmetric,
                  "Term is not symmetric");

      if (sym)
        return bricks[ib].cveclist_sym[ind_iter][ind_term];
      else
        return bricks[ib].cveclist[ind_iter][ind_term];
    }

    /** List the model variables and constant. */
    void listvar(std::ostream &ost) const;

    /** List the model bricks. */
    void listbricks(std::ostream &ost, size_type base_id = 0) const;

    /** Force the re-computation of a brick for the next assembly. */
    void touch_brick(size_type ind_brick) {
      GMM_ASSERT1(ind_brick < bricks.size(), "Inexistent brick");
      bricks[ind_brick].terms_to_be_computed = true;
    }

    /** Add a brick to the model. varname is the list of variable used
        and datanames the data used. If a variable is used as a data, it
        should be declared in the datanames (it will depend on the value of
        the variable not only on the fem). */
    size_type add_brick(pbrick pbr, const varnamelist &varnames,
                        const varnamelist &datanames,
                        const termlist &terms, const mimlist &mims,
                        size_type region);
    
    /** Add an integration method to a brick. */
    void add_mim_to_brick(size_type ib, const mesh_im &mim);

    /** Change the term list of a brick. Used for very special bricks only. */
    void change_terms_of_brick(size_type ib, const termlist &terms);

    /** Change the variable list of a brick. Used for very special bricks only.
     */
    void change_variables_of_brick(size_type ib, const varnamelist &vl);


    /** Add a time dispacther to a brick. */
    void add_time_dispatcher(size_type ibrick, pdispatcher pdispatch);

    void set_dispatch_coeff(void);

    /** For transient problems. Initialisation of iterations. */
    void first_iter(void);

    /** For transient problems. Prepare the next iterations. In particular
        shift the version of the variables.
    */
    void next_iter(void);

    /** Gives the name of the variable of index `ind_var` of the brick
        of index `ind_brick`. */
    const std::string &varname_of_brick(size_type ind_brick,
                                        size_type ind_var);

    /** Gives the name of the data of index `ind_data` of the brick
        of index `ind_brick`. */
    const std::string &dataname_of_brick(size_type ind_brick,
                                         size_type ind_data);

    /** Assembly of the tangent system taking into account the terms
        from all bricks. */
    void assembly(build_version version);

    void clear(void) {
      variables.clear();
      active_bricks.clear();
      rTM = model_real_sparse_matrix();
      cTM = model_complex_sparse_matrix();
      rrhs = model_real_plain_vector();
      crhs = model_complex_plain_vector();
    }

    model(bool comp_version = false) {
      init(); complex_version = comp_version;
      is_linear_ = is_symmetric_ = is_coercive_ = true;
      leading_dim = 0;
    }

	/**check consistency of RHS and Stiffness matrix for brick with 
	* @param  ind_brick  - index of the brick
	*/
	void check_brick_stiffness_rhs(size_type ind_brick) const;


  };

  //=========================================================================
  //
  //  Time dispatcher object.
  //
  //=========================================================================

  /** The time dispatcher object modify the result of a brick in order to
      apply a time integration scheme.
  **/
  class virtual_dispatcher : virtual public dal::static_stored_object {

  protected :

    void clear(model::real_veclist &v) const
    { for (size_type i = 0; i < v.size(); ++i) gmm::clear(v[i]); }

    void clear(model::complex_veclist &v) const
    { for (size_type i = 0; i < v.size(); ++i) gmm::clear(v[i]); }

    void transfert(model::real_veclist &v1,
                   model::real_veclist &v2) const
    { for (size_type i = 0; i < v1.size(); ++i) gmm::copy(v1[i], v2[i]); }

    void transfert(model::complex_veclist &v1,
                   model::complex_veclist &v2) const
    { for (size_type i = 0; i < v1.size(); ++i) gmm::copy(v1[i], v2[i]); }

    size_type nbrhs_;
    std::vector<std::string> param_names;

  public :

    size_type nbrhs(void) const { return nbrhs_; }

    typedef model::build_version build_version;

    virtual void set_dispatch_coeff(const model &, size_type) const
    { GMM_ASSERT1(false, "Time dispatcher with not set_dispatch_coeff !"); }

    virtual void next_real_iter
    (const model &, size_type, const model::varnamelist &,
     const model::varnamelist &,
     model::real_matlist &,
     std::vector<model::real_veclist> &,
     std::vector<model::real_veclist> &,
     bool) const {
      GMM_ASSERT1(false, "Time dispatcher with not defined first real iter !");
    }

    virtual void next_complex_iter
    (const model &, size_type, const model::varnamelist &,
     const model::varnamelist &,
     model::complex_matlist &,
     std::vector<model::complex_veclist> &,
     std::vector<model::complex_veclist> &,
     bool) const{
      GMM_ASSERT1(false,"Time dispatcher with not defined first comples iter");
    }

    virtual void asm_real_tangent_terms
    (const model &, size_type,
     model::real_matlist &, std::vector<model::real_veclist> &,
     std::vector<model::real_veclist> &,
     build_version) const {
      GMM_ASSERT1(false, "Time dispatcher with not defined real tangent "
                  "terms !");
    }

    virtual void asm_complex_tangent_terms
    (const model &, size_type,
     model::complex_matlist &, std::vector<model::complex_veclist> &,
     std::vector<model::complex_veclist> &,
     build_version) const {
      GMM_ASSERT1(false, "Time dispatcher with not defined complex tangent "
                  "terms !");
    }

    virtual_dispatcher(size_type _nbrhs) : nbrhs_(_nbrhs) {
      GMM_ASSERT1(_nbrhs > 0, "Time dispatcher with no rhs");
    }

  };

  //=========================================================================
  //
  //  Functions adding standard time dispatchers.
  //
  //=========================================================================

  /** Add a theta-method time dispatcher to a list of bricks. For instance,
      a matrix term $K$ will be replaced by
      $\theta K U^{n+1} + (1-\theta) K U^{n}$.
  */
  void add_theta_method_dispatcher(model &md, dal::bit_vector ibricks,
                                   const std::string &THETA);

  /** Function which udpate the velocity $v^{n+1}$ after the computation
      of the displacement $u^{n+1}$ and before the next iteration. Specific
      for theta-method and when the velocity is included in the data
      of the model.
  */
  void velocity_update_for_order_two_theta_method
  (model &md, const std::string &U, const std::string &V,
   const std::string &pdt, const std::string &ptheta);


  /** Add a midpoint time dispatcher to a list of bricks. For instance,
      a nonlinear term $K(U)$ will be replaced by
      $K((U^{n+1} +  U^{n})/2)$.
  */
  void add_midpoint_dispatcher(model &md, dal::bit_vector ibricks);

  /** Function which udpate the velocity $v^{n+1}$ after the computation
      of the displacement $u^{n+1}$ and before the next iteration. Specific
      for Newmark scheme and when the velocity is included in the data
      of the model. This version inverts the mass matrix by a conjugate
      gradient.
  */
  void velocity_update_for_Newmark_scheme
  (model &md, size_type id2dt2b, const std::string &U, const std::string &V,
   const std::string &pdt, const std::string &ptwobeta,
   const std::string &pgamma);

  //=========================================================================
  //
  //  Brick object.
  //
  //=========================================================================

  /** The virtual brick has to be derived to describe real model bricks.
      The set_flags method has to be called by the derived class.
      The virtual methods asm_real_tangent_terms and/or
      asm_complex_tangent_terms have to be defined.
      The brick should not store data. The data have to be stored in the
      model object.
  **/
  class virtual_brick : virtual public dal::static_stored_object {
  private :
    bool islinear;    // The brick add a linear term or not.
    bool issymmetric; // The brick add a symmetric term or not.
    bool iscoercive;  // The brick add a potentialy coercive terms or not.
    //   (in particular, not a term involving a multiplier)
    bool isreal;      // The brick admits a real version or not.
    bool iscomplex;   // The brick admits a complex version or not.
    bool isinit;      // internal flag.
    bool compute_each_time; // The brick is linear but needs to be computed
                            // each time it is evaluated.
    std::string name; // Name of the brick.

  public :

    typedef model::build_version build_version;

    virtual_brick(void) { isinit = false; }
    void set_flags(const std::string &bname, bool islin, bool issym,
                   bool iscoer, bool ire, bool isco, bool each_time = false) {
      name = bname;
      islinear = islin; issymmetric = issym; iscoercive = iscoer;
      isreal = ire; iscomplex = isco; isinit = true;
      compute_each_time = each_time;
    }

#   define BRICK_NOT_INIT GMM_ASSERT1(isinit, "Set brick flags !")
    bool is_linear(void)    const { BRICK_NOT_INIT; return islinear;    }
    bool is_symmetric(void) const { BRICK_NOT_INIT; return issymmetric; }
    bool is_coercive(void)  const { BRICK_NOT_INIT; return iscoercive;  }
    bool is_real(void)      const { BRICK_NOT_INIT; return isreal;      }
    bool is_complex(void)   const { BRICK_NOT_INIT; return iscomplex;   }
    bool is_to_be_computed_each_time(void) const
    { BRICK_NOT_INIT; return compute_each_time; }
    const std::string &brick_name(void) const { BRICK_NOT_INIT; return name; }

    virtual void asm_real_tangent_terms(const model &, size_type,
                                        const model::varnamelist &,
                                        const model::varnamelist &,
                                        const model::mimlist &,
                                        model::real_matlist &,
                                        model::real_veclist &,
                                        model::real_veclist &,
                                        size_type, build_version) const
    { GMM_ASSERT1(false, "Brick has no real tangent terms !"); }

    virtual void asm_complex_tangent_terms(const model &, size_type,
                                           const model::varnamelist &,
                                           const model::varnamelist &,
                                           const model::mimlist &,
                                           model::complex_matlist &,
                                           model::complex_veclist &,
                                           model::complex_veclist &,
                                           size_type, build_version) const
    { GMM_ASSERT1(false, "Brick has no complex tangent terms !"); }


    virtual scalar_type asm_real_pseudo_potential(const model &, size_type,
                                                  const model::varnamelist &,
                                                  const model::varnamelist &,
                                                  const model::mimlist &,
                                                  model::real_matlist &,
                                                  model::real_veclist &,
                                                  model::real_veclist &,
                                                  size_type) const {
      GMM_WARNING1("Brick " << name << " has no contribution to the "
                   << "pseudo potential !");
      return scalar_type(0);
    }

    virtual scalar_type asm_complex_pseudo_potential(const model &, size_type,
                                                     const model::varnamelist&,
                                                     const model::varnamelist&,
                                                     const model::mimlist &,
                                                     model::complex_matlist &,
                                                     model::complex_veclist &,
                                                     model::complex_veclist &,
                                                     size_type) const {
      GMM_WARNING1("Brick " << name << " has no contribution to the "
                   << "pseudo potential !");
      return scalar_type(0);
    }

	/**check consistency of stiffness matrix and rhs*/
	void check_stiffness_matrix_and_rhs(const model &, size_type,
                                        const model::varnamelist &,
                                        const model::varnamelist &,
                                        const model::mimlist &,
                                        model::real_matlist &,
                                        model::real_veclist &,
                                        model::real_veclist &, size_type rg,
										const scalar_type delta = 1e-8) const;




  };



  //=========================================================================
  //
  //  Functions adding standard bricks to the model.
  //
  //=========================================================================


  /** Add a Laplacian term on the variable `varname` (in fact with a minus :
      :math:`-\text{div}(\nabla u)`). If it is a vector
      valued variable, the Laplacian term is componentwise. `region` is an
      optional mesh region on which the term is added. Return the brick index
      in the model.
  */
  size_type add_Laplacian_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   size_type region = size_type(-1));


  /** Add an elliptic term on the variable `varname`. The shape of the elliptic
      term depends both on the variable and the data. This corresponds to a
      term $-\text{div}(a\nabla u)$ where $a$ is the data and $u$ the variable.
      The data can be a scalar, a matrix or an order four tensor. The variable
      can be vector valued or not. If the data is a scalar or a matrix and
      the variable is vector valued then the term is added componentwise.
      An order four tensor data is allowed for vector valued variable only.
      The data can be constant or describbed on a fem. Of course, when
      the data is a tensor describe on a finite element method (a tensor
      field) the data can be a huge vector. The components of the
      matrix/tensor have to be stored with the fortran order (columnwise) in
      the data vector (compatibility with blas). The symmetry and coercivity
      of the given matrix/tensor is not verified (but assumed). `region` is an
      optional mesh region on which the term is added. Return the brick index
      in the model.
  */
  size_type add_generic_elliptic_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &dataname, size_type region = size_type(-1));


  /** Add a source term on the variable `varname`. The source term is
      represented by the data `dataname` which could be constant or described
      on a fem.  `region` is an optional mesh region on which the term is
      added. An additional optional data `directdataname` can be provided. The
      corresponding data vector will be directly added to the right hand
      side without assembly. Return the brick index in the model.
  */
  size_type add_source_term_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &dataname, size_type region = size_type(-1),
   const std::string &directdataname = std::string());

  /** Add a source term on the variable `varname` on a boundary `region`.
      The source term is
      represented by the data `dataname` which could be constant or described
      on a fem. A sclar product with the outward normal unit vector to
      the boundary is performed. The main aim of this brick is to represent
      a Neumann condition with a vector data without performing the
      scalar product with the normal as a pre-processing.
  */
  size_type add_normal_source_term_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &dataname, size_type region);

  /** Add a Dirichlet condition on the variable `varname` and the mesh
      region `region`. This region should be a boundary. The Dirichlet
      condition is prescribed with a multiplier variable `multname` which
      should be first declared as a multiplier
      variable on the mesh region in the model. `dataname` is the optional
      right hand side of  the Dirichlet condition. It could be constant or
      described on a fem; scalar or vector valued, depending on the variable
      on which the Dirichlet condition is prescribed. Return the brick index
      in the model.
  */
  size_type add_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &multname, size_type region,
   const std::string &dataname = std::string());

  /** Same function as the previous one but the multipliers variable will
      be declared to the brick by the function. `mf_mult` is the finite element
      method on which the multiplier will be build (it will be restricted to
      the mesh region `region` and eventually some conflicting dofs with some
      other multiplier variables will be suppressed).
  */
  size_type add_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   const mesh_fem &mf_mult, size_type region,
   const std::string &dataname = std::string());

  /** Same function as the previous one but the `mf_mult` parameter is
      replaced by `degree`. The multiplier will be described on a standard
      finite element method of the corresponding degree.
   */
  size_type add_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   dim_type degree, size_type region,
   const std::string &dataname = std::string());

  /** When `ind_brick` is the index of a Dirichlet brick with multiplier on
      the model `md`, the function return the name of the multiplier variable.
      Otherwise, it has an undefined behavior.
  */
  const std::string &mult_varname_Dirichlet(model &md, size_type ind_brick);

  /** Add a Dirichlet condition on the variable `varname` and the mesh
      region `region`. This region should be a boundary. The Dirichlet
      condition is prescribed with penalization. The penalization coefficient
      is intially `penalization_coeff` and will be added to the data of
      the model. `dataname` is the optional
      right hand side of  the Dirichlet condition. It could be constant or
      described on a fem; scalar or vector valued, depending on the variable
      on which the Dirichlet condition is prescribed.
      `mf_mult` is an optional parameter which allows to weaken the
      Dirichlet condition specifying a multiplier space.
      Returns the brick index in the model.
  */
  size_type add_Dirichlet_condition_with_penalization
  (model &md, const mesh_im &mim, const std::string &varname,
   scalar_type penalization_coeff, size_type region,
   const std::string &dataname = std::string(),
   const mesh_fem *mf_mult = 0);

  /** Add a Dirichlet condition to the normal component of the vector
     (or tensor) valued variable `varname` and the mesh
      region `region`. This region should be a boundary. The Dirichlet
      condition is prescribed with a multiplier variable `multname` which
      should be first declared as a multiplier
      variable on the mesh region in the model. `dataname` is the optional
      right hand side of  the normal Dirichlet condition.
      It could be constant or
      described on a fem; scalar or vector valued, depending on the variable
      on which the Dirichlet condition is prescribed (scalar if the variable
      is vector valued, vector if the variable is tensor valued).
      Returns the brick index in the model.
  */
  size_type add_normal_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &multname, size_type region,
   const std::string &dataname = std::string());

  /** Same function as the previous one but the multipliers variable will
      be declared to the brick by the function. `mf_mult` is the finite element
      method on which the multiplier will be build (it will be restricted to
      the mesh region `region` and eventually some conflicting dofs with some
      other multiplier variables will be suppressed).
  */
  size_type add_normal_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   const mesh_fem &mf_mult, size_type region,
   const std::string &dataname = std::string());

  /** Same function as the previous one but the `mf_mult` parameter is
      replaced by `degree`. The multiplier will be described on a standard
      finite element method of the corresponding degree.
   */
  size_type add_normal_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   dim_type degree, size_type region,
   const std::string &dataname = std::string());

  /** Add a Dirichlet condition to the normal component of the vector
     (or tensor) valued variable `varname` and the mesh
      region `region`. This region should be a boundary. The Dirichlet
      condition is prescribed with penalization. The penalization coefficient
      is intially `penalization_coeff` and will be added to the data of
      the model. `dataname` is the optional
      right hand side of  the Dirichlet condition. It could be constant or
      described on a fem; scalar or vector valued, depending on the variable
      on which the Dirichlet condition is prescribed (scalar if the variable
      is vector valued, vector if the variable is tensor valued).
      `mf_mult` is an optional parameter which allows to weaken the
      Dirichlet condition specifying a multiplier space.
      Return the brick index in the model.
  */
  size_type add_normal_Dirichlet_condition_with_penalization
  (model &md, const mesh_im &mim, const std::string &varname,
   scalar_type penalization_coeff, size_type region,
   const std::string &dataname = std::string(),
   const mesh_fem *mf_mult = 0);


  /** Add some pointwise constraints on the variable `varname` thanks to
      a penalization. The penalization coefficient is initially
      `penalization_coeff` and will be added to the data of the model.
      The conditions are prescribed on a set of points given in the data
      `dataname_pt` whose dimension is the number of points times the dimension
      of the mesh. If the variable represents a vector field, the data
      `dataname_unitv` represents a vector of dimension the number of points
      times the dimension of the vector field which should store some
      unit vectors. In that case the prescribed constraint is the scalar
      product of the variable at the corresponding point with the corresponding
      unit vector.
      The optional data `dataname_val` is the vector of values to be prescribed
      at the different points.
      This brick is specifically designed to kill rigid displacement
      in a Neumann problem.
  */
  size_type add_pointwise_constraints_with_penalization
  (model &md, const std::string &varname,
   scalar_type penalisation_coeff, const std::string &dataname_pt,
   const std::string &dataname_unitv = std::string(),
   const std::string &dataname_val = std::string());


  /** Add some pointwise constraints on the variable `varname` using a given
      multiplier `multname`.
      The conditions are prescribed on a set of points given in the data
      `dataname_pt` whose dimension is the number of points times the dimension
      of the mesh.
      The multiplier variable should be a fixed size variable of size the
      number of points.
      If the variable represents a vector field, the data
      `dataname_unitv` represents a vector of dimension the number of points
      times the dimension of the vector field which should store some
      unit vectors. In that case the prescribed constraint is the scalar
      product of the variable at the corresponding point with the corresponding
      unit vector.
      The optional data `dataname_val` is the vector of values to be prescribed
      at the different points.
      This brick is specifically designed to kill rigid displacement
      in a Neumann problem.
  */
  size_type add_pointwise_constraints_with_given_multipliers
  (model &md, const std::string &varname,
   const std::string &multname, const std::string &dataname_pt,
   const std::string &dataname_unitv = std::string(),
   const std::string &dataname_val = std::string());

  /** Add some pointwise constraints on the variable `varname` using
      multiplier. The multiplier variable is automatically added to the model.
      The conditions are prescribed on a set of points given in the data
      `dataname_pt` whose dimension is the number of points times the dimension
      of the mesh.
      If the variable represents a vector field, the data
      `dataname_unitv` represents a vector of dimension the number of points
      times the dimension of the vector field which should store some
      unit vectors. In that case the prescribed constraint is the scalar
      product of the variable at the corresponding point with the corresponding
      unit vector.
      The optional data `dataname_val` is the vector of values to be prescribed
      at the different points.
      This brick is specifically designed to kill rigid displacement
      in a Neumann problem.
  */
  size_type add_pointwise_constraints_with_multipliers
  (model &md, const std::string &varname, const std::string &dataname_pt,
   const std::string &dataname_unitv = std::string(),
   const std::string &dataname_val = std::string());


  /** Change the penalization coefficient of a Dirichlet condition with
      penalization brick. If the brick is not of this kind,
      this function has an undefined behavior.
  */
  void change_penalization_coeff(model &md, size_type ind_brick,
                                 scalar_type penalisation_coeff);

  /** Add a generalized Dirichlet condition on the variable `varname` and
      the mesh region `region`. This version is for vector field.
      It prescribes a condition @f$ Hu = r @f$ where `H` is a matrix field.
      This region should be a boundary. The Dirichlet
      condition is prescribed with a multiplier variable `multname` which
      should be first declared as a multiplier
      variable on the mesh region in the model. `dataname` is the
      right hand side of  the Dirichlet condition. It could be constant or
      described on a fem; scalar or vector valued, depending on the variable
      on which the Dirichlet condition is prescribed. `Hname' is the data
      corresponding to the matrix field `H`. It has to be a constant matrix
      or described on a scalar fem. Return the brick index in the model.
  */
  size_type add_generalized_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &multname, size_type region,
   const std::string &dataname, const std::string &Hname);

  /** Same function as the preceeding one but the multipliers variable will
      be declared to the brick by the function. `mf_mult` is the finite element
      method on which the multiplier will be build (it will be restricted to
      the mesh region `region` and eventually some conflicting dofs with some
      other multiplier variables will be suppressed).
  */
  size_type add_generalized_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   const mesh_fem &mf_mult, size_type region,
   const std::string &dataname, const std::string &Hname);

  /** Same function as the preceeding one but the `mf_mult` parameter is
      replaced by `degree`. The multiplier will be described on a standard
      finite element method of the corresponding degree.
   */
  size_type add_generalized_Dirichlet_condition_with_multipliers
  (model &md, const mesh_im &mim, const std::string &varname,
   dim_type degree, size_type region,
   const std::string &dataname, const std::string &Hname);

  /** Add a Dirichlet condition on the variable `varname` and the mesh
      region `region`. This version is for vector field.
      It prescribes a condition @f$ Hu = r @f$ where `H` is a matrix field.
      This region should be a boundary. This region should be a boundary.
      The Dirichlet
      condition is prescribed with penalization. The penalization coefficient
      is intially `penalization_coeff` and will be added to the data of
      the model. `dataname` is the
      right hand side of  the Dirichlet condition. It could be constant or
      described on a fem; scalar or vector valued, depending on the variable
      on which the Dirichlet condition is prescribed. `Hname' is the data
      corresponding to the matrix field `H`. It has to be a constant matrix
      or described on a scalar fem. `mf_mult` is an optional parameter
      which allows to weaken the Dirichlet condition specifying a
      multiplier space. Return the brick index in the model.
  */
  size_type add_generalized_Dirichlet_condition_with_penalization
  (model &md, const mesh_im &mim, const std::string &varname,
   scalar_type penalization_coeff, size_type region,
   const std::string &dataname, const std::string &Hname,
   const mesh_fem *mf_mult = 0);



  /** Add a Helmoltz brick to the model. This corresponds to the scalar
      equation (@f$\Delta u + k^2u = 0@f$, with @f$K=k^2@f$).
      The weak formulation is (@f$\int k^2 u.v - \nabla u.\nabla v@f$)

      `dataname` should contain the wave number $k$. It can be real or
      complex, fem dependant or not.
  */
  size_type add_Helmholtz_brick(model &md, const mesh_im &mim,
                                const std::string &varname,
                                const std::string &dataname,
                                size_type region = size_type(-1));


  /** Add a Fourier-Robin brick to the model. This correspond to the weak term
      (@f$\int (qu).v @f$) on a boundary. It is used to represent a
      Fourier-Robin boundary condition.

      `dataname` should contain the parameter $q$ which should be a
      (@f$N\times N@f$) matrix term, where $N$ is the dimension of the
      variable `varname`. Note that an additional right hand
      side can be added with a source term brick.
  */
  size_type add_Fourier_Robin_brick(model &md, const mesh_im &mim,
                                    const std::string &varname,
                                    const std::string &dataname,
                                    size_type region);


  /** Add a brick representing a scalar term (@f$f(u)@f$) to the left-hand
      side of the model. In the weak form, one adds (@f$ +\int f(u)v@f$). The
      function $f$ may optionally depend on $\lambda$, i.e.,
      $f(u) = f(u, \lambda)$.

      `f` and `dfdu` should contain the expressions for $f(u)$ and
      $\frac{df}{du}(u)$, respectively. `region` is an
      optional mesh region on which the term is added. `dataname` represents
      the optional real scalar parameter $\lambda$ in the model. Return the
      brick index in the model.
   */
  size_type add_basic_nonlinear_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &f, const std::string &dfdu,
   size_type region = size_type(-1),
   const std::string &dataname = std::string());

  // Constraint brick.
  model_real_sparse_matrix &set_private_data_brick_real_matrix
  (model &md, size_type indbrick);
  model_real_plain_vector &set_private_data_brick_real_rhs
  (model &md, size_type indbrick);
  model_complex_sparse_matrix &set_private_data_brick_complex_matrix
  (model &md, size_type indbrick);
  model_complex_plain_vector &set_private_data_brick_complex_rhs
  (model &md, size_type indbrick);
  size_type add_constraint_with_penalization
  (model &md, const std::string &varname, scalar_type penalisation_coeff);
  size_type add_constraint_with_multipliers
  (model &md, const std::string &varname, const std::string &multname);

  template <typename VECT, typename T>
  void set_private_data_rhs(model &md, size_type ind,
                                const VECT &L, T) {
    model_real_plain_vector &LL = set_private_data_brick_real_rhs(md, ind);
    gmm::resize(LL, gmm::vect_size(L));
    gmm::copy(L, LL);
  }

  template <typename VECT, typename T>
  void set_private_data_rhs(model &md, size_type ind, const VECT &L,
                           std::complex<T>) {
    model_complex_plain_vector &LL=set_private_data_brick_complex_rhs(md, ind);
    gmm::resize(LL, gmm::vect_size(L));
    gmm::copy(L, LL);
  }

  /** For some specific bricks having an internal right hand side vector
      (explicit bricks: 'constraint brick' and 'explicit rhs brick'),
      set this rhs.
  */
  template <typename VECT>
  void set_private_data_rhs(model &md, size_type indbrick, const VECT &L) {
    typedef typename gmm::linalg_traits<VECT>::value_type T;
    set_private_data_rhs(md, indbrick, L, T());
  }

  template <typename MAT, typename T>
  void set_private_data_matrix(model &md, size_type ind,
                                   const MAT &B, T) {
    model_real_sparse_matrix &BB = set_private_data_brick_real_matrix(md, ind);
    gmm::resize(BB, gmm::mat_nrows(B), gmm::mat_ncols(B));
    gmm::copy(B, BB);
  }

  template <typename MAT, typename T>
  void set_private_data_matrix(model &md, size_type ind, const MAT &B,
                              std::complex<T>) {
    model_complex_sparse_matrix &BB
      = set_private_data_brick_complex_matrix(md, ind);
    gmm::resize(BB, gmm::mat_nrows(B), gmm::mat_ncols(B));
    gmm::copy(B, BB);
  }

  /** For some specific bricks having an internal sparse matrix
      (explicit bricks: 'constraint brick' and 'explicit matrix brick'),
      set this matrix. @*/
  template <typename MAT>
  void set_private_data_matrix(model &md, size_type indbrick,
                                   const MAT &B) {
    typedef typename gmm::linalg_traits<MAT>::value_type T;
    set_private_data_matrix(md, indbrick, B, T());
  }

  /** Add an additional explicit penalized constraint on the variable
      `varname`. The constraint is $BU=L$ with `B` being a rectangular
      sparse matrix.
      Be aware that `B` should not contain a plain row, otherwise the whole
      tangent matrix will be plain. It is possible to change the constraint
      at any time whith the methods set_private_matrix and set_private_rhs.
      The method change_penalization_coeff can also be used.
  */
  template <typename MAT, typename VECT>
  size_type add_constraint_with_penalization
  (model &md, const std::string &varname, scalar_type penalisation_coeff,
   const MAT &B, const VECT &L) {
    size_type ind
      = add_constraint_with_penalization(md, varname, penalisation_coeff);
    size_type n = gmm::mat_nrows(B), m = gmm::mat_ncols(B);
    set_private_data_rhs(md, ind, L);
    set_private_data_matrix(md, ind, B);
    return ind;
  }

  /** Add an additional explicit constraint on the variable `varname` thank to
    a multiplier `multname` peviously added to the model (should be a fixed
    size variable).
    The constraint is $BU=L$ with `B` being a rectangular sparse matrix.
    It is possible to change the constraint
    at any time whith the methods set_private_matrix
    and set_private_rhs.
  */
  template <typename MAT, typename VECT>
  size_type add_constraint_with_multipliers
  (model &md, const std::string &varname, const std::string &multname,
   const MAT &B, const VECT &L) {
    size_type ind = add_constraint_with_multipliers(md, varname, multname);
    set_private_data_rhs(md, ind, L);
    set_private_data_matrix(md, ind, B);
    return ind;
  }

  size_type add_explicit_matrix(model &md, const std::string &varname1,
                                const std::string &varname2,
                                bool issymmetric, bool iscoercive);
  size_type add_explicit_rhs(model &md, const std::string &varname);

  /** Add a brick reprenting an explicit matrix to be added to the tangent
      linear system relatively to the variables 'varname1' and 'varname2'.
      The given matrix should have as many rows as the dimension of
      'varname1' and as many columns as the dimension of 'varname2'.
      If the two variables are different and if `issymmetric' is set to true
      then the transpose of the matrix is also added to the tangent system
      (default is false). set `iscoercive` to true if the term does not
      affect the coercivity of the tangent system (default is false).
      The matrix can be changed by the command set_private_matrix.
  */
  template <typename MAT>
  size_type add_explicit_matrix(model &md, const std::string &varname1,
                                const std::string &varname2, const MAT &B,
                                bool issymmetric = false,
                                bool iscoercive = false) {
    size_type ind = add_explicit_matrix(md, varname1, varname2,
                                        issymmetric, iscoercive);
    set_private_data_matrix(md, ind, B);
    return ind;
  }

  /**  Add a brick representing an explicit right hand side to be added to
       the right hand side of the tangent
       linear system relatively to the variable 'varname'.
       The given rhs should have the same size than the dimension of
       'varname'. The rhs can be changed by the command set_private_rhs.
  */
  template <typename VECT>
  size_type add_explicit_rhs(model &md, const std::string &varname,
                             const VECT &L) {
    size_type ind = add_explicit_rhs(md, varname);
    set_private_data_rhs(md, ind, L);
    return ind;
  }


  /** Linear elasticity brick ( @f$ \int \sigma(u):\varepsilon(v) @f$ ).
      for isotropic material. Parametrized by the Lamé coefficients
      lambda and mu.
  */
  size_type add_isotropic_linearized_elasticity_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &dataname_lambda, const std::string &dataname_mu,
   size_type region = size_type(-1),
   const std::string &dataname_preconstraint = std::string());


  void compute_isotropic_linearized_Von_Mises_or_Tresca
  (model &md, const std::string &varname, const std::string &dataname_lambda,
   const std::string &dataname_mu, const mesh_fem &mf_vm,
   model_real_plain_vector &VM, bool tresca);

  /**
     Compute the Von-Mises stress or the Tresca stress of a field
     (only valid for isotropic linearized elasticity in 3D)
  */
  template <class VECTVM>
  void compute_isotropic_linearized_Von_Mises_or_Tresca
  (model &md, const std::string &varname, const std::string &dataname_lambda,
   const std::string &dataname_mu, const mesh_fem &mf_vm,
   VECTVM &VM, bool tresca) {
    model_real_plain_vector VMM(mf_vm.nb_dof());
    compute_isotropic_linearized_Von_Mises_or_Tresca
      (md, varname, dataname_lambda, dataname_mu, mf_vm, VMM, tresca);
    gmm::copy(VMM, VM);
  }

  /**
     Mixed linear incompressibility condition brick.

     Update the tangent matrix with a pressure term:
     @f[
     T \longrightarrow
     \begin{array}{ll} T & B \\ B^t & M \end{array}
     @f]
     with @f$ B = - \int p.div u @f$ and
     @f$ M = \int \epsilon p.q @f$ ( @f$ \epsilon @f$ is an optional
     penalization coefficient).

     Be aware that an inf-sup condition between the finite element method
     describing the rpressure and the primal variable has to be satisfied.

     For nearly incompressible elasticity,
     @f[ p = -\lambda \textrm{div}~u @f]
     @f[ \sigma = 2 \mu \varepsilon(u) -p I @f]
     @see asm_stokes_B
  */
  size_type add_linear_incompressibility
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &multname_pressure, size_type region = size_type(-1),
   const std::string &dataname_penal_coeff = std::string());

  /** Mass brick ( @f$ \int \rho u.v @f$ ).
      Add a mass matix on a variable (eventually with a specified region).
      If the parameter $\rho$ is omitted it is assumed to be equal to 1.
  */
  size_type add_mass_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &dataname_rho = std::string(),
   size_type region = size_type(-1));

  /** Basic d/dt brick ( @f$ \int \rho ((u^{n+1}-u^n)/dt).v @f$ ).
      Add the standard discretization of a first order time derivative. The
      parameter $rho$ is the density which could be omitted (the defaul value
      is 1). This brick should be used in addition to a time dispatcher for the
      other terms.
  */
  size_type add_basic_d_on_dt_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &dataname_dt,
   const std::string &dataname_rho = std::string(),
   size_type region = size_type(-1));

  /** Basic d2/dt2 brick ( @f$ \int \rho ((u^{n+1}-u^n)/(\alpha dt^2) - v^n/(\alpha dt) ).w @f$ ).
      Add the standard discretization of a second order time derivative. The
      parameter $rho$ is the density which could be omitted (the defaul value
      is 1). This brick should be used in addition to a time dispatcher for the
      other terms. The time derivative $v$ of the variable $u$ is preferably
      computed as a post-traitement which depends on each scheme.
  */
  size_type add_basic_d2_on_dt2_brick
  (model &md, const mesh_im &mim, const std::string &varnameU,
   const std::string &datanameV,
   const std::string &dataname_dt,
   const std::string &dataname_alpha,
   const std::string &dataname_rho = std::string(),
   size_type region = size_type(-1));


}  /* end of namespace getfem.                                             */


#endif /* GETFEM_MODELS_H__  */
