vd.h

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//
// Copyright (c) 2014 Limit Point Systems, Inc. 
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//   http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//


#ifndef VD_H
#define VD_H

#ifndef SHEAF_DLL_SPEC_H
#include "SheafSystem/sheaf_dll_spec.h"
#endif

#ifndef PRIMITIVE_TYPE_H
#include "SheafSystem/primitive_type.h"
#endif

#ifndef TUPLE_H
#include "SheafSystem/tuple.h"
#endif

#ifndef STD_CMATH_H
#include "SheafSystem/std_cmath.h"
#endif

#ifndef VD_TABLE_DOFS_TYPE_H
#include "SheafSystem/vd_table_dofs_type.h"
#endif
 
namespace fiber_bundle
{
  //
  // Forward declarations
  //

  class at0;
  class vd_space;  

//==============================================================================
// CLASS VD_ROW_DOFS_TYPE
//==============================================================================
 
template <typename T>
class vd_row_dofs_type
{
public:

  typedef T dof_type;

  typedef vd_row_dofs_type<T> row_dofs_type;

  static const std::string& static_class_name();
  
  T& operator[] (int xindex);

  const T& operator[] (int xindex) const;

  row_dofs_type* clone() const;
};


//==============================================================================
// CLASS VD_LITE
//==============================================================================

class tp_lite;
class atp_lite;
class stp_lite;

class SHEAF_DLL_SPEC vd_lite : public tuple_lite
{
  //============================================================================
  //============================================================================

public:

  typedef vd_dof_type dof_type;

  typedef vd_value_type value_type;

  typedef vd_table_dofs_type table_dofs_type;

  typedef vd_row_dofs_type<double> row_dofs_type;

  vd_lite();

  vd_lite(const vd_lite& xother);

  vd_lite& operator=(const vd_lite& xother);

  bool operator==(const vd_lite& xother) const;

  virtual ~vd_lite();

  vd_lite(const row_dofs_type& xrow_dofs);

  vd_lite& operator=(const row_dofs_type& xrow_dofs);

  virtual int d() const;

  value_type component(int xindex) const;

  void put_component(int xindex, value_type xcomp);

  virtual void components(dof_type xresult[], int comps_dimension) const;

  virtual void put_components(const dof_type xcomps[], int xcomps_dimension);

  vd_lite& operator=(const value_type& xvalue);

  bool operator==(const value_type& xvalue) const;

  virtual value_type& operator[] (int xindex);

  virtual const value_type& operator[] (int xindex) const;

  static const tp_lite& static_tp_prototype(int xp);

  virtual const tp_lite& tp_prototype(int xp) const;

  static const atp_lite& static_atp_prototype(int xp);

  virtual const atp_lite& atp_prototype(int xp) const;

  static const stp_lite& static_stp_prototype(int xp);

  virtual const stp_lite& stp_prototype(int xp) const;


protected:
private:



  //============================================================================
  //============================================================================

public:

  virtual int factor_ct() const;

protected:
private:



  //============================================================================
  //============================================================================

public:

  virtual const std::string& class_name() const;

  static const std::string& static_class_name();
  
  virtual vd_lite* clone() const;

  table_dofs_type table_dofs() const;

protected:
private:



  //============================================================================
  //============================================================================

public:

  virtual bool is_ancestor_of(const any_lite& xother) const;

  bool invariant() const;

protected:
private:

};


//==============================================================================
// CLASS VD
//==============================================================================


class SHEAF_DLL_SPEC vd : public tuple
{
  // ===========================================================
  // ===========================================================

public:

  typedef vd_space host_type;

  typedef at0 scalar_type;

  static const poset_path& standard_schema_path();

  static void make_standard_schema(namespace_poset& xns);

  static host_type& new_host(namespace_type& xns, 
                 const poset_path& xhost_path, 
                 const poset_path& xschema_path,
                 const poset_path& xscalar_space_path,
                 bool xauto_access);

protected:

private:

 
  //============================================================================
  //============================================================================

public:

  // Typedefs:

  typedef vd_table_dofs_type table_dofs_type;

  typedef vd_row_dofs_type<double> row_dofs_type;

  typedef vd_lite volatile_type;

  typedef vd_value_type value_type;

  //  same type.
  typedef vd_dof_type dof_type;

  //static const primitive_type sheaf_dof_type;

  vd();


  virtual vd& operator=(const abstract_poset_member& xother);

  vd& operator=(const vd& xother);

  virtual ~vd();

  vd(poset_state_handle* xhost, bool xauto_access = true);

  vd(const poset_state_handle* xhost, pod_index_type xhub_id);

  vd(const poset_state_handle* xhost, const scoped_index& xid);

  vd(const poset_state_handle* xhost, const std::string& xname);

  explicit vd(const abstract_poset_member* xother);

  virtual int d() const;

  virtual int d(bool xauto_access) const;

  poset_path scalar_space_path() const;

  poset_path scalar_space_path(bool xauto_access) const;
  
  virtual value_type component(int xindex) const;

  value_type component(int xindex, bool xauto_access) const;

  virtual void put_component(int xindex, value_type xvalue);

  void put_component(int xindex, value_type xvalue, bool xauto_access);

  void components(dof_type comps[], int comps_dimension) const;

  void put_components(const dof_type comps[], int comps_dimension);

  dof_type& operator[] (int xindex);

  const dof_type& operator[] (int xindex) const;

  virtual const volatile_type& lite_prototype() const;

  virtual volatile_type* lite_type() const;

  virtual bool is_vector(bool xauto_access) const;

  virtual void put_is_vector(bool xauto_access);

  virtual bool is_covector(bool xauto_access) const;;

  virtual void put_is_covector(bool xauto_access);

protected:
private:


  //============================================================================
  //============================================================================

public:

  virtual const std::string& class_name() const;

  static const std::string& static_class_name();

  inline vd* clone(bool xnew_state, bool xauto_access = true) const
  {
    return static_cast<vd*>(tuple::clone(xnew_state, xauto_access));
  }

protected:
private:


  // ===========================================================
  // ===========================================================

public:

  host_type* host() const;

  virtual bool host_is_ancestor_of(const poset_state_handle* other) const;

protected:

private:



  //============================================================================
  //============================================================================

public:

  bool is_ancestor_of(const any* other) const;
  
  virtual vd* clone() const;

  bool invariant() const;


protected:
private:

};

//==============================================================================
// NON-MEMBER FUNCTIONS
//==============================================================================

#ifndef DOXYGEN_1_5_4_SKIP_UNKNOWN

SHEAF_DLL_SPEC std::ostream& operator<<(std::ostream& xos, const vd_lite& x0);

SHEAF_DLL_SPEC std::ostream& operator<<(std::ostream& xos, const vd& x0);

#endif // ifndef DOXYGEN_1_5_4_SKIP_UNKNOWN

// ===========================================================
// TENSOR TRAITS
// ===========================================================

 

// Forward declarations needed for specialization:

class at2_lite;
class at3_lite;
class atp_lite;
class st2_lite;
class st3_lite;
class st4_lite;
class stp_lite;
class t2_lite;
class t3_lite;
class t4_lite;
class tp_lite;

template <int P, typename VECTOR_TYPE> class tensor_traits;

template <>
class tensor_traits<0, vd_lite>
{
public:
  typedef at0 tp_type;

  typedef at0 atp_type;

  typedef at0 stp_type;
};

template <>
class tensor_traits<1, vd_lite>
{
public:
  typedef vd_lite tp_type;

  typedef vd_lite atp_type;

  typedef vd_lite stp_type;
};

template <>
class tensor_traits<2, vd_lite>
{
public:
  typedef t2_lite tp_type;

  typedef at2_lite atp_type;

  typedef st2_lite stp_type;
};

template <>
class tensor_traits<3, vd_lite>
{
public:
  typedef t3_lite tp_type;

  typedef at3_lite atp_type;

  typedef st3_lite stp_type;
};

template <>
class tensor_traits<4, vd_lite>
{
public:
  typedef t4_lite tp_type;

  typedef void atp_type;

  typedef st4_lite stp_type;
};


// ===========================================================
// VECTOR ALGEBRA
// ===========================================================

namespace vd_algebra
{

// ===========================================================
// VECTOR ALGEBRA: ADDITION
// ===========================================================
 
SHEAF_DLL_SPEC void add(const vd& x0, const vd& x1, vd& xresult, bool xauto_access);

SHEAF_DLL_SPEC void add(const vd_lite& x0, const vd_lite& x1, vd_lite& xresult);

SHEAF_DLL_SPEC void add(const vd_lite& x0, const vd_lite& x1, vd_value_type xt, vd_lite& xresult);

template <typename T>
T* add(const T& x0, const T& x1);

SHEAF_DLL_SPEC void add_equal(vd& xresult, const vd& xother, bool xauto_access);

template <typename T>
void add_equal(T& xresult, const T& xother);

template <typename T>
T* operator+(const T& x0, const T& x1);

template <typename T>
T& operator+=(T& xresult, const T& xother);


// ===========================================================
// VECTOR ALGEBRA: SUBTRACTION
// ===========================================================

SHEAF_DLL_SPEC void subtract(const vd& x0, const vd& x1, vd& xresult, bool xauto_access);

SHEAF_DLL_SPEC void subtract(const vd_lite& x0, const vd_lite& x1, vd_lite& xresult);

template <typename T>
T* subtract(const T& x0, const T& x1);

SHEAF_DLL_SPEC void subtract_equal(vd& xresult, const vd& xother, bool xauto_access);

template <typename T>
void subtract_equal(T& xresult, const T& xother);

template <typename T>
T* operator-(const T& x0, const T& x1);

template <typename T>
T& operator-=(T& xresult, const T& xother);


// ===========================================================
// VECTOR ALGEBRA: SCALAR MULTIPLICATION
// ===========================================================

#ifndef DOXYGEN_1_5_4_SKIP_UNKNOWN

SHEAF_DLL_SPEC void multiply(const vd& x0, const vd_value_type& x1, vd& xresult, bool xauto_access);

SHEAF_DLL_SPEC void multiply(const vd_lite& x0, const vd_value_type& x1, vd_lite& xresult);

template <typename T>
T* multiply(const T& x0, const vd_value_type& x1);

SHEAF_DLL_SPEC void multiply_equal(vd& xresult, const vd_value_type& xother, bool xauto_access);

template <typename T>
void multiply_equal(T& xresult, const vd_value_type& xother);

template <typename T>
T* operator*(const T& x0, const vd_value_type& x1);

template <typename T>
T& operator*=(T& xresult, const vd_value_type& x1);

#endif // ifndef DOXYGEN_1_5_4_SKIP_UNKNOWN

// ===========================================================
// VECTOR ALGEBRA: SCALAR DIVISION
// ===========================================================

SHEAF_DLL_SPEC void divide(const vd& x0, const vd_value_type& x1, vd& xresult,
               bool xauto_access);

SHEAF_DLL_SPEC void divide(const vd_lite& x0, const vd_value_type& x1, vd_lite& xresult);

template <typename T>
T* divide(const T& x0, const vd_value_type& x1);

SHEAF_DLL_SPEC void divide_equal(vd& xresult, const vd_value_type& xother, bool xauto_access);

template <typename T>
void divide_equal(T& xresult, const vd_value_type& x1);

template <typename T>
T* operator/(const T& x0, const vd_value_type& x1);

template <typename T>
T& operator/=(T& xresult, const vd_value_type& x1);


#ifndef DOXYGEN_1_5_4_SKIP_UNKNOWN

// ===========================================================
// VECTOR ALGEBRA: COMPONENT EXTREMA
// ===========================================================

SHEAF_DLL_SPEC void max(const vd& x0, vd_value_type& xresult, bool xauto_access);

SHEAF_DLL_SPEC vd_value_type max(const vd& x0, bool xauto_access);

SHEAF_DLL_SPEC void min(const vd& x0, vd_value_type& xresult, bool xauto_access);

SHEAF_DLL_SPEC vd_value_type min(const vd& x0, bool xauto_access);

SHEAF_DLL_SPEC void max(const vd_lite& x0, vd_value_type& xresult);

SHEAF_DLL_SPEC vd_value_type max(const vd_lite& x0);

SHEAF_DLL_SPEC void min(const vd_lite& x0, vd_value_type& xresult);

SHEAF_DLL_SPEC vd_value_type min(const vd_lite& x0);

#endif // ifndef DOXYGEN_1_5_4_SKIP_UNKNOWN

// ===========================================================
// VECTOR ALGEBRA: CONTRACTION
// ===========================================================

// Bishop and Goldberg's "natural pairing" makes for a
// nice theoretical development, but in use it's clumsy nomenclature.
// Koenderink calls the "natural pairing" operation "contract",
// because, once you have the general contraction operator defined,
// you can think of the "natural pairing" of vector v and a covector c
// as contracting the tensor vc on its 2 indices to form a scalar.
// But you need the special case vector on covector in order to define
// tensors in the first place, which is why B&G
// introduce it as the "natural pairing".
//
// Furthermore, the "natural pairing" is just another name for the
// action of covector c as a map of vectors to reals. The action as
// a map notion generalizes to the fundamental definition of all
// tensor types. Every tensor type of degree p is a map that takes
// p vectors and/or covectors as arguments and produces a scalar.
// Since we can always form the tensor product of these p arguments,
// we can think of the general tensor map action as contraction.
//
// So we'll follow Koenderink and name the map actions "contract"
// for all tensors.

SHEAF_DLL_SPEC vd_value_type contract(const vd_lite& xvector, const vd_lite& xcovector);

SHEAF_DLL_SPEC vd_value_type contract(const vd& xvector, const vd& xcovector,
                      bool xauto_access);

// ===========================================================
// VECTOR ALGEBRA: TOLERANCE COMPARISON
// ===========================================================

SHEAF_DLL_SPEC bool a_eql(const vd_lite& x0, const vd_lite& x1);
  
SHEAF_DLL_SPEC bool a_eql(const vd_lite& x0, const vd_lite& x1, double xtolerance);
  
SHEAF_DLL_SPEC bool a_eql(const vd_lite& x0, const vd_lite& x1, const vd_lite& xtolerance);

SHEAF_DLL_SPEC bool r_eql(const vd_lite& x0, const vd_lite& x1);
  
SHEAF_DLL_SPEC bool r_eql(const vd_lite& x0, const vd_lite& x1, double xtolerance);
  
SHEAF_DLL_SPEC bool r_eql(const vd_lite& x0, const vd_lite& x1, const vd_lite& xtolerance);
  
SHEAF_DLL_SPEC bool c_eql(const vd_lite& x0, const vd_lite& x1);
  
SHEAF_DLL_SPEC bool c_eql(const vd_lite& x0, const vd_lite& x1, double xtolerance);
  
SHEAF_DLL_SPEC bool c_eql(const vd_lite& x0, const vd_lite& x1, const vd_lite& xtolerance);


// ===========================================================
// MISCELLANEOUS
// ===========================================================


// Putting these functions in the fiber_bundle namespace
// for convenience.

SHEAF_DLL_SPEC unsigned int factorial(unsigned int xi);

SHEAF_DLL_SPEC unsigned int binomial_coefficient(unsigned int xi, unsigned int xj);

//==============================================================================
  
} // namespace vd_algebra

} // namespace fiber_bundle

#endif // ifndef VD_H