symmetric_matrix_3x3.h

//
// 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.
//

// Interface for symmetric_matrix_3x3 classes.

#ifndef SYMMETRIC_MATRIX_3X3_H
#define SYMMETRIC_MATRIX_3X3_H

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

#ifndef STD_IOSTREAM_H
#include "SheafSystem/std_iostream.h"
#endif

namespace fiber_bundle
{

template <typename T> class general_matrix_1x3;
template <typename T> class general_matrix_3x1;
template <typename T> class general_matrix_3x2;
template <typename T> class general_matrix_3x3;

template <typename T> class met_e3_row_dofs_type;
template <typename T> class st2_e3_row_dofs_type;

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

template <typename T>
class symmetric_matrix_3x3
{
public:

  operator met_e3_row_dofs_type<T>& () const;

  operator st2_e3_row_dofs_type<T>& () const;

  static int number_of_rows();

  static int number_of_columns();

  static int d();

  T* operator[](int xrow);

  const T* operator[](int xrow) const;

  operator T* ();

  operator const T* () const;

  int row_index(int xrow) const;

  operator general_matrix_3x3<T> () const;

  general_matrix_1x3<T> row(int xrow) const;

  general_matrix_3x1<T> column(int xcolumn) const;

  T components[6];

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

  void adjoint(symmetric_matrix_3x3<T>& xresult) const;

  symmetric_matrix_3x3<T> adjoint() const;

  void assign(const T& xscalar);

  void determinant(T& xresult) const;

  T determinant() const;

  void diagonalization(symmetric_matrix_3x3<T>& xresult) const;

  symmetric_matrix_3x3<T> diagonalization() const;

  void identity(symmetric_matrix_3x3<T>& xresult) const;

  symmetric_matrix_3x3<T> identity() const;

  void inverse(symmetric_matrix_3x3<T>& xresult) const;

  symmetric_matrix_3x3<T> inverse() const;

  bool is_diagonal() const;

  bool is_identity() const;

  bool is_positive_definite() const;

  void multiply(const T& xscalar, symmetric_matrix_3x3<T>& xresult) const;

  symmetric_matrix_3x3<T> multiply(const T& xscalar) const;

  void multiply(const general_matrix_3x1<T>& xother,
                general_matrix_3x1<T>& xresult) const;

  general_matrix_3x1<T> multiply(const general_matrix_3x1<T>& xother) const;

  void multiply(const general_matrix_3x2<T>& xother,
                general_matrix_3x2<T>& xresult) const;

  general_matrix_3x2<T> multiply(const general_matrix_3x2<T>& xother) const;

  void multiply(const general_matrix_3x3<T>& xother,
                general_matrix_3x3<T>& xresult) const;

  general_matrix_3x3<T> multiply(const general_matrix_3x3<T>& xother) const;

  void multiply(const symmetric_matrix_3x3<T>& xother,
                general_matrix_3x3<T>& xresult) const;

  general_matrix_3x3<T> multiply(const symmetric_matrix_3x3<T>& xother) const;

  void trace(T& xresult) const;

  T trace() const;

  void transpose(symmetric_matrix_3x3<T>& xresult) const;

  symmetric_matrix_3x3<T> transpose() const;



protected:
private:

};

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

template <typename T>
std::ostream& operator<<(std::ostream& xos, const symmetric_matrix_3x3<T>& xm);

//  using the cyclic Jacobi iteration method.
template <typename T>
void jacobi_transformation(const symmetric_matrix_3x3<T>& xm,
                           general_matrix_3x3<T>& xeigenvectors,
                           T xeigenvalues[3]);

//  using the cyclic Jacobi iteration method.
template <typename T>
void jacobi_transformation(const symmetric_matrix_3x3<T>& xm,
                           general_matrix_3x3<T>& xeigenvectors,
                           symmetric_matrix_3x3<T>& xdiagonal);
template <typename T>
void sort_eigenvalues(general_matrix_3x3<T>& xeigenvectors,
                      T xeigenvalues[3]);

} // namespace fiber_bundle

#endif // ifndef SYMMETRIC_MATRIX_3X3_H