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

  Program:   Insight Segmentation & Registration Toolkit
  Module:    $RCSfile: itkSymmetricSecondRankTensor.h,v $
  Language:  C++
  Date:      $Date: 2006/04/21 00:09:54 $
  Version:   $Revision: 1.22 $

  Copyright (c) Insight Software Consortium. All rights reserved.
  See ITKCopyright.txt or http://www.itk.org/HTML/Copyright.htm for details.

     This software is distributed WITHOUT ANY WARRANTY; without even 
     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR 
     PURPOSE.  See the above copyright notices for more information.

=========================================================================*/
#ifndef __itkSymmetricSecondRankTensor_h
#define __itkSymmetricSecondRankTensor_h

// Undefine an eventual SymmetricSecondRankTensor macro
#ifdef SymmetricSecondRankTensor
#undef SymmetricSecondRankTensor
#endif

#include <itkIndent.h>
#include <itkFixedArray.h>
#include <itkMatrix.h>
#include "itkSymmetricEigenAnalysis.h"

namespace itk
{

/** \class SymmetricSecondRankTensor
 * \brief Represent a symmetric tensor of second rank.
 *
 * This class implements a ND symmetric tensor of second rank.
 *
 * Since SymmetricSecondRankTensor is a subclass of FixedArray,
 * you can access its components as:
 *
 * typedef itk::SymmetricSecondRankTensor< float >    TensorPixelType;
 * TensorPixelType tensor;
 *
 *   tensor[0] = 1.233;
 *   tensor[1] = 1.456;
 *
 * for convenience the indexed access is also available as
 *
 *   tensor(0,0) = 1.233;
 *   tensor(2,0) = 1.233;
 *
 * The Tensor in principle represents a NxN matrix, but given that it is always
 * symmetric the representation can be compacted into a N*(N+1)/2 elements
 * array that derives from the itk::FixedArray<T>
 *
 * \author Jeffrey Duda from School of Engineering at University of Pennsylvania
 * \author Torsten Rohlfing from SRI International Neuroscience Program.
 *
 * This class was mostly based on files that Jeffrey Duda, Torsten Rohlfing and
 * Martin Styner contributed to the ITK users list during a discussion on
 * support for DiffusionTensorImages. The funding for creating this class was
 * largely provided by NAMIC (National Alliance for Medical Image Computing)
 * (http://www.na-mic.org). A discussion on the design of this class can be
 * found in the WIKI pages of NAMIC:
 *
 * http://www.na-mic.org/Wiki/index.php/NAMIC_Wiki:DTI:ITK-DiffusionTensorPixelType
 *
 * \sa DiffusionTensor3D
 *
 * \ingroup ImageObjects   TensorObjects   Geometry
 */

template < typename TComponent, unsigned int NDimension=3 >
class SymmetricSecondRankTensor: public 
        FixedArray<TComponent,NDimension*(NDimension+1)/2>
{
public:
  /** Standard class typedefs. */
  typedef SymmetricSecondRankTensor  Self;
  typedef FixedArray<TComponent,NDimension*(NDimension+1)/2> Superclass;
  
  /** Dimension of the vector space. */
  itkStaticConstMacro(Dimension, unsigned int, NDimension);
  itkStaticConstMacro(InternalDimension, unsigned int, NDimension*(NDimension+1)/2);

  /** Convenience typedefs. */
  typedef FixedArray<TComponent,
          itkGetStaticConstMacro(InternalDimension)> BaseArray;
  
  /** Array of eigen-values. */
  typedef FixedArray<TComponent, NDimension> EigenValuesArrayType;
  
  /** Matrix of eigen-vectors. */
  typedef Matrix<TComponent, NDimension, NDimension> MatrixType;
  typedef Matrix<TComponent, NDimension, NDimension> EigenVectorsMatrixType;
  
  /**  Define the component type. */
  typedef TComponent ComponentType;
  typedef typename Superclass::ValueType ValueType;
  typedef typename NumericTraits<ValueType>::RealType AccumulateValueType;
  typedef typename NumericTraits<ValueType>::RealType RealValueType;
  
  typedef SymmetricEigenAnalysis< MatrixType, 
            EigenValuesArrayType, EigenVectorsMatrixType >  SymmetricEigenAnalysisType;

  /** Default constructor has nothing to do. */
  SymmetricSecondRankTensor() {this->Fill(0);}
  
  SymmetricSecondRankTensor (const ComponentType& r) { this->Fill(r); }
  
  typedef ComponentType ComponentArrayType[ itkGetStaticConstMacro(InternalDimension) ];

  /** Pass-through constructor for the Array base class. */
  SymmetricSecondRankTensor(const Self& r): BaseArray(r) {}
  SymmetricSecondRankTensor(const ComponentArrayType r): BaseArray(r) {}    
  
  /** Pass-through assignment operator for the Array base class. */
  Self& operator= (const Self& r);
  Self& operator= (const ComponentType& r);
  Self& operator= (const ComponentArrayType r);

  /** Aritmetic operations between pixels. Return a new SymmetricSecondRankTensor. */
  Self operator+(const Self &vec) const;
  Self operator-(const Self &vec) const;
  const Self & operator+=(const Self &vec);
  const Self & operator-=(const Self &vec);

  /** Arithmetic operations between tensors and scalars */
  Self operator*(const RealValueType & scalar ) const;
  Self operator/(const RealValueType & scalar ) const;
  const Self & operator*=(const RealValueType & scalar );
  const Self & operator/=(const RealValueType & scalar );
 
  /** Return the number of components. */
  static unsigned int GetNumberOfComponents() 
    { 
    return itkGetStaticConstMacro(InternalDimension);
    }

  /** Return the value for the Nth component. */
  ComponentType GetNthComponent(int c) const
    { return this->operator[](c); }

  /** Set the Nth component to v. */
  void SetNthComponent(int c, const ComponentType& v)  
    {  this->operator[](c) = v; }

  /** Matrix notation, in const and non-const forms. */
  ValueType & operator()( unsigned int row, unsigned int col );
  const ValueType & operator()( unsigned int row, unsigned int col ) const;

  /** Set the tensor to an identity tensor. This has 1 in its diagonal elements
   * zero elsewhere */
  void SetIdentity();

  /** Get Trace value */
  AccumulateValueType GetTrace() const;

  /** Return an array containing EigenValues. */
  void ComputeEigenValues( EigenValuesArrayType & eigenValues ) const;
 
  /** Return an array containing EigenValues, and a matrix containing Eigen
   * vectors. */
  void ComputeEigenAnalysis( EigenValuesArrayType & eigenValues,
                             EigenVectorsMatrixType & eigenVectors ) const;

private:

  
};

/** This extra typedef is necessary for preventing an Internal Compiler Error in
 * Microsoft Visual C++ 6.0. This typedef is not needed for any other compiler. */
typedef std::ostream               OutputStreamType;
typedef std::istream               InputStreamType;

template< typename TComponent, unsigned int NDimension  >  
ITK_EXPORT OutputStreamType& operator<<(OutputStreamType& os, 
              const SymmetricSecondRankTensor<TComponent,NDimension> & c); 
template< typename TComponent, unsigned int NDimension  >  
ITK_EXPORT InputStreamType& operator>>(InputStreamType& is, 
                    SymmetricSecondRankTensor<TComponent,NDimension> & c); 

template <typename TValueType, unsigned int VLength>
inline SymmetricSecondRankTensor< TValueType, VLength> operator* 
    (double d, const SymmetricSecondRankTensor< TValueType, VLength > & f)
{
  return f * d;
}



} // end namespace itk

#include "itkNumericTraitsTensorPixel.h"

#ifndef ITK_MANUAL_INSTANTIATION
#include "itkSymmetricSecondRankTensor.txx"
#endif

#endif
