itkMultivariateLegendrePolynomial.h

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

Program:   Insight Segmentation & Registration Toolkit
Module:    $RCSfile: itkMultivariateLegendrePolynomial.h,v $
Language:  C++
Date:      $Date: 2009-01-25 12:45:06 $
Version:   $Revision: 1.26 $

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 __itkMultivariateLegendrePolynomial_h
#define __itkMultivariateLegendrePolynomial_h

#include "itkIndent.h"
#include <vector>
#include "itkArray.h"

namespace itk {

class MultivariateLegendrePolynomial
{
public:
  typedef MultivariateLegendrePolynomial Self;

  typedef std::vector< double >        DoubleArrayType;
  typedef std::vector< unsigned long > ULongArrayType;
  typedef std::vector< long >          LongArrayType;

  typedef DoubleArrayType CoefficientArrayType;

  typedef Array< double > ParametersType;

  typedef ULongArrayType DomainSizeType;
  typedef LongArrayType  IndexType;

  MultivariateLegendrePolynomial( unsigned int dimension, 
                                  unsigned int degree,
                                  const DomainSizeType & domainSize );

  virtual ~MultivariateLegendrePolynomial();

  unsigned int GetDimension(void) const 
    { return m_Dimension; }

  unsigned int GetDegree(void) const 
    { return m_Degree; } 

  unsigned int GetNumberOfCoefficients(void) const
    { return m_NumberOfCoefficients; }

  const DomainSizeType & GetDomainSize( void ) const 
    { return m_DomainSize; }

  class CoefficientVectorSizeMismatch 
    {
  public:
    CoefficientVectorSizeMismatch(int given, int required)
      {
      m_Required = required;
      m_Given = given;
      }
    
    int m_Required;
    int m_Given;
    };

  void SetCoefficients(const CoefficientArrayType& coef) 
    throw (CoefficientVectorSizeMismatch);

  void SetCoefficients(const ParametersType& coef) 
    throw (CoefficientVectorSizeMismatch);

  const CoefficientArrayType& GetCoefficients(void) const;
 
  double Evaluate(IndexType& index) 
    {
    if (m_Dimension == 2)
      {
      if (index[1] != m_PrevY)
        {
        // normalized y [-1, 1]
        double norm_y =  m_NormFactor[1] *
          static_cast<double>( index[1] - 1 );
        this->CalculateXCoef(norm_y, m_CoefficientArray);
        m_PrevY = index[1];
        }

      // normalized x [-1, 1]
      double norm_x =  m_NormFactor[0] *
        static_cast<double>( index[0] - 1 );
        
      return LegendreSum(norm_x, m_Degree, m_CachedXCoef);
      }
    else if (m_Dimension == 3)
      {
      if (index[2] != m_PrevZ )
        {
        // normalized z [-1, 1]  
        double norm_z =  m_NormFactor[2] *
          static_cast<double>( index[2] - 1 );
        this->CalculateYCoef(norm_z, m_CoefficientArray);
        m_PrevZ = index[2];
        }
        
      if (index[1] != m_PrevY)
        {
        // normalized y [-1, 1]
        double norm_y =  m_NormFactor[1] *
          static_cast<double>( index[1] - 1 ); 
        this->CalculateXCoef(norm_y, m_CachedYCoef);
        m_PrevY = index[1];
        }
        
      // normalized x [-1, 1]
      double norm_x =  m_NormFactor[0] *
        static_cast<double>( index[0] - 1 ); 
      return this->LegendreSum(norm_x, m_Degree, m_CachedXCoef);
      }
    return 0;
    }

  unsigned int GetNumberOfCoefficients();

  unsigned int GetNumberOfCoefficients(unsigned int dimension, unsigned int degree);

  class SimpleForwardIterator
    {
    public:
      SimpleForwardIterator (MultivariateLegendrePolynomial* polynomial) 
      {
      m_MultivariateLegendrePolynomial = polynomial;
      m_Dimension   = m_MultivariateLegendrePolynomial->GetDimension();
      m_DomainSize  = m_MultivariateLegendrePolynomial->GetDomainSize();
      m_Index.resize(m_Dimension);
      std::fill(m_Index.begin(), m_Index.end(), 0);
      }
    
    void Begin( void ) 
      { 
      m_IsAtEnd = false;
      for (unsigned int dim = 0; dim < m_Dimension; dim++)
        {
        m_Index[dim] = 0;
        }
      }
      
    bool IsAtEnd()
      { return m_IsAtEnd; }
    
    SimpleForwardIterator& operator++()
      {
      for (unsigned int dim = 0; dim < m_Dimension; dim++)
        {
        if (m_Index[dim] < static_cast<int>(m_DomainSize[dim] - 1))
          {
          m_Index[dim] += 1;
          return *this;
          }
        else
          {
          if (dim == m_Dimension - 1 )
            {
            m_IsAtEnd = true;
            break;
            }
          else
            {
            m_Index[dim] = 0;
            }
          }
        }
      return *this;
      }
      
    double Get()
      { return m_MultivariateLegendrePolynomial->Evaluate(m_Index); }
    
  private:
    MultivariateLegendrePolynomial* m_MultivariateLegendrePolynomial;
    unsigned int      m_Dimension; 
    DomainSizeType    m_DomainSize;
    IndexType         m_Index;
    bool              m_IsAtEnd;
    }; // end of class Iterator 
  
  void Print(std::ostream& os);

protected:
  void PrintSelf(std::ostream& os, Indent indent) const;
  double LegendreSum(const double x, int n, 
                     const CoefficientArrayType& coef,
                     int offset = 0); 
  void CalculateXCoef(double norm_y, const CoefficientArrayType& coef);
  void CalculateYCoef(double norm_z, const CoefficientArrayType& coef);

private:
  DomainSizeType m_DomainSize;
  unsigned int   m_Dimension;
  unsigned int   m_Degree;
  unsigned int   m_NumberOfCoefficients;
  bool           m_MultiplicativeBias; 
  
  CoefficientArrayType m_CoefficientArray;
  CoefficientArrayType m_CachedXCoef;
  CoefficientArrayType m_CachedYCoef;
  CoefficientArrayType m_CachedZCoef;

  DoubleArrayType m_NormFactor;
  long            m_PrevY;
  long            m_PrevZ;
}; // end of class

std::ostream& operator<< (std::ostream& os, 
                          MultivariateLegendrePolynomial& poly);
} // end of namespace itk
#endif